url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOps_singleton
|
[1318, 1]
|
[1322, 2]
|
simp[denoteOps]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
op : Op Δ
⊢ run (denoteOps Δ [op]) env = run (denoteOp Δ op) env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOp
|
[1324, 1]
|
[1350, 2]
|
simp [denoteOp]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : String
res args : List (TypedSSAVal Δ)
regions : List (Region Δ)
attrs : AttrDict Δ
⊢ run (denoteOp Δ (Op.mk name res args regions attrs)) env =
run
(do
let args ← denoteOpArgs Δ args
let ret ←
OpM.toTopM (TopM.mapDenoteRegion Δ regions)
(Semantics.semantics_op (IOp.mk name (List.map Prod.snd res) args (OpM.denoteRegions regions 0) attrs))
match res with
| [] => pure ret
| [res] =>
match ret with
| [{ fst := τ, snd := v }] => do
TopM.set τ res.fst v
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 1 return value, got '" ++ toString ret ++ toString "'")
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 0 or 1 results, got '" ++ toString res ++ toString "'")
pure ret)
env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_
|
[1356, 1]
|
[1364, 2]
|
simp[denoteOpArgs]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : SSAVal
ty : MLIRType Δ
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_TopM_get_
|
[1370, 1]
|
[1382, 2]
|
simp[TopM.get, run, StateT.run, StateT.get, bind, StateT.bind, Except.bind, pure,
Except.pure, StateT.pure]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ run (TopM.get ty name) env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env)
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ (match SSAEnv.get name ty env with
| some v => fun s => Except.ok (v, s)
| none => fun s => Except.ok (default, s))
env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_TopM_get_
|
[1370, 1]
|
[1382, 2]
|
cases H:SSAEnv.get name ty env <;> simp
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ (match SSAEnv.get name ty env with
| some v => fun s => Except.ok (v, s)
| none => fun s => Except.ok (default, s))
env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_TopM_get_success
|
[1384, 1]
|
[1394, 2]
|
simp[run_TopM_get_, ENV]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
⊢ run (TopM.get ty name) env = Except.ok (v, env)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_success
|
[1400, 1]
|
[1417, 2]
|
simp[run_denoteOpArgs_cons_]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_success
|
[1400, 1]
|
[1417, 2]
|
simp [run_bind]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (TopM.get ty name) env with
| Except.ok (a, env') =>
match run (denoteOpArgs Δ args) env' with
| Except.ok (a_1, env') => run (pure ({ fst := ty, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_success
|
[1400, 1]
|
[1417, 2]
|
simp[run_TopM_get_success (ENV := ENV)]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (TopM.get ty name) env with
| Except.ok (a, env') =>
match run (denoteOpArgs Δ args) env' with
| Except.ok (a_1, env') => run (pure ({ fst := ty, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (denoteOpArgs Δ args) env with
| Except.ok (a, env') => run (pure ({ fst := ty, snd := v } :: a)) env'
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_success
|
[1400, 1]
|
[1417, 2]
|
simp[pure, StateT.pure, run, StateT.run, Except.pure]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (denoteOpArgs Δ args) env with
| Except.ok (a, env') => run (pure ({ fst := ty, snd := v } :: a)) env'
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e) =
match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_cons_success
|
[1400, 1]
|
[1417, 2]
|
cases denoteOpArgs Δ args env <;> simp
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e) =
match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_nil
|
[1421, 1]
|
[1426, 2]
|
simp[denoteOpArgs]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (denoteOpArgs Δ []) env = Except.ok ([], env)
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (pure []) env = Except.ok ([], env)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_denoteOpArgs_nil
|
[1421, 1]
|
[1426, 2]
|
simp[run, pure, StateT.run, StateT.pure, Except.pure]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (pure []) env = Except.ok ([], env)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_pure
|
[1428, 1]
|
[1433, 2]
|
simp[run, pure, StateT.run, StateT.pure, Except.pure]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
a : Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : a
⊢ run (pure v) env = Except.ok (v, env)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
OpM_toTopM_denoteRegion
|
[1435, 1]
|
[1444, 2]
|
simp[OpM.denoteRegion]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.denoteRegion r ix args) = TopM.denoteRegionsByIx rs ix args
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals) = TopM.denoteRegionsByIx rs ix args
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
OpM_toTopM_denoteRegion
|
[1435, 1]
|
[1444, 2]
|
simp[OpM.toTopM]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals) = TopM.denoteRegionsByIx rs ix args
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_OpM_toTopM_denoteRegion
|
[1446, 1]
|
[1456, 2]
|
simp[OpM.denoteRegion]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.denoteRegion r ix args)) env = run (TopM.denoteRegionsByIx rs ix args) env
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals)) env =
run (TopM.denoteRegionsByIx rs ix args) env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_OpM_toTopM_denoteRegion
|
[1446, 1]
|
[1456, 2]
|
simp[OpM.toTopM]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals)) env =
run (TopM.denoteRegionsByIx rs ix args) env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_OpM_toTopM_Ret
|
[1458, 1]
|
[1467, 3]
|
simp[OpM.toTopM]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.Ret v)) env = Except.ok (v, env)
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (pure v) env = Except.ok (v, env)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_OpM_toTopM_Ret
|
[1458, 1]
|
[1467, 3]
|
simp[run_pure]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (pure v) env = Except.ok (v, env)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
TopM_mapDenoteRegion_cons
|
[1469, 1]
|
[1476, 2]
|
simp[TopM.mapDenoteRegion]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
r : Region Δ
rs : List (Region Δ)
⊢ TopM.mapDenoteRegion Δ (r :: rs) = TopM.scoped ∘ denoteRegion Δ r :: TopM.mapDenoteRegion Δ rs
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
TopM_mapDenoteRegion_nil
|
[1477, 1]
|
[1481, 2]
|
simp[TopM.mapDenoteRegion]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
⊢ TopM.mapDenoteRegion Δ [] = []
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
OpM_denoteRegions_cons
|
[1483, 1]
|
[1492, 2]
|
simp[OpM.denoteRegions]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
r : Region Δ
rs : List (Region Δ)
ix : ℕ
⊢ OpM.denoteRegions (r :: rs) ix = OpM.denoteRegion r ix :: OpM.denoteRegions rs (ix + 1)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
OpM_denoteRegions_nil
|
[1493, 1]
|
[1497, 2]
|
simp[OpM.denoteRegions]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
⊢ OpM.denoteRegions [] ix = []
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Semantics.lean
|
run_TopM_denoteRegionsByIx_cons
|
[1499, 1]
|
[1511, 2]
|
simp[TopM.denoteRegionsByIx]
|
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
r : TypedArgs Δ → TopM Δ (TypedArgs Δ)
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
args : TypedArgs Δ
env : SSAEnv Δ
⊢ run (TopM.denoteRegionsByIx (r :: rs) ix args) env =
run
(match ix with
| 0 => r args
| Nat.succ ix' => TopM.denoteRegionsByIx rs ix' args)
env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_ret'
|
[200, 9]
|
[204, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => ret r) = t
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_ret'
|
[200, 9]
|
[204, 34]
|
rfl
|
case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => ret r) = Ret r✝
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_ret'
|
[200, 9]
|
[204, 34]
|
simp [bind, ih]
|
case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => ret r) = Vis e✝ k✝
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_Ret'
|
[206, 9]
|
[210, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => Ret r) = t
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_Ret'
|
[206, 9]
|
[210, 34]
|
rfl
|
case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => Ret r) = Ret r✝
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_Ret'
|
[206, 9]
|
[210, 34]
|
simp [bind, ih]
|
case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => Ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => Ret r) = Vis e✝ k✝
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_bind
|
[212, 9]
|
[217, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
E✝ : Type → Type
R✝² : Type
t : Fitree E✝ R✝²
R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
⊢ bind (bind t k) k' = bind t fun x => bind (k x) k'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_bind
|
[212, 9]
|
[217, 34]
|
rfl
|
case Ret
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
r✝ : R✝²
⊢ bind (bind (Ret r✝) k) k' = bind (Ret r✝) fun x => bind (k x) k'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.bind_bind
|
[212, 9]
|
[217, 34]
|
simp [bind, ih]
|
case Vis
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝²
ih : ∀ (a : T✝), bind (bind (k✝ a) k) k' = bind (k✝ a) fun x => bind (k x) k'
⊢ bind (bind (Vis e✝ k✝) k) k' = bind (Vis e✝ k✝) fun x => bind (k x) k'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interp_bind
|
[353, 1]
|
[358, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ : Type
t : Fitree E✝¹ R✝¹
R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
⊢ interp h (bind t k) = bind (interp h t) fun x => interp h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interp_bind
|
[353, 1]
|
[358, 34]
|
rfl
|
case Ret
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
r✝ : R✝¹
⊢ interp h (bind (Ret r✝) k) = bind (interp h (Ret r✝)) fun x => interp h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interp_bind
|
[353, 1]
|
[358, 34]
|
simp [bind, ih]
|
case Vis
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
T✝ : Type
e✝ : E✝¹ T✝
k✝ : T✝ → Fitree E✝¹ R✝¹
ih : ∀ (a : T✝), interp h (bind (k✝ a) k) = bind (interp h (k✝ a)) fun x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) = bind (interp h (Vis e✝ k✝)) fun x => interp h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interp'_bind
|
[360, 1]
|
[363, 30]
|
simp [interp', interp_bind]
|
E✝ : Type → Type
h : E✝ ~> Fitree Void1
F✝ : Type → Type
R✝¹ : Type
t : Fitree (E✝ +' F✝) R✝¹
R✝ : Type
k : R✝¹ → Fitree (E✝ +' F✝) R✝
⊢ interp' h (bind t k) = bind (interp' h t) fun x => interp' h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
revert s
|
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
s : S
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ ∀ {s : S},
interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
induction t with
| Ret _ => intros s; rfl
| Vis _ _ ih =>
simp [interpState] at *
simp [interp, Bind.bind, StateT.bind]
simp [ih]
|
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ ∀ {s : S},
interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
intros s
|
case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
⊢ ∀ {s : S},
interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
s : S
⊢ interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
rfl
|
case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
s : S
⊢ interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
simp [interpState] at *
|
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih :
∀ (a : T✝) {s : S},
interpState h (bind (k✝ a) k) s =
bind (interpState h (k✝ a) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
⊢ ∀ {s : S},
interpState h (bind (Vis e✝ k✝) k) s =
bind (interpState h (Vis e✝ k✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
|
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S}, interp h (bind (Vis e✝ k✝) k) s = bind (interp h (Vis e✝ k✝) s) fun x => interp h (k x.fst) x.snd
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
simp [interp, Bind.bind, StateT.bind]
|
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S}, interp h (bind (Vis e✝ k✝) k) s = bind (interp h (Vis e✝ k✝) s) fun x => interp h (k x.fst) x.snd
|
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S},
(bind (h T✝ e✝ s) fun __discr => interp h (bind (k✝ __discr.fst) k) __discr.snd) =
bind (h T✝ e✝ s) fun x => bind (interp h (k✝ x.fst) x.snd) fun x => interp h (k x.fst) x.snd
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpState_bind
|
[368, 1]
|
[378, 14]
|
simp [ih]
|
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S},
(bind (h T✝ e✝ s) fun __discr => interp h (bind (k✝ __discr.fst) k) __discr.snd) =
bind (h T✝ e✝ s) fun x => bind (interp h (k✝ x.fst) x.snd) fun x => interp h (k x.fst) x.snd
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
induction t with
| Ret _ =>
simp [bind, interpWriter]
have h₁: forall x, "" ++ x = x := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.nil_append]
simp [h₁]
have h₂: forall (α β: Type) (x: α × β), (x.fst, x.snd) = x := by simp
simp [h₂]
| Vis _ _ ih =>
simp [interpWriter] at *
simp [interp, Bind.bind, WriterT.bindCont, WriterT.mk]
have h: forall (x y z: String), x ++ (y ++ z) = x ++ y ++ z := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.append_assoc]
simp [ih, h]
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpWriter h (bind t k) =
bind (interpWriter h t) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [bind, interpWriter]
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpWriter h (bind (Ret r✝) k) =
bind (interpWriter h (Ret r✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
have h₁: forall x, "" ++ x = x := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.nil_append]
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [h₁]
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
have h₂: forall (α β: Type) (x: α × β), (x.fst, x.snd) = x := by simp
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
h₂ : ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [h₂]
|
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
h₂ : ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [HAppend.hAppend, Append.append, String.append]
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), "" ++ x = x
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), { data := [] ++ x.data } = x
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [List.nil_append]
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), { data := [] ++ x.data } = x
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [interpWriter] at *
|
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpWriter h (bind (k✝ a) k) =
bind (interpWriter h (k✝ a)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
⊢ interpWriter h (bind (Vis e✝ k✝) k) =
bind (interpWriter h (Vis e✝ k✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
|
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [interp, Bind.bind, WriterT.bindCont, WriterT.mk]
|
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
|
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ (bind (h T✝ e✝) fun x => bind (interp h (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h T✝ e✝) fun x =>
bind (interp h (k✝ x.fst)) fun x_1 =>
bind (interp h (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
have h: forall (x y z: String), x ++ (y ++ z) = x ++ y ++ z := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.append_assoc]
|
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ (bind (h T✝ e✝) fun x => bind (interp h (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h T✝ e✝) fun x =>
bind (interp h (k✝ x.fst)) fun x_1 =>
bind (interp h (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
|
case Vis
E F : Type → Type
T R : Type
h✝ : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h✝ (bind (k✝ a) k) =
bind (interp h✝ (k✝ a)) fun x => bind (interp h✝ (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
h : ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
⊢ (bind (h✝ T✝ e✝) fun x => bind (interp h✝ (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h✝ T✝ e✝) fun x =>
bind (interp h✝ (k✝ x.fst)) fun x_1 =>
bind (interp h✝ (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [ih, h]
|
case Vis
E F : Type → Type
T R : Type
h✝ : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h✝ (bind (k✝ a) k) =
bind (interp h✝ (k✝ a)) fun x => bind (interp h✝ (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
h : ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
⊢ (bind (h✝ T✝ e✝) fun x => bind (interp h✝ (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h✝ T✝ e✝) fun x =>
bind (interp h✝ (k✝ x.fst)) fun x_1 =>
bind (interp h✝ (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [HAppend.hAppend, Append.append, String.append]
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), { data := x.data ++ (y.data ++ z.data) } = { data := x.data ++ y.data ++ z.data }
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpWriter_bind
|
[383, 1]
|
[404, 19]
|
simp [List.append_assoc]
|
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), { data := x.data ++ (y.data ++ z.data) } = { data := x.data ++ y.data ++ z.data }
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpOption] at *
simp [interp, bind, Bind.bind, OptionT.bind, OptionT.mk]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih]
|
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpOption h (bind t k) =
bind (interpOption h t) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
rfl
|
case Ret
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpOption h (bind (Ret r✝) k) =
bind (interpOption h (Ret r✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
simp [interpOption] at *
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpOption h (bind (k✝ a) k) =
bind (interpOption h (k✝ a)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
⊢ interpOption h (bind (Vis e✝ k✝) k) =
bind (interpOption h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
simp [interp, bind, Bind.bind, OptionT.bind, OptionT.mk]
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α : Sort ?u.47259) (β : Sort ?u.47260) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
apply fequal2
|
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α : Sort ?u.47259) (β : Sort ?u.47260) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
rfl
|
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
funext x
|
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
case Vis.a.h
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Option T✝
⊢ (match x with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
cases x <;> simp [ih]
|
case Vis.a.h
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Option T✝
⊢ (match x with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpOption_bind
|
[406, 1]
|
[422, 28]
|
simp [h₁, h₂]
|
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
α : Sort ?u.47259
β : Sort ?u.47260
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpExcept] at *
simp [interp, bind, Bind.bind]
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih]
|
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpExcept h (bind t k) =
bind (interpExcept h t) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
rfl
|
case Ret
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpExcept h (bind (Ret r✝) k) =
bind (interpExcept h (Ret r✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
simp [interpExcept] at *
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpExcept h (bind (k✝ a) k) =
bind (interpExcept h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
⊢ interpExcept h (bind (Vis e✝ k✝) k) =
bind (interpExcept h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
simp [interp, bind, Bind.bind]
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ bind (h T✝ e✝) (ExceptT.bindCont fun t => interp h (bind (k✝ t) k)) =
bind (h T✝ e✝) fun x =>
bind (ExceptT.bindCont (fun t => interp h (k✝ t)) x) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ bind (h T✝ e✝) (ExceptT.bindCont fun t => interp h (bind (k✝ t) k)) =
bind (h T✝ e✝) fun x =>
bind (ExceptT.bindCont (fun t => interp h (k✝ t)) x) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α : Sort ?u.50273) (β : Sort ?u.50274) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
apply fequal2
|
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α : Sort ?u.50273) (β : Sort ?u.50274) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
rfl
|
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
funext x
|
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
case Vis.a.h
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except ε T✝
⊢ (match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
cases x <;> simp [ih]
|
case Vis.a.h
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except ε T✝
⊢ (match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/Fitree.lean
|
Fitree.interpExcept_bind
|
[424, 1]
|
[441, 28]
|
simp [h₁, h₂]
|
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
α : Sort ?u.50273
β : Sort ?u.50274
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
intros t1
|
⊢ ∀ (t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp [double_transpose, toy_semantics_region, toy_semantics_op]
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.bind
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString ""))
fun x =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp_itree
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.bind
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString ""))
fun x =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") r)))
fun r =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp [interpUB'!]
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") r)))
fun r =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun x =>
Fitree.bind (Fitree.trigger (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x))) fun x =>
Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") x)))
fun x =>
Fitree.interp (Fitree.case UBE.handle! fun T => Fitree.trigger)
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp_itree
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun x =>
Fitree.bind (Fitree.trigger (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x))) fun x =>
Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") x)))
fun x =>
Fitree.interp (Fitree.case UBE.handle! fun T => Fitree.trigger)
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
interpSSA' (Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp [interpSSA', Fitree.interpState, SSAEnvE.handle]
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
interpSSA' (Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.interp
(Fitree.case
(fun x e env =>
match x, e with
| .(MLIRType.eval τ), SSAEnvE.Get τ name =>
match SSAEnv.get name τ env with
| some v => Fitree.ret (v, env)
| none => Fitree.ret (default, env)
| .(Unit), SSAEnvE.Set τ name v => Fitree.ret ((), SSAEnv.set name τ v env))
Fitree.liftHandler)
(Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp_itree
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.interp
(Fitree.case
(fun x e env =>
match x, e with
| .(MLIRType.eval τ), SSAEnvE.Get τ name =>
match SSAEnv.get name τ env with
| some v => Fitree.ret (v, env)
| none => Fitree.ret (default, env)
| .(Unit), SSAEnvE.Set τ name v => Fitree.ret ((), SSAEnv.set name τ v env))
Fitree.liftHandler)
(Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.Ret
((),
SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp [SSAEnv.get, SSAEnv.getT, SSAEnv.set]
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.Ret
((),
SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ (Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 t1))
fun x =>
Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x))
fun x_1 =>
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := x }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := x_1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
simp_itree
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ (Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 t1))
fun x =>
Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x))
fun x_1 =>
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := x }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := x_1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ [(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := transpose (transpose t1) })] =
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 })]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToySemantics.lean
|
double_transpose_correct
|
[136, 1]
|
[153, 28]
|
rw [transpose_involutive]
|
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ [(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := transpose (transpose t1) })] =
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 })]
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpUB, Fitree.interpExcept] at *
simp [Fitree.interp, Fitree.bind, Bind.bind]
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih]
|
T R : Type
t : Fitree UBE T
k : T → Fitree UBE R
⊢ interpUB (Fitree.bind t k) =
Fitree.bind (interpUB t) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
rfl
|
case Ret
T R : Type
k : T → Fitree UBE R
r✝ : T
⊢ interpUB (Fitree.bind (Fitree.Ret r✝) k) =
Fitree.bind (interpUB (Fitree.Ret r✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
simp [interpUB, Fitree.interpExcept] at *
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
interpUB (Fitree.bind (k✝ a) k) =
Fitree.bind (interpUB (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
⊢ interpUB (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (interpUB (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.interp UBE.handle (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (Fitree.interp UBE.handle (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
simp [Fitree.interp, Fitree.bind, Bind.bind]
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.interp UBE.handle (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (Fitree.interp UBE.handle (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.bind (UBE.handle T✝ e✝) (ExceptT.bindCont fun t => Fitree.interp UBE.handle (Fitree.bind (k✝ t) k)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind (ExceptT.bindCont (fun t => Fitree.interp UBE.handle (k✝ t)) x) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.bind (UBE.handle T✝ e✝) (ExceptT.bindCont fun t => Fitree.interp UBE.handle (Fitree.bind (k✝ t) k)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind (ExceptT.bindCont (fun t => Fitree.interp UBE.handle (k✝ t)) x) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α : Sort ?u.7562) (β : Sort ?u.7563) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
apply fequal2
|
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α : Sort ?u.7562) (β : Sort ?u.7563) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ Fitree.bind (UBE.handle T✝ e✝) = Fitree.bind (UBE.handle T✝ e✝)
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
rfl
|
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ Fitree.bind (UBE.handle T✝ e✝) = Fitree.bind (UBE.handle T✝ e✝)
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/UB.lean
|
interpUB_bind
|
[64, 1]
|
[81, 28]
|
funext x
|
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
case Vis.a.h
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except String T✝
⊢ (match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
|
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