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/SSAEnv.lean
|
SSAScope.get_set_ne_type
|
[207, 1]
|
[218, 50]
|
simp
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (set v τ' val (head :: tail)) τ = none
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (if head.fst = v then (head.fst, { fst := τ', snd := val }) :: tail else head :: set v τ' val tail) τ = none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_ne_type
|
[207, 1]
|
[218, 50]
|
byCases H: head.fst = v
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
⊢ get v (if head.fst = v then (head.fst, { fst := τ', snd := val }) :: tail else head :: set v τ' val tail) τ = none
|
case cons.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get head.fst (set head.fst τ' val tail) τ = none
⊢ τ' = τ → False
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
⊢ get v (set v τ' val tail) τ = none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_ne_type
|
[207, 1]
|
[218, 50]
|
. simp [Hne]
|
case cons.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get head.fst (set head.fst τ' val tail) τ = none
⊢ τ' = τ → False
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
⊢ get v (set v τ' val tail) τ = none
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
⊢ get v (set v τ' val tail) τ = none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_ne_type
|
[207, 1]
|
[218, 50]
|
. byCases H2: head.fst = v <;> try assumption
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H : ¬head.fst = v
⊢ get v (set v τ' val tail) τ = none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_ne_type
|
[207, 1]
|
[218, 50]
|
assumption
|
case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
τ τ' : MLIRType δ
Hne : τ' ≠ τ
v : SSAVal
val : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : get v (set v τ' val tail) τ = none
H H2 : ¬head.fst = v
⊢ get v (set v τ' val tail) τ = none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_eq
|
[220, 1]
|
[227, 15]
|
induction scope with
| nil => simp;
| cons head nil =>
simp
byCases H: head.fst = v <;> try apply cast_eq
assumption
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
scope : SSAScope δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v (set v τ val scope) τ = some val
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_eq
|
[220, 1]
|
[227, 15]
|
simp
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v (set v τ val []) τ = some val
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_eq
|
[220, 1]
|
[227, 15]
|
simp
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (set v τ val (head :: nil)) τ = some val
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (if head.fst = v then (head.fst, { fst := τ, snd := val }) :: nil else head :: set v τ val nil) τ = some val
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_eq
|
[220, 1]
|
[227, 15]
|
byCases H: head.fst = v <;> try apply cast_eq
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
⊢ get v (if head.fst = v then (head.fst, { fst := τ, snd := val }) :: nil else head :: set v τ val nil) τ = some val
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
H : ¬head.fst = v
⊢ get v (set v τ val nil) τ = some val
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.get_set_eq
|
[220, 1]
|
[227, 15]
|
assumption
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
nil : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
tail_ih✝ : get v (set v τ val nil) τ = some val
H : ¬head.fst = v
⊢ get v (set v τ val nil) τ = some val
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
intros Hne scope τ τ' val val'
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v →
∀ ⦃scope : SSAScope δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄ ⦃val' : MLIRType.eval τ'⦄,
equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope))
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
scope : SSAScope δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
induction scope with
| nil =>
simp; simp [Hne, Hne.symm]
simp [equiv]; intros name τ''
byCases Hv: v' = name
byCases Hτ: τ' = τ'' <;> simp [Hne.symm]
| cons head tail Hind =>
simp [equiv] at *
intros name; specialize Hind name
simp at *
byCases Hv': head.fst = v' <;> simp [Hne]
byCases Hv: head.fst = v <;> simp [Hv']
byCases Hname: head.fst = name <;> assumption
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
scope : SSAScope δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' scope)) (set v' τ' val' (set v τ val scope))
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
simp
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv (set v τ val (set v' τ' val' [])) (set v' τ' val' (set v τ val []))
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv
(if v' = v then [(v', { fst := τ, snd := val })]
else [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })])
(if v = v' then [(v, { fst := τ', snd := val' })]
else [(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
simp [Hne, Hne.symm]
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv
(if v' = v then [(v', { fst := τ, snd := val })]
else [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })])
(if v = v' then [(v, { fst := τ', snd := val' })]
else [(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })])
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })]
[(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
simp [equiv]
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ equiv [(v', { fst := τ', snd := val' }), (v, { fst := τ, snd := val })]
[(v, { fst := τ, snd := val }), (v', { fst := τ', snd := val' })]
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
(if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = name then
if h : τ = τ_1 then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else none) =
if v = name then
if h : τ = τ_1 then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
intros name τ''
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
(if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = name then
if h : τ = τ_1 then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else none) =
if v = name then
if h : τ = τ_1 then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = name then
if h : τ' = τ_1 then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else none
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
⊢ (if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else none) =
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
byCases Hv: v' = name
|
case nil
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
⊢ (if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else none) =
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = name then
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else none
|
case nil.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
Hne : name ≠ v
⊢ (if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none) =
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
byCases Hτ: τ' = τ'' <;> simp [Hne.symm]
|
case nil.h1
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
name : SSAVal
τ'' : MLIRType δ
Hne : name ≠ v
⊢ (if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none) =
if v = name then
if h : τ = τ'' then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if h : τ' = τ'' then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ'' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
simp [equiv] at *
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind : equiv (set v τ val (set v' τ' val' tail)) (set v' τ' val' (set v τ val tail))
⊢ equiv (set v τ val (set v' τ' val' (head :: tail))) (set v' τ' val' (set v τ val (head :: tail)))
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
intros name
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
⊢ ∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
name : SSAVal
⊢ ∀ (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
specialize Hind name
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
Hind :
∀ (name : SSAVal) (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
name : SSAVal
⊢ ∀ (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
⊢ ∀ (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
byCases Hv': head.fst = v' <;> simp [Hne]
|
case cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
⊢ ∀ (τ_1 : MLIRType δ),
get name
(set v τ val
(if head.fst = v' then (head.fst, { fst := τ', snd := val' }) :: tail else head :: set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
Hv' : ¬head.fst = v'
⊢ ∀ (τ_1 : MLIRType δ),
get name
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: set v' τ' val' tail
else head :: set v τ val (set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
byCases Hv: head.fst = v <;> simp [Hv']
|
case cons.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
Hv' : ¬head.fst = v'
⊢ ∀ (τ_1 : MLIRType δ),
get name
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: set v' τ' val' tail
else head :: set v τ val (set v' τ' val' tail))
τ_1 =
get name
(set v' τ' val'
(if head.fst = v then (head.fst, { fst := τ, snd := val }) :: tail else head :: set v τ val tail))
τ_1
|
case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
Hv' : ¬head.fst = v'
Hv : ¬head.fst = v
⊢ ∀ (τ_1 : MLIRType δ),
(if head.fst = name then
if h : head.2.fst = τ_1 then
some
(cast
(_ :
(match head.2.fst with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
head.2.snd)
else none
else get name (set v τ val (set v' τ' val' tail)) τ_1) =
if head.fst = name then
if h : head.2.fst = τ_1 then
some
(cast
(_ :
(match head.2.fst with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
head.2.snd)
else none
else get name (set v' τ' val' (set v τ val tail)) τ_1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAScope.set_commutes
|
[229, 1]
|
[246, 50]
|
byCases Hname: head.fst = name <;> assumption
|
case cons.h2.h2
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : ¬v' = v
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
head : SSAVal × (τ : MLIRType δ) × MLIRType.eval τ
tail : List (SSAVal × (τ : MLIRType δ) × MLIRType.eval τ)
name : SSAVal
Hind :
∀ (τ_1 : MLIRType δ),
get name (set v τ val (set v' τ' val' tail)) τ_1 = get name (set v' τ' val' (set v τ val tail)) τ_1
Hv' : ¬head.fst = v'
Hv : ¬head.fst = v
⊢ ∀ (τ_1 : MLIRType δ),
(if head.fst = name then
if h : head.2.fst = τ_1 then
some
(cast
(_ :
(match head.2.fst with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
head.2.snd)
else none
else get name (set v τ val (set v' τ' val' tail)) τ_1) =
if head.fst = name then
if h : head.2.fst = τ_1 then
some
(cast
(_ :
(match head.2.fst with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ_1 with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
head.2.snd)
else none
else get name (set v' τ' val' (set v τ val tail)) τ_1
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_rfl
|
[309, 1]
|
[310, 38]
|
intros v τ
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
⊢ equiv env env
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
⊢ get v τ env = get v τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_rfl
|
[309, 1]
|
[310, 38]
|
rfl
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
⊢ get v τ env = get v τ env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_symm
|
[312, 1]
|
[316, 11]
|
intros H name
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
⊢ equiv env env' → equiv env' env
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
H : equiv env env'
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_symm
|
[312, 1]
|
[316, 11]
|
specialize H name
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
H : equiv env env'
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
name : SSAVal
H : ∀ (τ : MLIRType δ), get name τ env = get name τ env'
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_symm
|
[312, 1]
|
[316, 11]
|
simp [H]
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env env' : SSAEnv δ
name : SSAVal
H : ∀ (τ : MLIRType δ), get name τ env = get name τ env'
⊢ ∀ (τ : MLIRType δ), get name τ env' = get name τ env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_trans
|
[318, 1]
|
[325, 16]
|
intros _ _ H1 _ H2 name
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
⊢ ∀ ⦃env₁ env₂ : SSAEnv δ⦄, equiv env₁ env₂ → ∀ ⦃env₃ : SSAEnv δ⦄, equiv env₂ env₃ → equiv env₁ env₃
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ : SSAEnv δ
H1 : equiv env₁✝ env₂✝
env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_trans
|
[318, 1]
|
[325, 16]
|
specialize H1 name
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ : SSAEnv δ
H1 : equiv env₁✝ env₂✝
env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_trans
|
[318, 1]
|
[325, 16]
|
specialize H2 name
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
H2 : equiv env₂✝ env₃✝
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
H2 : ∀ (τ : MLIRType δ), get name τ env₂✝ = get name τ env₃✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_trans
|
[318, 1]
|
[325, 16]
|
simp [H1, H2]
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁✝ env₂✝ env₃✝ : SSAEnv δ
name : SSAVal
H1 : ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₂✝
H2 : ∀ (τ : MLIRType δ), get name τ env₂✝ = get name τ env₃✝
⊢ ∀ (τ : MLIRType δ), get name τ env₁✝ = get name τ env₃✝
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
intros Hne env τ val
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v → ∀ ⦃env : SSAEnv δ⦄ ⦃τ : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄, getT v (set v' τ val env) = getT v env
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v' τ val env) = getT v env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
cases env with
| One s =>
simp [getT, set]
rw [SSAScope.getT_set_ne]
assumption
| Cons head tail =>
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
rw [SSAScope.getT_set_ne]
assumption
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v' τ val env) = getT v env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
simp [getT, set]
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ getT v (set v' τ val (One s)) = getT v (One s)
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v' τ val s) = SSAScope.getT v s
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
rw [SSAScope.getT_set_ne]
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v' τ val s) = SSAScope.getT v s
|
case One.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ v' ≠ v
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
assumption
|
case One.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ v' ≠ v
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ getT v (set v' τ val (Cons head tail)) = getT v (Cons head tail)
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v' τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
match SSAScope.getT v head, fun x => getT v tail with
| some a, x => some a
| none, b => b ()
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
rw [SSAScope.getT_set_ne]
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v' τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
match SSAScope.getT v head, fun x => getT v tail with
| some a, x => some a
| none, b => b ()
|
case Cons.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ v' ≠ v
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_ne
|
[327, 1]
|
[340, 15]
|
assumption
|
case Cons.a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ v' ≠ v
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_eq
|
[342, 1]
|
[350, 32]
|
cases env with
| One s =>
simp [getT, set]
rw [SSAScope.getT_set_eq]
| Cons head tail =>
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
simp [SSAScope.getT_set_eq]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
env : SSAEnv δ
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
⊢ getT v (set v τ val env) = some { fst := τ, snd := val }
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_eq
|
[342, 1]
|
[350, 32]
|
simp [getT, set]
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ getT v (set v τ val (One s)) = some { fst := τ, snd := val }
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v τ val s) = some { fst := τ, snd := val }
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_eq
|
[342, 1]
|
[350, 32]
|
rw [SSAScope.getT_set_eq]
|
case One
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
s : SSAScope δ
⊢ SSAScope.getT v (SSAScope.set v τ val s) = some { fst := τ, snd := val }
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_eq
|
[342, 1]
|
[350, 32]
|
simp [getT, set, HOrElse.hOrElse, OrElse.orElse, Option.orElse]
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ getT v (set v τ val (Cons head tail)) = some { fst := τ, snd := val }
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
some { fst := τ, snd := val }
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.getT_set_eq
|
[342, 1]
|
[350, 32]
|
simp [SSAScope.getT_set_eq]
|
case Cons
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
τ : MLIRType δ
val : MLIRType.eval τ
head : SSAScope δ
tail : SSAEnv δ
⊢ (match SSAScope.getT v (SSAScope.set v τ val head), fun x => getT v tail with
| some a, x => some a
| none, b => b ()) =
some { fst := τ, snd := val }
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_ne_val
|
[352, 1]
|
[359, 13]
|
intros Hne env τ τ' val
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v → ∀ ⦃env : SSAEnv δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ'⦄, get v τ (set v' τ' val env) = get v τ env
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) = get v τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_ne_val
|
[352, 1]
|
[359, 13]
|
simp [get]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) = get v τ env
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ (match getT v (set v' τ' val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none) =
match getT v env with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_ne_val
|
[352, 1]
|
[359, 13]
|
rw [SSAEnv.getT_set_ne]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ (match getT v (set v' τ' val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none) =
match getT v env with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none
|
case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ v' ≠ v
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_ne_val
|
[352, 1]
|
[359, 13]
|
assumption
|
case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ'
⊢ v' ≠ v
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_eq_val
|
[361, 1]
|
[368, 26]
|
simp [H']
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
H' : τ' = τ
⊢ MLIRType.eval τ' = MLIRType.eval τ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_eq_val
|
[361, 1]
|
[368, 26]
|
simp [get, getT_set_eq]
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if H' : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit)
val)
else none
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set
|
[370, 1]
|
[383, 15]
|
simp [H]
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : τ' = τ
⊢ MLIRType.eval τ' = MLIRType.eval τ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set
|
[370, 1]
|
[383, 15]
|
byCases H: v' = v
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v' τ' val env) =
if v' = v then
if H : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit)
val)
else none
else get v τ env
|
case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit)
val)
else none
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set
|
[370, 1]
|
[383, 15]
|
. simp [get_set_eq_val]
|
case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v : SSAVal
val : MLIRType.eval τ'
⊢ get v τ (set v τ' val env) =
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε σ
| MLIRType.erased => Unit)
val)
else none
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set
|
[370, 1]
|
[383, 15]
|
. rw [get_set_ne_val]
assumption
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
τ τ' : MLIRType δ
env : SSAEnv δ
v v' : SSAVal
val : MLIRType.eval τ'
H : ¬v' = v
⊢ get v τ (set v' τ' val env) = get v τ env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_eq
|
[385, 1]
|
[387, 26]
|
simp [get, getT_set_eq]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v : SSAVal
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v τ (set v τ val env) = some val
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_neq
|
[389, 1]
|
[392, 42]
|
simp[get]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ get v τ (set v' τ val env) = get v τ env
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ (match getT v (set v' τ val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none) =
match getT v env with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_neq
|
[389, 1]
|
[392, 42]
|
rw[SSAEnv.getT_set_ne]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ (match getT v (set v' τ val env) with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none) =
match getT v env with
| none => none
| some { fst := τ', snd := v' } =>
if h : τ' = τ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
v')
else none
|
case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_neq
|
[389, 1]
|
[392, 42]
|
try assumption;
|
case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.get_set_neq
|
[389, 1]
|
[392, 42]
|
assumption
|
case a
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
NEQ : v' ≠ v
env : SSAEnv δ
τ : MLIRType δ
val : MLIRType.eval τ
⊢ v' ≠ v
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
intros HEnv name τ v name' τ'
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
⊢ equiv env₁ env₂ →
∀ ⦃name : SSAVal⦄ ⦃τ : MLIRType δ⦄ ⦃v : MLIRType.eval τ⦄, equiv (set name τ v env₁) (set name τ v env₂)
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
byCases Hname: name = name'
|
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name' τ v env₁) = get name' τ' (set name' τ v env₂)
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
. simp [get_set_eq_val]
|
case h1
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
⊢ get name' τ' (set name' τ v env₁) = get name' τ' (set name' τ v env₂)
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
. repeat rw [get_set_ne_val] <;> try assumption
apply HEnv
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' (set name τ v env₁) = get name' τ' (set name τ v env₂)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
rw [get_set_ne_val] <;> try assumption
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' env₁ = get name' τ' (set name τ v env₂)
|
case h2
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ get name' τ' env₁ = get name' τ' env₂
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.equiv_set
|
[394, 1]
|
[401, 15]
|
assumption
|
case h2.a
α σ : Type
ε : σ → Type
δ : Dialect α σ ε
env₁ env₂ : SSAEnv δ
HEnv : equiv env₁ env₂
name : SSAVal
τ : MLIRType δ
v : MLIRType.eval τ
name' : SSAVal
τ' : MLIRType δ
Hname : ¬name = name'
⊢ name ≠ name'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
intros Hne env τ τ' val val' v₂ τ₂
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
⊢ v' ≠ v →
∀ ⦃env : SSAEnv δ⦄ ⦃τ τ' : MLIRType δ⦄ ⦃val : MLIRType.eval τ⦄ ⦃val' : MLIRType.eval τ'⦄,
equiv (set v τ val (set v' τ' val' env)) (set v' τ' val' (set v τ val env))
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ get v₂ τ₂ (set v τ val (set v' τ' val' env)) = get v₂ τ₂ (set v' τ' val' (set v τ val env))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
repeat rw [get_set]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ get v₂ τ₂ (set v τ val (set v' τ' val' env)) = get v₂ τ₂ (set v' τ' val' (set v τ val env))
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else get v₂ τ₂ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
split
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else get v₂ τ₂ env
|
case inl
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : v = v₂
⊢ (if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
. subst v
simp [Hne]
|
case inl
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : v = v₂
⊢ (if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env
|
case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
. split <;> simp
|
case inr
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
h✝ : ¬v = v₂
⊢ (if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
SSAEnv.set_commutes
|
[403, 1]
|
[412, 19]
|
rw [get_set]
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ (set v τ val env)
|
α σ : Type
ε : σ → Type
α✝ σ✝ : Type
ε✝ : σ✝ → Type
δ : Dialect α✝ σ✝ ε✝
v v' : SSAVal
Hne : v' ≠ v
env : SSAEnv δ
τ τ' : MLIRType δ
val : MLIRType.eval τ
val' : MLIRType.eval τ'
v₂ : SSAVal
τ₂ : MLIRType δ
⊢ (if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else get v₂ τ₂ env) =
if v' = v₂ then
if H : τ' = τ₂ then
some
(cast
(_ :
(match τ' with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val')
else none
else
if v = v₂ then
if H : τ = τ₂ then
some
(cast
(_ :
(match τ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit) =
match τ₂ with
| MLIRType.float a => Float
| MLIRType.int signedness sz => FinInt sz
| MLIRType.tensor1d => Tensor1D
| MLIRType.tensor2d => Tensor2D
| MLIRType.tensor4d => Tensor4D
| MLIRType.index => ℤ
| MLIRType.undefined a => Unit
| MLIRType.extended σ => ε✝ σ
| MLIRType.erased => Unit)
val)
else none
else get v₂ τ₂ env
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
interpSSA'_trigger_MemberSumL
|
[499, 9]
|
[503, 34]
|
simp [Fitree.trigger, pair_eta]
|
α σ : Type
ε : σ → Type
α' σ' : Type
ε' : σ' → Type
T : Type
E : Type → Type
Δ : Dialect α' σ' ε'
e : SSAEnvE Δ T
s₁ : SSAEnv Δ
⊢ interpSSA' (Fitree.trigger e) s₁ = SSAEnvE.handle T e s₁
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/SSAEnv.lean
|
interpSSA'_bind
|
[505, 1]
|
[510, 32]
|
apply Fitree.interpState_bind
|
α σ : Type
ε : σ → Type
E : Type → Type
T R : Type
δ : Dialect α σ ε
t : Fitree (SSAEnvE δ +' E) T
k : T → Fitree (SSAEnvE δ +' E) R
s₁ : SSAEnv δ
⊢ interpSSA' (Fitree.bind t k) s₁ =
Fitree.bind (interpSSA' t s₁) fun x =>
match x with
| (x, s₂) => interpSSA' (k x) s₂
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
BubbleUpExtractSlice.bubble_up_extract_slice
|
[145, 1]
|
[151, 2]
|
cases t
|
M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
t : Tensor1D
f : FinInt 32 → M (FinInt 32)
⊢ (fun s => Tensor1D.extract s len) <$> Tensor1D.mapM t f = Tensor1D.mapM (Tensor1D.extract t len) f
|
case mk
M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
f : FinInt 32 → M (FinInt 32)
size0✝ : ℕ
data✝ : List (FinInt 32)
h_data_size✝ : List.length data✝ = size0✝
⊢ (fun s => Tensor1D.extract s len) <$>
Tensor1D.mapM { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } f =
Tensor1D.mapM (Tensor1D.extract { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } len) f
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
BubbleUpExtractSlice.bubble_up_extract_slice
|
[145, 1]
|
[151, 2]
|
sorry
|
case mk
M : Type → Type
len : ℕ
MM : Monad M
LM : LawfulMonad M
f : FinInt 32 → M (FinInt 32)
size0✝ : ℕ
data✝ : List (FinInt 32)
h_data_size✝ : List.length data✝ = size0✝
⊢ (fun s => Tensor1D.extract s len) <$>
Tensor1D.mapM { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } f =
Tensor1D.mapM (Tensor1D.extract { size0 := size0✝, data := data✝, h_data_size := h_data_size✝ } len) f
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
simp [Tensor1D.fill, Tensor1D.extract]
|
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ Tensor1D.fill (Tensor1D.extract t extractlen) fillval = Tensor1D.extract (Tensor1D.fill t fillval) extractlen
|
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.replicate (min extractlen t.size0) fillval = List.take extractlen (List.replicate t.size0 fillval)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
apply List.extF
|
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.replicate (min extractlen t.size0) fillval = List.take extractlen (List.replicate t.size0 fillval)
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ ∀ (n : ℕ) (h : n < List.length (List.replicate (min extractlen t.size0) fillval)),
List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen (List.replicate t.size0 fillval)))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
intros n h
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ ∀ (n : ℕ) (h : n < List.length (List.replicate (min extractlen t.size0) fillval)),
List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen (List.replicate t.size0 fillval)))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen (List.replicate t.size0 fillval)))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
simp
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.take extractlen (List.replicate t.size0 fillval)) n
(_ : n < List.length (List.take extractlen (List.replicate t.size0 fillval)))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
simp at h
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h : n < List.length (List.replicate (min extractlen t.size0) fillval)
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h✝ : n < List.length (List.replicate (min extractlen t.size0) fillval)
h : n < extractlen ∧ n < t.size0
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h✝ =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
sorry
|
case a
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
n : ℕ
h✝ : n < List.length (List.replicate (min extractlen t.size0) fillval)
h : n < extractlen ∧ n < t.size0
⊢ List.getF (List.replicate (min extractlen t.size0) fillval) n h✝ =
List.getF (List.replicate t.size0 fillval) n (_ : n < List.length (List.replicate t.size0 fillval))
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceFillCommuteOneD.extract_fill_commute
|
[181, 1]
|
[195, 3]
|
sorry
|
case h_len
t : Tensor1D
extractlen : ℕ
fillval : FinInt 32
⊢ List.length (List.replicate (min extractlen t.size0) fillval) =
List.length (List.take extractlen (List.replicate t.size0 fillval))
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceGenericCommute1D.equiv
|
[248, 1]
|
[264, 6]
|
intros valid_r
|
r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
⊢ validGenericRegion r rSpec →
run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })])
|
r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceGenericCommute1D.equiv
|
[248, 1]
|
[264, 6]
|
simp[LHS, RHS]
|
r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run ⟦ LHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run ⟦ RHS r ⟧ (SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })])
|
r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] (AttrDict.mk [AttrEntry.mk "len" (AttrValue.int 10 MLIRType.index)]),
Op.mk "linalg.fill1d" [(SSAVal.SSAVal "out", MLIRType.tensor1d)] [(SSAVal.SSAVal "x", MLIRType.tensor1d)] []
(AttrDict.mk [AttrEntry.mk "cst" (AttrValue.int 42 MLIRType.index)])])
[])
(SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] (AttrDict.mk [AttrEntry.mk "cst" (AttrValue.int 42 MLIRType.index)]),
Op.mk "linalg.extractslice1d" [(SSAVal.SSAVal "out", MLIRType.tensor1d)]
[(SSAVal.SSAVal "x", MLIRType.tensor1d)] []
(AttrDict.mk [AttrEntry.mk "len" (AttrValue.int 10 MLIRType.index)])])
[])
(SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })])
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
ExtractSliceGenericCommute1D.equiv
|
[248, 1]
|
[264, 6]
|
sorry
|
r✝ : Region linalg
t : Tensor1D
r : Region linalg
rSpec : ℤ → FinInt 32 → FinInt 32
valid_r : validGenericRegion r rSpec
⊢ run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] (AttrDict.mk [AttrEntry.mk "len" (AttrValue.int 10 MLIRType.index)]),
Op.mk "linalg.fill1d" [(SSAVal.SSAVal "out", MLIRType.tensor1d)] [(SSAVal.SSAVal "x", MLIRType.tensor1d)] []
(AttrDict.mk [AttrEntry.mk "cst" (AttrValue.int 42 MLIRType.index)])])
[])
(SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })]) =
run
(denoteRegion linalg
(Region.mk "entry" []
[Op.mk "linalg.generic1d" [(SSAVal.SSAVal "x", MLIRType.tensor1d)] [(SSAVal.SSAVal "t", MLIRType.tensor1d)]
[r] (AttrDict.mk [AttrEntry.mk "cst" (AttrValue.int 42 MLIRType.index)]),
Op.mk "linalg.extractslice1d" [(SSAVal.SSAVal "out", MLIRType.tensor1d)]
[(SSAVal.SSAVal "x", MLIRType.tensor1d)] []
(AttrDict.mk [AttrEntry.mk "len" (AttrValue.int 10 MLIRType.index)])])
[])
(SSAEnv.One [(SSAVal.SSAVal "t", { fst := MLIRType.tensor1d, snd := t })])
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_cons
|
[270, 1]
|
[274, 2]
|
simp[List.mapM, List.mapM.loop]
|
m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ mapM f (x :: xs) = do
let b_1 ← f x
let bs ← mapM f xs
pure (b_1 :: bs)
|
m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ (do
let __do_lift ← f x
List.mapM.loop f xs [__do_lift]) =
do
let b_1 ← f x
let bs ← List.mapM.loop f xs []
pure (b_1 :: bs)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_cons
|
[270, 1]
|
[274, 2]
|
sorry
|
m : Type u_1 → Type u_2
a : Type u_3
b : Type u_1
M : Monad m
LM : LawfulMonad m
x : a
xs : List a
f : a → m b
⊢ (do
let __do_lift ← f x
List.mapM.loop f xs [__do_lift]) =
do
let b_1 ← f x
let bs ← List.mapM.loop f xs []
pure (b_1 :: bs)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.commute_implies_mapM_commute
|
[275, 1]
|
[280, 107]
|
sorry
|
m : Type → Type u_1
a b : Type
xs : List a
y : a
inst✝¹ : Monad m
inst✝ : LawfulMonad m
f g : a → m a
k : List a → a → m b
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ (do
let r1 ← mapM f xs
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← mapM f xs
k r1 r2
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
funext x
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) = mapM (fish f g)
|
case h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
x : List a
⊢ fish (mapM f) (mapM g) x = mapM (fish f g) x
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
induction x
|
case h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
x : List a
⊢ fish (mapM f) (mapM g) x = mapM (fish f g) x
|
case h.nil
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) []
case h.cons
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head✝ : a
tail✝ : List a
tail_ih✝ : fish (mapM f) (mapM g) tail✝ = mapM (fish f g) tail✝
⊢ fish (mapM f) (mapM g) (head✝ :: tail✝) = mapM (fish f g) (head✝ :: tail✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
case nil => {
simp[fish, List.mapM, List.mapM.loop];
}
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) []
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
case cons head tail IH => {
rewrite [mapM_cons];
simp[fish];
simp [bind_assoc]
simp[mapM_cons];
congr; funext x';
rewrite [commute_implies_mapM_commute];
congr;
funext x';
simp [fish] at IH;
rewrite [<- IH];
simp[bind_assoc];
apply COMMUTE;
}
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ fish (mapM f) (mapM g) (head :: tail) = mapM (fish f g) (head :: tail)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
simp[fish, List.mapM, List.mapM.loop]
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
⊢ fish (mapM f) (mapM g) [] = mapM (fish f g) []
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
rewrite [mapM_cons]
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ fish (mapM f) (mapM g) (head :: tail) = mapM (fish f g) (head :: tail)
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ fish (mapM f) (mapM g) (head :: tail) = do
let b ← fish f g head
let bs ← mapM (fish f g) tail
pure (b :: bs)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
simp[fish]
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ fish (mapM f) (mapM g) (head :: tail) = do
let b ← fish f g head
let bs ← mapM (fish f g) tail
pure (b :: bs)
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ (do
let x ← f head
let x_1 ← mapM f tail
let __do_lift ← g x
let __do_lift_1 ← mapM g x_1
pure (__do_lift :: __do_lift_1)) =
do
let x ← f head
let b ← g x
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
congr
|
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ (do
let x ← f head
let x_1 ← mapM f tail
let __do_lift ← g x
let __do_lift_1 ← mapM g x_1
pure (__do_lift :: __do_lift_1)) =
do
let x ← f head
let b ← g x
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
case e_a
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ (fun x => do
let x_1 ← mapM f tail
let __do_lift ← g x
let __do_lift_1 ← mapM g x_1
pure (__do_lift :: __do_lift_1)) =
fun x => do
let b ← g x
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
funext x'
|
case e_a
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
⊢ (fun x => do
let x_1 ← mapM f tail
let __do_lift ← g x
let __do_lift_1 ← mapM g x_1
pure (__do_lift :: __do_lift_1)) =
fun x => do
let b ← g x
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
x' : a
⊢ (do
let x ← mapM f tail
let __do_lift ← g x'
let __do_lift_1 ← mapM g x
pure (__do_lift :: __do_lift_1)) =
do
let b ← g x'
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/LinalgSemantics.lean
|
mapMCommute.mapM_commute
|
[282, 1]
|
[312, 2]
|
rewrite [commute_implies_mapM_commute]
|
case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
x' : a
⊢ (do
let x ← mapM f tail
let __do_lift ← g x'
let __do_lift_1 ← mapM g x
pure (__do_lift :: __do_lift_1)) =
do
let b ← g x'
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
|
case e_a.h
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
x' : a
⊢ (do
let r2 ← g x'
let r1 ← mapM f tail
let __do_lift ← mapM g r1
pure (r2 :: __do_lift)) =
do
let b ← g x'
let bs ← mapM (fun a_1 => f a_1 >>= g) tail
pure (b :: bs)
case e_a.h.COMMUTE
m : Type → Type u_1
a : Type
M : Monad m
LM : LawfulMonad m
f g : a → m a
COMMUTE :
∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
head : a
tail : List a
IH : fish (mapM f) (mapM g) tail = mapM (fish f g) tail
x' : a
⊢ ∀ {b : Type} (x y : a) (k : a → a → m b),
(do
let r1 ← f x
let r2 ← g y
k r1 r2) =
do
let r2 ← g y
let r1 ← f x
k r1 r2
|
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