discuss CCC aspect

discuss CCC aspect

-- Modeling Opetopes
-- here is Eric's editor: http://sma.epfl.ch/~finster/opetope/opetope.html
--
-- Note: Kock et al. use a similar scheme, where
--          - dots    <-->   lines
--          - spheres <-->   dots
--          - lines disappear
--          -                spheres appear

-- Note: In Eric's new work (at IAS) there are no
--       dots any more, instead he uses 'external cards', so
--          - (external) cards   <-->  lines
--          - space between stacked cards <--> external cards
--          - lines disappear
--          -                (regular) cards appear

import "../src/LangPrelude.prg" (maybeM)
import "../tests/Nat.prg"

##bounds backchain 10

-- GLOBAL TODOs
----------------

-- Naming: Seems essential for identifying things Hor(Name), Ver(Tree)
--         Name can be Label, then Niches (= sequences of opetope names).
--         the latter arise from the composition rule.
--         Note: don't store names in Stacks, that kills alpha
--               conversion. Instead names should be pushed into nodes
--               'singleton style' from outside: (node :: Tree (Hor `g))

-- Morphisms: given an opetope and a pointer to one of its cards
--            extract the opetope of that face (do we need a label
--            space to reliably find it?). This must be a type
--            function, with an algorithm accompanying it to extract
--            the face proper.

-- Composition: grafting of trees to external cards, but only if the
--              morphisms (faces) match. lower-dim stuff is unaffected.

-- Swapping: given a proof of equality between two niches, provide an
--           operation to swap them, replacing old faces by new ones,
--           FGL-style (functional graph library), just note that
--           certain morphisms are gone, others appeared.

-- References: a disciplined way of saying "I am an identical node to that guy",
--             by corollary these always obtain the same names.
--             a topologist would say 'surgery' (http://en.wikipedia.org/wiki/Surgery_theory)
--             We get a new Tree flavour, Ref, at least one up, followed by
--             naturals to index a node in a subtree.
--             At this point we are doing algebraic topology, and dealing with
--             closed manifolds, so that we can do homology etc. on them.
--             In logic this corresponds to relations, satisfiability.

-- Quoting: So far we have only dealt with data, i.e. quoted (inert) syntax.
--          we need a way to convert this syntax to code (e.g. at some stage),
--          to obtain semantics. We can have the usual splicing game.
--          Lisp does this with sexprs and macros.
--          The code needs then be executed (run, decreasing stage), when
--          it becomes active, and we can observe the manifestation of its
--          semantics. The reduction system could go along the lines of the
--          (typed) LambdaGraph.

-- NbE: I fully believe we can use this technique to reduce opetopic terms
--      to normal form. ('many syntax', 'one semantics' adjunction:
--                       http://www.logicmatters.net/resources/pdfs/Galois.pdf)

-- Cartesian Closure: Creating 'lambda cards' by the above technology
--                    seems very ad-hoc and arbitrary. Contrast it with more
--                    serious attempts like higher-order containers
--                    (http://www.cs.nott.ac.uk/~txa/publ/hocont.pdf)
--                    or other ways to create internal languages.

-- TODO: these three must be LeftLists
--
kind Trees = NoTree | Pre (Tree d) Trees deriving syntax (ts) List(NoTree, Pre)

data ZoomCompley :: Tree e ~> Tree f ~> * where
  Nily :: ZoomCompley a a
  Consy :: Stack a b -> ZoomCompley b c -> ZoomCompley a c
 deriving List(cply)

data ZoomComplex :: Trees ~> * where
  Nilx :: ZoomComplex [()tr]ts
  Endx :: Stack a b -> ZoomComplex [a, b]ts
  Consx :: Stack a b -> ZoomComplex [b; c]ts -> ZoomComplex [a, b; c]ts
 deriving syntax (cplx) List(Nilx, Consx) Item(Endx)

data Dir :: *2 where
  Hor :: Dir
  Ver :: Dir

-- define the Tree kind, a rose tree
-- note: we may need a two-level kind, since we need to track disjointness
--       of subtrees
-- todo: later we may want to have a label kind parameter too

data Tree :: Dir ~> *1 where
  Unit :: Tree Ver
  Ni :: Tree Hor
  Fork :: Tree d ~> Tree Hor ~> Tree Hor
 deriving syntax (tr) List(Ni, Fork) Unit(Unit)

-- make it singleton

data Tree' :: Tree d ~> * where
  In :: Tree' ()tr
  Fork :: treelike head -> Tree' tail -> Tree' [head; tail]tr
  Done :: Tree' []tr
 deriving syntax (ar) List(Done, Fork) Unit(In) -- "arbre"
-- http://www.papoulipoesique.com/wp-content/uploads/2013/06/arbre.jpg

-- define a proposition for subtrees
-- to be checked: TakeHead must ensure that all the node is consumed

prop Subtree :: Tree d ~> Tree e ~> * where
  UnitSub :: Subtree ()tr tr
  BothNil :: Subtree []tr []tr
  TakeHead :: Subtree head head' -> Subtree tail tail' -> Subtree [head; tail]tr [head'; tail']tr

-- TODO: separate the notions of Niche / Frame / Cell
kind Volume = FramedHollow | FilledCell
kind Diagram = Closed Volume | OpenNiche
-- should be a parameter to Stack

-- now we can stack cards (these are zooms in Kock et al. parlance)

data Stack :: Tree d ~> Tree e ~> * where
  Corolla :: Corolla tr => Tree' tr -> Stack tr ()tr

  -- TODO: needed?
  --Expand :: (Subtree consumed tr, {nodeValence consumed} `Equal` {nodeValence tr}) => Stack consumed prod -> Stack tr prod

  -- add another target face to a web
  Target :: ({nodes tr} `Equal` {nodeValence out}) => Stack tr out -> Stack tr out

  -- the following three grab a node (and possibly its offsprings) and incorporate it into a single card
  NodeDone :: Stack []tr [()tr]tr
  Pick :: {- EntireNode => -} Stack head prodhead -> Stack tail prodtail -> Stack [head; tail]tr [prodhead; prodtail]tr
  Exclude :: {- EntireNode => -} Stack tail prod -> Stack [()tr; tail]tr prod
  -- TODO: maybe just specify a subtree (Tree') and that's it

  On :: (Subtree tr' tr, Pointers 1t at out) => Stack tr' out' -> Stack tr out -> Tree' at -> Stack tr {graft out' at out}

  -- building niches (pasting diagrams)
  -- TODO: these must produce a composite labelled Hor
  NicheDone :: Stack ()tr []tr
  Niche :: Stack tr out -> Stack tr [out]tr
  Also :: Pointers 1t at tr
       => Tree' at -> Stack tr' out' -> Stack tr out -> Stack {extgraft tr' at tr} [out'; out]tr

  -- put a frame around a niche
  Frame :: (Corolla out, {nodes tr}  `Equal` {nodeValence out}) => Stack tr out -> Stack tr out

 deriving syntax(z) Record(NicheDone, Also) Item(Target)

stop = ({}z)z

-- this is bogus, just make it compile again...
up :: Reference tr => Stack ()tr tr -> Stack ()tr [tr]tr
up inner = ({()ar=inner}z)z

-- it remains to define corollas

-- TODO: one could say {nodes tr} == 1
prop Corolla :: Tree d ~> * where
  None' :: Corolla []tr
  One' :: Corolla tail -> Corolla [()tr; tail]tr

--  o   --->  |
--  |         |

lolliCell :: Stack []tr ()tr
lolliCell = Corolla Done

--  |         |
--  o   --->  |
--  |         |

dolliCell :: Stack [()tr]tr ()tr
dolliCell = Corolla $ Fork In Done

--              |
--  [o]   --->  o
--   |          |

lolliFrame :: Stack []tr [()tr]tr
lolliFrame = Target NodeDone

--   |          |
--  [o]   --->  o
--   |          |

dolliFrame :: Stack [()tr]tr [()tr]tr
dolliFrame = Target (Exclude NodeDone)

--   |          |
--   |          o
-- [[o]]  --->  |
--   |          o
--   |          |

stacked :: Stack [()tr]tr [[()tr]tr]tr
stacked = (dolliFrame `On` dolliFrame) (In `Fork` Done)

--   |
--  [|]   --->  o
--   |          |

crossed :: Stack ()tr []tr
crossed = stop

-- we can now join things
--
dolliForever = [dolliFrame; dolliForever]cply
nopetope = [crossed, lolliFrame; dolliForever]cply

-- back to unit as fast as possible...
--
stopetope = [crossed, lolliFrame, dolliCell]cply
neverstopetope = [crossed, lolliFrame, dolliCell; neverstopetope]cply
stopetope' = [crossed, lolliFrame; (dolliCell)cplx]cplx
stopetope'' = [crossed, lolliFrame, dolliCell]cplx

--   |          o
-- [[|]]  --->  |
--   |          o
--   |          |

drossed :: Stack ()tr [[]tr]tr
drossed = up stop

-- ################################
-- ############  Niches ###########
-- ################################

--  |          +
--  |          |

-- this is a niche, but assume to be a frame
niche0 :: Stack ()tr []tr
niche0 = {}z

--  |           |
-- [|]          +
--  |           |

-- this is a niche, but assume to be a frame
niche1 :: Stack ()tr [[]tr]tr
niche1 = {()ar=stop; {}z}z

--  |         o   o
-- [|]  --->   \ /
-- [|]          +
--  |           |

-- this is a niche, but assume to be a frame
niche2 :: Stack ()tr [[]tr, []tr]tr
niche2 = {()ar=stop; niche1}z

--                |
--  |         o   o
-- [o]  --->   \ /
-- [|]          +
--  |           |

niche10 :: Stack [()tr]tr [[()tr]tr, []tr]tr
niche10 = {()ar=Exclude NodeDone; Niche stop}z

-- ################################
-- ############  Frames ###########
-- ################################

--   |              |
--  /|\         o   o
-- |[o]|  --->   \ /
-- |[|]|          o
--  \|/           |
--   |

cyclops :: Stack [()tr]tr [[()tr]tr, []tr]tr
cyclops = (niche10)z

-- Stacking, Valence, Affine subtree, Substitute at an affine position

-- counting Units in a tree

valence :: Tree d ~> Nat
{valence []tr} = 0t
{valence [head; tail]tr} = {plus {valence head} {valence tail}}
{valence ()tr} = 1t

-- counting siblings of a tree

nodeValence :: Tree d ~> Nat
{nodeValence []tr} = 0t
{nodeValence [head; tail]tr} = (1+{nodeValence tail})t

-- counting nodes in a tree

nodes :: Tree d ~> Nat
{nodes ()tr} = t
{nodes []tr} = 1t
{nodes [head; tail]tr} = {plus {nodes head} {nodes tail}}

-- nodeValenceAt: given a (multi)pointer, determine the node valences at those positions
--               WHERE     IN
nodeValenceAt :: Tree d ~> Tree e ~> Nat
{nodeValenceAt ()tr tree} = {nodeValence tree}
{nodeValenceAt []tr []tr} = 0t
{nodeValenceAt [head'; tail']tr [head; tail]tr} = {plus {nodeValenceAt head' head} {nodeValenceAt tail' tail}}

-- a pointer is a valence-1 subtree of a tree
-- it is used to mark a unit in a tree where substitution will occur
--
prop Pointers :: Nat ~> Tree d ~> Tree e ~> * where
  Finger :: Pointers 1t ()tr ()tr
  Finished :: Pointers 0t []tr []tr
  ThisWay :: Pointers 1t head' head -> Pointers n tail' tail -> Pointers (1+n)t [head'; tail']tr [head; tail]tr
  ElseWhere :: Pointers n tail' tail -> Pointers n [[]tr; tail']tr [head; tail]tr

-- http://en.wikipedia.org/wiki/Grafting
--
-- graft WHAT      WHERE     IN
graft :: Tree d ~> Tree e ~> Tree f ~> Tree f
{graft what ()tr ()tr} = what
{graft what []tr tr} = tr
{graft what [head'; tail']tr [head; tail]tr} = [{graft what head' head}; {graft what tail' tail}]tr

-- extgraft: extend and graft
--
extgraft :: Tree what ~> Tree wher ~> Tree tree ~> Tree tree'
{extgraft what ()tr ()tr} = what
{extgraft what []tr ()tr} = ()tr
{extgraft what [head; tail]tr ()tr} = {extgrafthor what [head; tail]tr}
{extgraft what []tr []tr} = []tr
{extgraft what []tr [head; tail]tr} = [head; tail]tr
{extgraft what [head'; tail']tr [head; tail]tr} = [{extgraft what head' head}; {extgraft what tail' tail}]tr

-- helper:
extgrafthor :: Tree what ~> Tree Hor ~> Tree Hor
{extgrafthor what []tr} = []tr
{extgrafthor what [head; tail]tr} = [{extgraft what head ()tr}; {extgrafthor what tail}]tr

{- NOTE: we have an Omega bug here:

prompt> :norm {graft []tr ()tr ()tr}
Normalizes to:
  []tr

prompt> :kind []tr
[]tr :: Tree Hor  = []tr

prompt> :kind {graft []tr ()tr ()tr}
{graft []tr ()tr ()tr} :: Tree Ver  = {graft []tr ()tr ()tr}

... BUT: Hor /= Ver :-(
-}

-- substitution: replace a pointed node (of valence n) in a tree with an
-- other tree of (valence n) -- TODO

-- HERE IS A NICE RESEARCH QUESTION:
-- is it possible to "proof search" a Zoom?
-- i.e.
{-

class ZoomLike (int :: Tree) (out :: Tree) where
  zoom :: (Nodes int ~ Valence out) => Zoom int out

-}

prop Reference :: Tree Hor ~> * where
  Stop :: Reference []tr
  Up :: Reference tr -> Reference [tr]tr
 deriving Nat(d) -- de Bruijn index

prop Teleport :: Tree Hor ~> * where
  Gate :: Teleport [()tr]tr
  Tele :: Teleport tr -> Teleport [tr]tr
 deriving Nat(sk) -- skips

{-

0
|   |
1   L  (lambda node)
|   |
2   1  (how many skips)
 \ /
  o
  |
  B  (binds here)
  |

Encodes \x.xx

-}

r2 = 2d
t1 = 1sk

lamX_XX = addBinder $ [r2, t1]ar

prop BindsUp :: Nat ~> Tree Hor ~> * where
  LastSkip :: BindsUp 1t [()tr]tr
  MoreSkip :: Teleport tr -> BindsUp n tr -> BindsUp (1+n)t [tr]tr
  -- prove Application node
  HeadBindsUp :: Nat' n -> BindsUp (1+n)t head -> BindsUp n [head; tail]tr
  TailBindsUp :: BindsUp n [head; tail]tr -> BindsUp n [nonempty, head; tail]tr

-- TODO: make sure that something teleports here
addBinder :: BindsUp 1t tr => Tree' tr -> Tree' [tr]tr
addBinder term = [term]ar

testB :: BindsUp 0t [[[[]tr]tr]tr,[()tr]tr]tr -> Tree' [[[[]tr]tr]tr,[()tr]tr]tr
testB ev = [r2, 0sk]ar
testB' = testB (TailBindsUp (HeadBindsUp 0v (LastSkip)))

testC :: BindsUp 0t [[[[[]tr]tr]tr,[[()tr]tr]tr]tr]tr -> Tree' [[[[[]tr]tr]tr,[[()tr]tr]tr]tr]tr
testC ev = lamX_XX
testC' = testC (HeadBindsUp 0v (TailBindsUp (HeadBindsUp 1v (MoreSkip 0sk LastSkip))))

--TODO: prop Lambda :: Tree Hor ~> * where

{-
The slogan is: binder nodes do not count as result nodes:
 - just consider the next node upstream
 - incoming (external) cards, when identified to a binder do not count as inputs to application
 - incoming (external) cards, when identified to an (iterated) application become pattern matching (sigma).

In the end all identifications have a semantics (hopefully!), when the counting rules are ensured.

-}

-- Now some fun stuff

data LC :: Shape ~> (k ~> *) ~> * where
  Var :: tf a -> LC (Rf a) tf
  App :: LC fsh tf -> LC ash tf -> LC (fsh `Ap` ash) tf
  Lam :: tf a -> LC sh tf -> LC (Lm sh) tf
  LetRec :: tf a -> LC ish tf -> LC esh tf -> LC ((Lm esh) `Ap` ish) tf
 deriving syntax (lc) Applicative(Var, App, Lam, LetRec)

alamX_XX = (\x->x x)lc

kind Dict key value = Dempty | Dextend (Dict key value) key value deriving LeftRecord(dict)

-- Contexts map keys to some value
--
data Context :: (key ~> *) ~> (value ~> *) ~> Dict key value ~> * where
  Empty :: Context key value {}dict
  Extend :: Context key value dict -> key k -> value v -> Context key value {dict; k = v}dict
 deriving LeftRecord(ctx)

-- DeBruijn levels as keys
--
dictSize :: Dict key value ~> Nat
{dictSize {}dict} = 0t
{dictSize {pre; k = v}dict} = (1+{dictSize pre})t

data DeBruijnContext :: (value ~> *) ~> Dict Nat value ~> * where
  DeBruijnEmpty :: DeBruijnContext value {}dict
  DeBruijnExtend :: DeBruijnContext value dict -> value v -> DeBruijnContext value {dict; {dictSize dict} = v}dict
 deriving LeftList(dtx)

getDeBruijnIndex :: Dict key value ~> value ~> Nat ~> Nat
{getDeBruijnIndex {pre; k = v}dict v acc} = acc
{getDeBruijnIndex {pre; k = v'}dict v acc} = {getDeBruijnIndex pre v (1+acc)t}

lookUpDeBruijn :: DeBruijnContext Label dict -> Label l -> Nat' acc -> Maybe (Nat' {getDeBruijnIndex dict l acc})
lookUpDeBruijn []dtx _ _ = Nothing
lookUpDeBruijn [pre; known]dtx lab acc = case sameLabel known lab of
                                         R _ -> lookUpDeBruijn pre lab (1+acc)t
                                         L Eq -> Just acc

monad maybeM

l2n :: Shape ~> Shape
{l2n (Lm sh)} = Lm {l2n sh}
{l2n (Ap f a)} = Ap {l2n f} {l2n a}
{l2n (Rf t)} = Rf n -- getDeBruijnIndex!!! FIXME

toDeBruijn :: DeBruijnContext Label dict -> LC sh Label -> Maybe (LC {l2n sh} Nat')
toDeBruijn ctx (Var a) = do idx <- lookUpDeBruijn ctx a 0t
                            return $ Var idx
toDeBruijn ctx (Lam l a) = do a' <- toDeBruijn [ctx; l]dtx a
                              return $ Lam 0t a'
toDeBruijn ctx (App f a) = do f' <- toDeBruijn ctx f
                              a' <- toDeBruijn ctx a
                              return $ App f' a'

-- we should get a pair (Nat, Context) -- TODO
-- this is not good yet!
--
{-
toFullContext :: DeBruijnContext Nat' dict -> Shape' sh -> LC sh Nat' -> LC sh (Context Nat' Shape')
toFullContext ctx (Rf a') (Var a) = Var ctx
toFullContext ctx sh (Lam l a) = Lam ctx $ toFullContext [ctx; l]dtx a
toFullContext ctx sh (App f a) = App (toFullContext ctx f) (toFullContext ctx a)
-}

-- Let :: tf a -> LC tf -> LC tf -> LC tf -- not needed!
pattern Let n v exp = App (Lam n exp) v

-- fun with church encoding

true = (\t->\f->t)lc
--false = (\t f->f)lc -- BUG!
false = (\t->\f->f)lc

-- church 'if'
chif = (\v->\iftrue->\iffalse->v iftrue iffalse)lc

chtest = (chif true false true)lc -- will not do what you expect
--chtest' = ($chif $true $false $true)lc -- not ready yet!

chtest'' = (let { true = \t->\f->t
                ; false = \t->\f->f
                ; chif = \v->\iftrue->\iffalse -> v iftrue iffalse
                }
            in chif true false true)lc -- this still does not work :-(

letrecToLet :: LC sh k -> LC sh k
letrecToLet (App f a) = App (letrecToLet f) (letrecToLet a)
letrecToLet (v@Var _) = v
letrecToLet (l@Lam _ _) = l
letrecToLet (LetRec n v e) = App (Lam n e) v -- Let n v e -- Omega pattern bug???

l2l = letrecToLet (let a = a in a)lc

-- shapes

kind Shape = Lm Shape | Ap Shape Shape | Rf k

data Shape' :: Shape ~> * where
  Ref :: Nat' n -> Shape' (Rf n)
  Nam :: Label n -> Shape' (Rf n)
  Lm :: Shape' inner -> Shape' (Lm inner)
  Ap :: Shape' f -> Shape' a -> Shape' (f `Ap` a)

shape :: LC sh Nat' -> Shape' sh
shape (Var n) = Ref n
shape (Lam n e) = Lm $ shape e
shape (App f a) = shape f `Ap` shape a

{-
data Dictionary :: Dict a b ~> * where
  Funny :: Dictionary {}dict

context :: DeBruijnContext Nat' dict -> LC sh Nat' -> LC sh Dictionary
context ctx (Var n) = Var undefined
-}

-- abstractly interpret
-- this should be parameterized by a monad!

--interp :: Monad m -> LC (context tr) -> m (LC (context tr))

-- Modeling Opetopes
-- here is Eric's editor: http://sma.epfl.ch/~finster/opetope/opetope.html
--
-- Note: Kock et al. use a similar scheme, where
--          - dots    <-->   lines
--          - spheres <-->   dots
--          - lines disappear
--          -                spheres appear

-- Note: In Eric's new work (at IAS) there are no
--       dots any more, instead he uses 'external cards', so
--          - (external) cards   <-->  lines
--          - space between stacked cards <--> external cards
--          - lines disappear
--          -                (regular) cards appear

import "../src/LangPrelude.prg" (maybeM)
import "../tests/Nat.prg"

##bounds backchain 10

-- GLOBAL TODOs
----------------

-- Naming: Seems essential for identifying things Hor(Name), Ver(Tree)
--         Name can be Label, then Niches (= sequences of opetope names).
--         the latter arise from the composition rule.
--         Note: don't store names in Stacks, that kills alpha
--               conversion. Instead names should be pushed into nodes
--               'singleton style' from outside: (node :: Tree (Hor `g))

-- Morphisms: given an opetope and a pointer to one of its cards
--            extract the opetope of that face (do we need a label
--            space to reliably find it?). This must be a type
--            function, with an algorithm accompanying it to extract
--            the face proper.

-- Composition: grafting of trees to external cards, but only if the
--              morphisms (faces) match. lower-dim stuff is unaffected.

-- Swapping: given a proof of equality between two niches, provide an
--           operation to swap them, replacing old faces by new ones,
--           FGL-style (functional graph library), just note that
--           certain morphisms are gone, others appeared.

-- References: a disciplined way of saying "I am an identical node to that guy",
--             by corollary these always obtain the same names.
--             a topologist would say 'surgery' (http://en.wikipedia.org/wiki/Surgery_theory)
--             We get a new Tree flavour, Ref, at least one up, followed by
--             naturals to index a node in a subtree.
--             At this point we are doing algebraic topology, and dealing with
--             closed manifolds, so that we can do homology etc. on them.
--             In logic this corresponds to relations, satisfiability.

-- Quoting: So far we have only dealt with data, i.e. quoted (inert) syntax.
--          we need a way to convert this syntax to code (e.g. at some stage),
--          to obtain semantics. We can have the usual splicing game.
--          Lisp does this with sexprs and macros.
--          The code needs then be executed (run, decreasing stage), when
--          it becomes active, and we can observe the manifestation of its
--          semantics. The reduction system could go along the lines of the
--          (typed) LambdaGraph.

-- NbE: I fully believe we can use this technique to reduce opetopic terms
--      to normal form. ('many syntax', 'one semantics' adjunction:
--                       http://www.logicmatters.net/resources/pdfs/Galois.pdf)

-- TODO: these three must be LeftLists
--
kind Trees = NoTree | Pre (Tree d) Trees deriving syntax (ts) List(NoTree, Pre)

data ZoomCompley :: Tree e ~> Tree f ~> * where
  Nily :: ZoomCompley a a
  Consy :: Stack a b -> ZoomCompley b c -> ZoomCompley a c
 deriving List(cply)

data ZoomComplex :: Trees ~> * where
  Nilx :: ZoomComplex [()tr]ts
  Endx :: Stack a b -> ZoomComplex [a, b]ts
  Consx :: Stack a b -> ZoomComplex [b; c]ts -> ZoomComplex [a, b; c]ts
 deriving syntax (cplx) List(Nilx, Consx) Item(Endx)

data Dir :: *2 where
  Hor :: Dir
  Ver :: Dir

-- define the Tree kind, a rose tree
-- note: we may need a two-level kind, since we need to track disjointness
--       of subtrees
-- todo: later we may want to have a label kind parameter too

data Tree :: Dir ~> *1 where
  Unit :: Tree Ver
  Ni :: Tree Hor
  Fork :: Tree d ~> Tree Hor ~> Tree Hor
 deriving syntax (tr) List(Ni, Fork) Unit(Unit)

-- make it singleton

data Tree' :: Tree d ~> * where
  In :: Tree' ()tr
  Fork :: treelike head -> Tree' tail -> Tree' [head; tail]tr
  Done :: Tree' []tr
 deriving syntax (ar) List(Done, Fork) Unit(In) -- "arbre"
-- http://www.papoulipoesique.com/wp-content/uploads/2013/06/arbre.jpg

-- define a proposition for subtrees
-- to be checked: TakeHead must ensure that all the node is consumed

prop Subtree :: Tree d ~> Tree e ~> * where
  UnitSub :: Subtree ()tr tr
  BothNil :: Subtree []tr []tr
  TakeHead :: Subtree head head' -> Subtree tail tail' -> Subtree [head; tail]tr [head'; tail']tr

-- TODO: separate the notions of Niche / Frame / Cell
kind Volume = FramedHollow | FilledCell
kind Diagram = Closed Volume | OpenNiche
-- should be a parameter to Stack

-- now we can stack cards (these are zooms in Kock et al. parlance)

data Stack :: Tree d ~> Tree e ~> * where
  Corolla :: Corolla tr => Tree' tr -> Stack tr ()tr

  -- TODO: needed?
  --Expand :: (Subtree consumed tr, {nodeValence consumed} `Equal` {nodeValence tr}) => Stack consumed prod -> Stack tr prod

  -- add another target face to a web
  Target :: ({nodes tr} `Equal` {nodeValence out}) => Stack tr out -> Stack tr out

  -- the following three grab a node (and possibly its offsprings) and incorporate it into a single card
  NodeDone :: Stack []tr [()tr]tr
  Pick :: {- EntireNode => -} Stack head prodhead -> Stack tail prodtail -> Stack [head; tail]tr [prodhead; prodtail]tr
  Exclude :: {- EntireNode => -} Stack tail prod -> Stack [()tr; tail]tr prod
  -- TODO: maybe just specify a subtree (Tree') and that's it

  On :: (Subtree tr' tr, Pointers 1t at out) => Stack tr' out' -> Stack tr out -> Tree' at -> Stack tr {graft out' at out}

  -- building niches (pasting diagrams)
  -- TODO: these must produce a composite labelled Hor
  NicheDone :: Stack ()tr []tr
  Niche :: Stack tr out -> Stack tr [out]tr
  Also :: Pointers 1t at tr
       => Tree' at -> Stack tr' out' -> Stack tr out -> Stack {extgraft tr' at tr} [out'; out]tr

  -- put a frame around a niche
  Frame :: (Corolla out, {nodes tr}  `Equal` {nodeValence out}) => Stack tr out -> Stack tr out

 deriving syntax(z) Record(NicheDone, Also) Item(Target)

stop = ({}z)z

-- this is bogus, just make it compile again...
up :: Reference tr => Stack ()tr tr -> Stack ()tr [tr]tr
up inner = ({()ar=inner}z)z

-- it remains to define corollas

-- TODO: one could say {nodes tr} == 1
prop Corolla :: Tree d ~> * where
  None' :: Corolla []tr
  One' :: Corolla tail -> Corolla [()tr; tail]tr

--  o   --->  |
--  |         |

lolliCell :: Stack []tr ()tr
lolliCell = Corolla Done

--  |         |
--  o   --->  |
--  |         |

dolliCell :: Stack [()tr]tr ()tr
dolliCell = Corolla $ Fork In Done

--              |
--  [o]   --->  o
--   |          |

lolliFrame :: Stack []tr [()tr]tr
lolliFrame = Target NodeDone

--   |          |
--  [o]   --->  o
--   |          |

dolliFrame :: Stack [()tr]tr [()tr]tr
dolliFrame = Target (Exclude NodeDone)

--   |          |
--   |          o
-- [[o]]  --->  |
--   |          o
--   |          |

stacked :: Stack [()tr]tr [[()tr]tr]tr
stacked = (dolliFrame `On` dolliFrame) (In `Fork` Done)

--   |
--  [|]   --->  o
--   |          |

crossed :: Stack ()tr []tr
crossed = stop

-- we can now join things
--
dolliForever = [dolliFrame; dolliForever]cply
nopetope = [crossed, lolliFrame; dolliForever]cply

-- back to unit as fast as possible...
--
stopetope = [crossed, lolliFrame, dolliCell]cply
neverstopetope = [crossed, lolliFrame, dolliCell; neverstopetope]cply
stopetope' = [crossed, lolliFrame; (dolliCell)cplx]cplx
stopetope'' = [crossed, lolliFrame, dolliCell]cplx

--   |          o
-- [[|]]  --->  |
--   |          o
--   |          |

drossed :: Stack ()tr [[]tr]tr
drossed = up stop

-- ################################
-- ############  Niches ###########
-- ################################

--  |          +
--  |          |

-- this is a niche, but assume to be a frame
niche0 :: Stack ()tr []tr
niche0 = {}z

--  |           |
-- [|]          +
--  |           |

-- this is a niche, but assume to be a frame
niche1 :: Stack ()tr [[]tr]tr
niche1 = {()ar=stop; {}z}z

--  |         o   o
-- [|]  --->   \ /
-- [|]          +
--  |           |

-- this is a niche, but assume to be a frame
niche2 :: Stack ()tr [[]tr, []tr]tr
niche2 = {()ar=stop; niche1}z

--                |
--  |         o   o
-- [o]  --->   \ /
-- [|]          +
--  |           |

niche10 :: Stack [()tr]tr [[()tr]tr, []tr]tr
niche10 = {()ar=Exclude NodeDone; Niche stop}z

-- ################################
-- ############  Frames ###########
-- ################################

--   |              |
--  /|\         o   o
-- |[o]|  --->   \ /
-- |[|]|          o
--  \|/           |
--   |

cyclops :: Stack [()tr]tr [[()tr]tr, []tr]tr
cyclops = (niche10)z

-- Stacking, Valence, Affine subtree, Substitute at an affine position

-- counting Units in a tree

valence :: Tree d ~> Nat
{valence []tr} = 0t
{valence [head; tail]tr} = {plus {valence head} {valence tail}}
{valence ()tr} = 1t

-- counting siblings of a tree

nodeValence :: Tree d ~> Nat
{nodeValence []tr} = 0t
{nodeValence [head; tail]tr} = (1+{nodeValence tail})t

-- counting nodes in a tree

nodes :: Tree d ~> Nat
{nodes ()tr} = t
{nodes []tr} = 1t
{nodes [head; tail]tr} = {plus {nodes head} {nodes tail}}

-- nodeValenceAt: given a (multi)pointer, determine the node valences at those positions
--               WHERE     IN
nodeValenceAt :: Tree d ~> Tree e ~> Nat
{nodeValenceAt ()tr tree} = {nodeValence tree}
{nodeValenceAt []tr []tr} = 0t
{nodeValenceAt [head'; tail']tr [head; tail]tr} = {plus {nodeValenceAt head' head} {nodeValenceAt tail' tail}}

-- a pointer is a valence-1 subtree of a tree
-- it is used to mark a unit in a tree where substitution will occur
--
prop Pointers :: Nat ~> Tree d ~> Tree e ~> * where
  Finger :: Pointers 1t ()tr ()tr
  Finished :: Pointers 0t []tr []tr
  ThisWay :: Pointers 1t head' head -> Pointers n tail' tail -> Pointers (1+n)t [head'; tail']tr [head; tail]tr
  ElseWhere :: Pointers n tail' tail -> Pointers n [[]tr; tail']tr [head; tail]tr

-- http://en.wikipedia.org/wiki/Grafting
--
-- graft WHAT      WHERE     IN
graft :: Tree d ~> Tree e ~> Tree f ~> Tree f
{graft what ()tr ()tr} = what
{graft what []tr tr} = tr
{graft what [head'; tail']tr [head; tail]tr} = [{graft what head' head}; {graft what tail' tail}]tr

-- extgraft: extend and graft
--
extgraft :: Tree what ~> Tree wher ~> Tree tree ~> Tree tree'
{extgraft what ()tr ()tr} = what
{extgraft what []tr ()tr} = ()tr
{extgraft what [head; tail]tr ()tr} = {extgrafthor what [head; tail]tr}
{extgraft what []tr []tr} = []tr
{extgraft what []tr [head; tail]tr} = [head; tail]tr
{extgraft what [head'; tail']tr [head; tail]tr} = [{extgraft what head' head}; {extgraft what tail' tail}]tr

-- helper:
extgrafthor :: Tree what ~> Tree Hor ~> Tree Hor
{extgrafthor what []tr} = []tr
{extgrafthor what [head; tail]tr} = [{extgraft what head ()tr}; {extgrafthor what tail}]tr

{- NOTE: we have an Omega bug here:

prompt> :norm {graft []tr ()tr ()tr}
Normalizes to:
  []tr

prompt> :kind []tr
[]tr :: Tree Hor  = []tr

prompt> :kind {graft []tr ()tr ()tr}
{graft []tr ()tr ()tr} :: Tree Ver  = {graft []tr ()tr ()tr}

... BUT: Hor /= Ver :-(
-}

-- substitution: replace a pointed node (of valence n) in a tree with an
-- other tree of (valence n) -- TODO

-- HERE IS A NICE RESEARCH QUESTION:
-- is it possible to "proof search" a Zoom?
-- i.e.
{-

class ZoomLike (int :: Tree) (out :: Tree) where
  zoom :: (Nodes int ~ Valence out) => Zoom int out

-}

prop Reference :: Tree Hor ~> * where
  Stop :: Reference []tr
  Up :: Reference tr -> Reference [tr]tr
 deriving Nat(d) -- de Bruijn index

prop Teleport :: Tree Hor ~> * where
  Gate :: Teleport [()tr]tr
  Tele :: Teleport tr -> Teleport [tr]tr
 deriving Nat(sk) -- skips

{-

0
|   |
1   L  (lambda node)
|   |
2   1  (how many skips)
 \ /
  o
  |
  B  (binds here)
  |

Encodes \x.xx

-}

r2 = 2d
t1 = 1sk

lamX_XX = addBinder $ [r2, t1]ar

prop BindsUp :: Nat ~> Tree Hor ~> * where
  LastSkip :: BindsUp 1t [()tr]tr
  MoreSkip :: Teleport tr -> BindsUp n tr -> BindsUp (1+n)t [tr]tr
  -- prove Application node
  HeadBindsUp :: Nat' n -> BindsUp (1+n)t head -> BindsUp n [head; tail]tr
  TailBindsUp :: BindsUp n [head; tail]tr -> BindsUp n [nonempty, head; tail]tr

-- TODO: make sure that something teleports here
addBinder :: BindsUp 1t tr => Tree' tr -> Tree' [tr]tr
addBinder term = [term]ar

testB :: BindsUp 0t [[[[]tr]tr]tr,[()tr]tr]tr -> Tree' [[[[]tr]tr]tr,[()tr]tr]tr
testB ev = [r2, 0sk]ar
testB' = testB (TailBindsUp (HeadBindsUp 0v (LastSkip)))

testC :: BindsUp 0t [[[[[]tr]tr]tr,[[()tr]tr]tr]tr]tr -> Tree' [[[[[]tr]tr]tr,[[()tr]tr]tr]tr]tr
testC ev = lamX_XX
testC' = testC (HeadBindsUp 0v (TailBindsUp (HeadBindsUp 1v (MoreSkip 0sk LastSkip))))

--TODO: prop Lambda :: Tree Hor ~> * where

{-
The slogan is: binder nodes do not count as result nodes:
 - just consider the next node upstream
 - incoming (external) cards, when identified to a binder do not count as inputs to application
 - incoming (external) cards, when identified to an (iterated) application become pattern matching (sigma).

In the end all identifications have a semantics (hopefully!), when the counting rules are ensured.

-}

-- Now some fun stuff

data LC :: Shape ~> (k ~> *) ~> * where
  Var :: tf a -> LC (Rf a) tf
  App :: LC fsh tf -> LC ash tf -> LC (fsh `Ap` ash) tf
  Lam :: tf a -> LC sh tf -> LC (Lm sh) tf
  LetRec :: tf a -> LC ish tf -> LC esh tf -> LC ((Lm esh) `Ap` ish) tf
 deriving syntax (lc) Applicative(Var, App, Lam, LetRec)

alamX_XX = (\x->x x)lc

kind Dict key value = Dempty | Dextend (Dict key value) key value deriving LeftRecord(dict)

-- Contexts map keys to some value
--
data Context :: (key ~> *) ~> (value ~> *) ~> Dict key value ~> * where
  Empty :: Context key value {}dict
  Extend :: Context key value dict -> key k -> value v -> Context key value {dict; k = v}dict
 deriving LeftRecord(ctx)

-- DeBruijn levels as keys
--
dictSize :: Dict key value ~> Nat
{dictSize {}dict} = 0t
{dictSize {pre; k = v}dict} = (1+{dictSize pre})t

data DeBruijnContext :: (value ~> *) ~> Dict Nat value ~> * where
  DeBruijnEmpty :: DeBruijnContext value {}dict
  DeBruijnExtend :: DeBruijnContext value dict -> value v -> DeBruijnContext value {dict; {dictSize dict} = v}dict
 deriving LeftList(dtx)

getDeBruijnIndex :: Dict key value ~> value ~> Nat ~> Nat
{getDeBruijnIndex {pre; k = v}dict v acc} = acc
{getDeBruijnIndex {pre; k = v'}dict v acc} = {getDeBruijnIndex pre v (1+acc)t}

lookUpDeBruijn :: DeBruijnContext Label dict -> Label l -> Nat' acc -> Maybe (Nat' {getDeBruijnIndex dict l acc})
lookUpDeBruijn []dtx _ _ = Nothing
lookUpDeBruijn [pre; known]dtx lab acc = case sameLabel known lab of
                                         R _ -> lookUpDeBruijn pre lab (1+acc)t
                                         L Eq -> Just acc

monad maybeM

l2n :: Shape ~> Shape
{l2n (Lm sh)} = Lm {l2n sh}
{l2n (Ap f a)} = Ap {l2n f} {l2n a}
{l2n (Rf t)} = Rf n -- getDeBruijnIndex!!! FIXME

toDeBruijn :: DeBruijnContext Label dict -> LC sh Label -> Maybe (LC {l2n sh} Nat')
toDeBruijn ctx (Var a) = do idx <- lookUpDeBruijn ctx a 0t
                            return $ Var idx
toDeBruijn ctx (Lam l a) = do a' <- toDeBruijn [ctx; l]dtx a
                              return $ Lam 0t a'
toDeBruijn ctx (App f a) = do f' <- toDeBruijn ctx f
                              a' <- toDeBruijn ctx a
                              return $ App f' a'

-- we should get a pair (Nat, Context) -- TODO
-- this is not good yet!
--
{-
toFullContext :: DeBruijnContext Nat' dict -> Shape' sh -> LC sh Nat' -> LC sh (Context Nat' Shape')
toFullContext ctx (Rf a') (Var a) = Var ctx
toFullContext ctx sh (Lam l a) = Lam ctx $ toFullContext [ctx; l]dtx a
toFullContext ctx sh (App f a) = App (toFullContext ctx f) (toFullContext ctx a)
-}

-- Let :: tf a -> LC tf -> LC tf -> LC tf -- not needed!
pattern Let n v exp = App (Lam n exp) v

-- fun with church encoding

true = (\t->\f->t)lc
--false = (\t f->f)lc -- BUG!
false = (\t->\f->f)lc

-- church 'if'
chif = (\v->\iftrue->\iffalse->v iftrue iffalse)lc

chtest = (chif true false true)lc -- will not do what you expect
--chtest' = ($chif $true $false $true)lc -- not ready yet!

chtest'' = (let { true = \t->\f->t
                ; false = \t->\f->f
                ; chif = \v->\iftrue->\iffalse -> v iftrue iffalse
                }
            in chif true false true)lc -- this still does not work :-(

letrecToLet :: LC sh k -> LC sh k
letrecToLet (App f a) = App (letrecToLet f) (letrecToLet a)
letrecToLet (v@Var _) = v
letrecToLet (l@Lam _ _) = l
letrecToLet (LetRec n v e) = App (Lam n e) v -- Let n v e -- Omega pattern bug???

l2l = letrecToLet (let a = a in a)lc

-- shapes

kind Shape = Lm Shape | Ap Shape Shape | Rf k

data Shape' :: Shape ~> * where
  Ref :: Nat' n -> Shape' (Rf n)
  Nam :: Label n -> Shape' (Rf n)
  Lm :: Shape' inner -> Shape' (Lm inner)
  Ap :: Shape' f -> Shape' a -> Shape' (f `Ap` a)

shape :: LC sh Nat' -> Shape' sh
shape (Var n) = Ref n
shape (Lam n e) = Lm $ shape e
shape (App f a) = shape f `Ap` shape a

{-
data Dictionary :: Dict a b ~> * where
  Funny :: Dictionary {}dict

context :: DeBruijnContext Nat' dict -> LC sh Nat' -> LC sh Dictionary
context ctx (Var n) = Var undefined
-}

-- abstractly interpret
-- this should be parameterized by a monad!

--interp :: Monad m -> LC (context tr) -> m (LC (context tr))


crossed: the pre-nopetope!

crossed: the pre-nopetope!

-- Modeling Opetopes
-- here is Eric's editor: http://sma.epfl.ch/~finster/opetope/opetope.html
--
-- Note: Kock et al. use a similar scheme, where
--          - dots    <-->   lines
--          - spheres <-->   dots
--          - lines disappear
--          -                spheres appear

-- Note: In Eric's new work (at IAS) there are no
--       dots any more, instead he uses 'output cards', so
--          - (output) cards   <-->  lines
--          - space between stacked cards <--> output cards
--          - lines disappear
--          -                (regular) cards appear

import "../tests/Nat.prg"

data Dir :: *2 where
  Hor :: Dir
  Ver :: Dir

-- define the Tree kind, a rose tree
-- note: we may need a two-level kind, since we need to track disjointness
--       of subtrees
-- todo: later we may want to have a label kind parameter too

data Tree :: Dir ~> *1 where
  Unit :: Tree Ver
  Ni :: Tree Hor
  Fork :: Tree d ~> Tree Hor ~> Tree Hor
 deriving syntax (tr) List(Ni, Fork) Unit(Unit)

-- make it singleton

data Tree' :: Tree d ~> * where
  In :: Tree' ()tr
  Fork :: Tree' head -> Tree' tail -> Tree' [head; tail]tr
  Done :: Tree' []tr
 deriving syntax (ar) List(Done, Fork) Unit(In) -- "arbre"
-- http://www.papoulipoesique.com/wp-content/uploads/2013/06/arbre.jpg

-- define a proposition for subtrees
-- to be checked: TakeHead must ensure that all the node is consumed

prop Subtree :: Tree d ~> Tree e ~> * where
  UnitSub :: Subtree ()tr tr
  BothNil :: Subtree []tr []tr
  TakeHead :: Subtree head head' -> Subtree tail tail' -> Subtree [head; tail]tr [head'; tail']tr

-- now we can stack cards (these are zooms in Kock et al. parlance)

data Stack :: Tree d ~> Tree e ~> * where
  Empty :: Corolla tr => Tree' tr -> Stack tr ()tr
  SubDone :: Stack ()tr []tr
  Subdivision :: Stack ()tr sub -> Stack tr rest -> Stack tr [sub; rest]tr
  Encompass :: Subtree consumed tr => Stack consumed prod -> Stack tr prod
  -- the following three grab a node (and possibly its offsprings) and incorporate it into a single card
  NodeDone :: Stack []tr [()tr]tr
  Pick :: {- EntireNode => -} Stack head prodhead -> Stack tail prodtail -> Stack [head; tail]tr [prodhead; prodtail]tr
  Exclude :: {- EntireNode => -} Stack tail prod -> Stack [()tr; tail]tr prod
  -- we need a way to sequence cards
  -- MultiCard :: ??? Disjoint a b 0 => Subtree a -> Subtree b -> Stack tr a [proda, prodb]tr

  On :: (Subtree tr' tr, Pointers 1t at out) => Stack tr' out' -> Stack tr out -> Tree' at -> Stack tr {graft out' at out}

-- it remains to define corollas

prop Corolla :: Tree d ~> * where
  None' :: Corolla []tr
  One' :: Corolla tail -> Corolla [()tr; tail]tr

--  o   --->  |
--  |         |

lolliCell :: Stack []tr ()tr
lolliCell = Empty Done

--  |         |
--  o   --->  |
--  |         |

dolliCell :: Stack [()tr]tr ()tr
dolliCell = Empty $ Fork In Done

--              |
--  [o]   --->  o
--   |          |

lolliFrame :: Stack []tr [()tr]tr
lolliFrame = Encompass NodeDone

--   |          |
--  [o]   --->  o
--   |          |

dolliFrame :: Stack [()tr]tr [()tr]tr
dolliFrame = Encompass (Exclude NodeDone)

--   |          |
--   |          o
-- [[o]]  --->  |
--   |          o
--   |          |

stacked :: Stack [()tr]tr [[()tr]tr]tr
stacked = (dolliFrame `On` dolliFrame) (In `Fork` Done)

--   |
--  [|]   --->  o
--   |          |

crossed :: Stack ()tr []tr
crossed = SubDone

--    |           o   |
-- | [o] |  --->   \ /
-- | [|] |          o
--    |             |

--cyclops :: Stack [()tr]tr [[]tr, ()tr]tr
--cyclops = Subdivision SubDone (Exclude NodeDone)

-- Stacking, Valence, Affine subtree, Substitute at an affine position

-- counting Units in a tree

valence :: Tree d ~> Nat
{valence []tr} = 0t
{valence [head; tail]tr} = {plus {valence head} {valence tail}}
{valence ()tr} = 1t

-- counting siblings of a tree

nodeValence :: Tree d ~> Nat
{nodeValence []tr} = 0t
{nodeValence [head; tail]tr} = (1+{nodeValence tail})t

-- nodeValenceAt: given a (multi)pointer, determine the node valences at those positions
--               WHERE     IN
nodeValenceAt :: Tree d ~> Tree e ~> Nat
{nodeValenceAt ()tr tree} = {nodeValence tree}
{nodeValenceAt []tr []tr} = 0t
{nodeValenceAt [head'; tail']tr [head; tail]tr} = {plus {nodeValenceAt head' head} {nodeValenceAt tail' tail}}

-- a pointer is a valence-1 subtree of a tree
-- it is used to mark a unit in a tree where substitution will occur
--
prop Pointers :: Nat ~> Tree d ~> Tree e ~> * where
  Finger :: Pointers 1t ()tr ()tr
  Finished :: Pointers 0t []tr []tr
  ThisWay :: Pointers 1t head' head -> Pointers n tail' tail -> Pointers (1+n)t [head'; tail']tr [head; tail]tr
  ElseWhere :: Pointers n tail' tail -> Pointers n [[]tr; tail']tr [head; tail]tr

-- http://en.wikipedia.org/wiki/Grafting
--
-- graft WHAT      WHERE     IN
graft :: Tree d ~> Tree e ~> Tree f ~> Tree f
{graft what ()tr ()tr} = what
{graft what []tr tr} = tr
{graft what [head'; tail']tr [head; tail]tr} = [{graft what head' head}; {graft what tail' tail}]tr

{- NOTE: we have an Omega bug here:

prompt> :norm {graft []tr ()tr ()tr}
Normalizes to:
  []tr

prompt> :kind []tr
[]tr :: Tree Hor  = []tr

prompt> :kind {graft []tr ()tr ()tr}
{graft []tr ()tr ()tr} :: Tree Ver  = {graft []tr ()tr ()tr}

... BUT: Hor /= Ver :-(
-}

-- substitution: replace a pointed node (of valence n) in a tree with an
-- other tree of (valence n) -- TODO

-- Modeling Opetopes
-- here is Eric's editor: http://sma.epfl.ch/~finster/opetope/opetope.html
--
-- Note: Kock et al. use a similar scheme, where
--          - dots    <-->   lines
--          - spheres <-->   dots
--          - lines disappear
--          -                spheres appear

-- Note: In Eric's new work (at IAS) there are no
--       dots any more, instead he uses 'output cards', so
--          - (output) cards   <-->  lines
--          - space between stacked cards <--> output cards
--          - lines disappear
--          -                (regular) cards appear

import "../tests/Nat.prg"

data Dir :: *2 where
  Hor :: Dir
  Ver :: Dir

-- define the Tree kind, a rose tree
-- note: we may need a two-level kind, since we need to track disjointness
--       of subtrees
-- todo: later we may want to have a label kind parameter too

data Tree :: Dir ~> *1 where
  Unit :: Tree Ver
  Ni :: Tree Hor
  Fork :: Tree d ~> Tree Hor ~> Tree Hor
 deriving syntax (tr) List(Ni, Fork) Unit(Unit)

-- make it singleton

data Tree' :: Tree d ~> * where
  In :: Tree' ()tr
  Fork :: Tree' head -> Tree' tail -> Tree' [head; tail]tr
  Done :: Tree' []tr
 deriving syntax (ar) List(Done, Fork) Unit(In) -- "arbre"
-- http://www.papoulipoesique.com/wp-content/uploads/2013/06/arbre.jpg

-- define a proposition for subtrees
-- to be checked: TakeHead must ensure that all the node is consumed

prop Subtree :: Tree d ~> Tree e ~> * where
  UnitSub :: Subtree ()tr tr
  BothNil :: Subtree []tr []tr
  TakeHead :: Subtree head head' -> Subtree tail tail' -> Subtree [head; tail]tr [head'; tail']tr

-- now we can stack cards (these are zooms in Kock et al. parlance)

data Stack :: Tree d ~> Tree e ~> * where
  Empty :: Corolla tr => Tree' tr -> Stack tr ()tr
  SubDone :: Stack ()tr []tr
  Subdivision :: Stack ()tr sub -> Stack tr rest -> Stack tr [sub; rest]tr
  Encompass :: Subtree consumed tr => Stack consumed prod -> Stack tr prod
  -- the following three grab a node (and possibly its offsprings) and incorporate it into a single card
  NodeDone :: Stack []tr [()tr]tr
  Pick :: {- EntireNode => -} Stack head prodhead -> Stack tail prodtail -> Stack [head; tail]tr [prodhead; prodtail]tr
  Exclude :: {- EntireNode => -} Stack tail prod -> Stack [()tr; tail]tr prod
  -- we need a way to sequence cards
  -- MultiCard :: ??? Disjoint a b 0 => Subtree a -> Subtree b -> Stack tr a [proda, prodb]tr

  On :: (Subtree tr' tr, Pointers 1t at out) => Stack tr' out' -> Stack tr out -> Tree' at -> Stack tr {graft out' at out}

-- it remains to define corollas

prop Corolla :: Tree d ~> * where
  None' :: Corolla []tr
  One' :: Corolla tail -> Corolla [()tr; tail]tr

--  o   --->  |
--  |         |

lolliCell :: Stack []tr ()tr
lolliCell = Empty Done

--  |         |
--  o   --->  |
--  |         |

dolliCell :: Stack [()tr]tr ()tr
dolliCell = Empty $ Fork In Done

--              |
--  [o]   --->  o
--   |          |

lolliFrame :: Stack []tr [()tr]tr
lolliFrame = Encompass NodeDone

--   |          |
--  [o]   --->  o
--   |          |

dolliFrame :: Stack [()tr]tr [()tr]tr
dolliFrame = Encompass (Exclude NodeDone)

--   |          |
--   |          o
-- [[o]]  --->  |
--   |          o
--   |          |

stacked :: Stack [()tr]tr [[()tr]tr]tr
stacked = (dolliFrame `On` dolliFrame) (In `Fork` Done)

--    |           o   |
-- | [o] |  --->   \ /
-- | [|] |          o
--    |             |

--cyclops :: Stack [()tr]tr [[]tr, ()tr]tr
--cyclops = Subdivision SubDone (Exclude NodeDone)

-- Stacking, Valence, Affine subtree, Substitute at an affine position

-- counting Units in a tree

valence :: Tree d ~> Nat
{valence []tr} = 0t
{valence [head; tail]tr} = {plus {valence head} {valence tail}}
{valence ()tr} = 1t

-- counting siblings of a tree

nodeValence :: Tree d ~> Nat
{nodeValence []tr} = 0t
{nodeValence [head; tail]tr} = (1+{nodeValence tail})t

-- nodeValenceAt: given a (multi)pointer, determine the node valences at those positions
--               WHERE     IN
nodeValenceAt :: Tree d ~> Tree e ~> Nat
{nodeValenceAt ()tr tree} = {nodeValence tree}
{nodeValenceAt []tr []tr} = 0t
{nodeValenceAt [head'; tail']tr [head; tail]tr} = {plus {nodeValenceAt head' head} {nodeValenceAt tail' tail}}

-- a pointer is a valence-1 subtree of a tree
-- it is used to mark a unit in a tree where substitution will occur
--
prop Pointers :: Nat ~> Tree d ~> Tree e ~> * where
  Finger :: Pointers 1t ()tr ()tr
  Finished :: Pointers 0t []tr []tr
  ThisWay :: Pointers 1t head' head -> Pointers n tail' tail -> Pointers (1+n)t [head'; tail']tr [head; tail]tr
  ElseWhere :: Pointers n tail' tail -> Pointers n [[]tr; tail']tr [head; tail]tr

-- http://en.wikipedia.org/wiki/Grafting
--
-- graft WHAT      WHERE     IN
graft :: Tree d ~> Tree e ~> Tree f ~> Tree f
{graft what ()tr ()tr} = what
{graft what []tr tr} = tr
{graft what [head'; tail']tr [head; tail]tr} = [{graft what head' head}; {graft what tail' tail}]tr

{- NOTE: we have an Omega bug here:

prompt> :norm {graft []tr ()tr ()tr}
Normalizes to:
  []tr

prompt> :kind []tr
[]tr :: Tree Hor  = []tr

prompt> :kind {graft []tr ()tr ()tr}
{graft []tr ()tr ()tr} :: Tree Ver  = {graft []tr ()tr ()tr}

... BUT: Hor /= Ver :-(
-}

-- substitution: replace a pointed node (of valence n) in a tree with an
-- other tree of (valence n) -- TODO


source/QtQuickWidgets: updated

source/QtQuickWidgets: updated

Modified:
source/QtQuickWidgets/QQuickWidget.prg

/*

  Qt5xHb - Bindings libraries for Harbour/xHarbour and Qt Framework 5

  Copyright (C) 2018 Marcos Antonio Gambeta <marcosgambeta AT outlook DOT com>

*/

/*
  DO NOT EDIT THIS FILE - the content was created using a source code generator
*/

#include "hbclass.ch"

#ifndef QT5XHB_NO_REQUESTS
REQUEST QQMLCONTEXT
REQUEST QQMLENGINE
REQUEST QQMLERROR
REQUEST QQUICKITEM
REQUEST QSIZE
REQUEST QSURFACEFORMAT
REQUEST QURL
#endif

CLASS QQuickWidget INHERIT QWidget

   METHOD new
   METHOD delete
   METHOD source
   METHOD setSource
   METHOD engine
   METHOD rootContext
   METHOD rootObject
   METHOD resizeMode
   METHOD setResizeMode
   METHOD status
   METHOD errors
   METHOD sizeHint
   METHOD initialSize
   METHOD setContent
   METHOD format
   METHOD setFormat

   METHOD onStatusChanged
   METHOD onSceneGraphError

   DESTRUCTOR destroyObject

END CLASS

PROCEDURE destroyObject () CLASS QQuickWidget
   IF ::self_destruction
      ::delete()
   ENDIF
RETURN

#pragma BEGINDUMP

#include <Qt>

#ifndef __XHARBOUR__
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
#include <QQuickWidget>
#endif
#endif

#include "qt5xhb_common.h"
#include "qt5xhb_macros.h"
#include "qt5xhb_utils.h"

#ifdef __XHARBOUR__
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
#include <QQuickWidget>
#endif
#endif

#include <QQmlError>
#include <QQmlEngine>
#include <QQmlContext>
#include <QQuickItem>

/*
explicit QQuickWidget(QWidget *parent = 0)
*/
void QQuickWidget_new1 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( OPQWIDGET(1,0) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

/*
QQuickWidget(QQmlEngine* engine, QWidget *parent)
*/
void QQuickWidget_new2 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( PQQMLENGINE(1), PQWIDGET(2) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

/*
QQuickWidget(const QUrl &source, QWidget *parent = 0)
*/
void QQuickWidget_new3 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( *PQURL(1), OPQWIDGET(2,0) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

//[1]explicit QQuickWidget(QWidget *parent = 0)
//[2]QQuickWidget(QQmlEngine* engine, QWidget *parent)
//[3]QQuickWidget(const QUrl &source, QWidget *parent = 0)

HB_FUNC_STATIC( QQUICKWIDGET_NEW )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  if( ISBETWEEN(0,1) && ISOPTQWIDGET(1) )
  {
    QQuickWidget_new1();
  }
  else if( ISNUMPAR(2) && ISQQMLENGINE(1) && ISQWIDGET(2) )
  {
    QQuickWidget_new2();
  }
  else if( ISBETWEEN(1,2) && ISQURL(1) && ISOPTQWIDGET(2) )
  {
    QQuickWidget_new3();
  }
  else
  {
    hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
  }
#endif
}

HB_FUNC_STATIC( QQUICKWIDGET_DELETE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    delete obj;
    obj = NULL;
    PHB_ITEM self = hb_stackSelfItem();
    PHB_ITEM ptr = hb_itemPutPtr( NULL, NULL );
    hb_objSendMsg( self, "_pointer", 1, ptr );
    hb_itemRelease( ptr );
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QUrl source() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_SOURCE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QUrl * ptr = new QUrl( obj->source () );
      _qt5xhb_createReturnClass ( ptr, "QURL", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setSource(const QUrl&)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETSOURCE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISQURL(1) )
    {
      obj->setSource ( *PQURL(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QQmlEngine* engine() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ENGINE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQmlEngine * ptr = obj->engine ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQMLENGINE" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QQmlContext* rootContext() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ROOTCONTEXT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQmlContext * ptr = obj->rootContext ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQMLCONTEXT" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QQuickItem *rootObject() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ROOTOBJECT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQuickItem * ptr = obj->rootObject ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQUICKITEM" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
ResizeMode resizeMode() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_RESIZEMODE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      RENUM( obj->resizeMode () );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setResizeMode(ResizeMode)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETRESIZEMODE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISNUM(1) )
    {
      obj->setResizeMode ( (QQuickWidget::ResizeMode) hb_parni(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
Status status() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_STATUS )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      RENUM( obj->status () );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QList<QQmlError> errors() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ERRORS )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QList<QQmlError> list = obj->errors ();
      PHB_DYNS pDynSym = hb_dynsymFindName( "QQMLERROR" );
      PHB_ITEM pArray = hb_itemArrayNew(0);
      int i;
      for(i=0;i<list.count();i++)
      {
        if( pDynSym )
        {
          hb_vmPushDynSym( pDynSym );
          hb_vmPushNil();
          hb_vmDo( 0 );
          PHB_ITEM pObject = hb_itemNew( NULL );
          hb_itemCopy( pObject, hb_stackReturnItem() );
          PHB_ITEM pItem = hb_itemNew( NULL );
          hb_itemPutPtr( pItem, (QQmlError *) new QQmlError ( list[i] ) );
          hb_objSendMsg( pObject, "_POINTER", 1, pItem );
          hb_itemRelease( pItem );
          PHB_ITEM pDestroy = hb_itemNew( NULL );
          hb_itemPutL( pDestroy, true );
          hb_objSendMsg( pObject, "_SELF_DESTRUCTION", 1, pDestroy );
          hb_itemRelease( pDestroy );
          hb_arrayAddForward( pArray, pObject );
          hb_itemRelease( pObject );
        }
        else
        {
          hb_errRT_BASE( EG_NOFUNC, 1001, NULL, "QQMLERROR", HB_ERR_ARGS_BASEPARAMS );
        }
      }
      hb_itemReturnRelease(pArray);
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QSize sizeHint() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_SIZEHINT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSize * ptr = new QSize( obj->sizeHint () );
      _qt5xhb_createReturnClass ( ptr, "QSIZE", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QSize initialSize() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_INITIALSIZE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSize * ptr = new QSize( obj->initialSize () );
      _qt5xhb_createReturnClass ( ptr, "QSIZE", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setContent(const QUrl& url, QQmlComponent *component, QObject *item)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETCONTENT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(3) && ISQURL(1) && ISQQMLCOMPONENT(2) && ISQOBJECT(3) )
    {
      obj->setContent ( *PQURL(1), PQQMLCOMPONENT(2), PQOBJECT(3) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QSurfaceFormat format() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_FORMAT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSurfaceFormat * ptr = new QSurfaceFormat( obj->format () );
      _qt5xhb_createReturnClass ( ptr, "QSURFACEFORMAT", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setFormat(const QSurfaceFormat &format)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETFORMAT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISQSURFACEFORMAT(1) )
    {
      obj->setFormat ( *PQSURFACEFORMAT(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

void QQuickWidgetSlots_connect_signal ( const QString & signal, const QString & slot );

HB_FUNC_STATIC( QQUICKWIDGET_ONSTATUSCHANGED )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidgetSlots_connect_signal( "statusChanged(QQuickWidget::Status)", "statusChanged(QQuickWidget::Status)" );
#else
  hb_retl( false );
#endif
}

HB_FUNC_STATIC( QQUICKWIDGET_ONSCENEGRAPHERROR )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidgetSlots_connect_signal( "sceneGraphError(QQuickWindow::SceneGraphError,QString)", "sceneGraphError(QQuickWindow::SceneGraphError,QString)" );
#else
  hb_retl( false );
#endif
}

#pragma ENDDUMP

/*

  Qt5xHb - Bindings libraries for Harbour/xHarbour and Qt Framework 5

  Copyright (C) 2018 Marcos Antonio Gambeta <marcosgambeta AT outlook DOT com>

*/

/*
  DO NOT EDIT THIS FILE - the content was created using a source code generator
*/

#include "hbclass.ch"

#ifndef QT5XHB_NO_REQUESTS
REQUEST QURL
REQUEST QQMLENGINE
REQUEST QQMLCONTEXT
REQUEST QQUICKITEM
REQUEST QQMLERROR
REQUEST QSIZE
REQUEST QSURFACEFORMAT
#endif

CLASS QQuickWidget INHERIT QWidget

   METHOD new
   METHOD delete
   METHOD source
   METHOD setSource
   METHOD engine
   METHOD rootContext
   METHOD rootObject
   METHOD resizeMode
   METHOD setResizeMode
   METHOD status
   METHOD errors
   METHOD sizeHint
   METHOD initialSize
   METHOD setContent
   METHOD format
   METHOD setFormat

   METHOD onStatusChanged
   METHOD onSceneGraphError

   DESTRUCTOR destroyObject

END CLASS

PROCEDURE destroyObject () CLASS QQuickWidget
   IF ::self_destruction
      ::delete()
   ENDIF
RETURN

#pragma BEGINDUMP

#include <Qt>

#ifndef __XHARBOUR__
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
#include <QQuickWidget>
#endif
#endif

#include "qt5xhb_common.h"
#include "qt5xhb_macros.h"
#include "qt5xhb_utils.h"

#ifdef __XHARBOUR__
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
#include <QQuickWidget>
#endif
#endif

#include <QQmlError>
#include <QQmlEngine>
#include <QQmlContext>
#include <QQuickItem>

/*
explicit QQuickWidget(QWidget *parent = 0)
*/
void QQuickWidget_new1 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( OPQWIDGET(1,0) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

/*
QQuickWidget(QQmlEngine* engine, QWidget *parent)
*/
void QQuickWidget_new2 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( PQQMLENGINE(1), PQWIDGET(2) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

/*
QQuickWidget(const QUrl &source, QWidget *parent = 0)
*/
void QQuickWidget_new3 ()
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * o = new QQuickWidget ( *PQURL(1), OPQWIDGET(2,0) );
  _qt5xhb_returnNewObject( o, false );
#endif
}

//[1]explicit QQuickWidget(QWidget *parent = 0)
//[2]QQuickWidget(QQmlEngine* engine, QWidget *parent)
//[3]QQuickWidget(const QUrl &source, QWidget *parent = 0)

HB_FUNC_STATIC( QQUICKWIDGET_NEW )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  if( ISBETWEEN(0,1) && ISOPTQWIDGET(1) )
  {
    QQuickWidget_new1();
  }
  else if( ISNUMPAR(2) && ISQQMLENGINE(1) && ISQWIDGET(2) )
  {
    QQuickWidget_new2();
  }
  else if( ISBETWEEN(1,2) && ISQURL(1) && ISOPTQWIDGET(2) )
  {
    QQuickWidget_new3();
  }
  else
  {
    hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
  }
#endif
}

HB_FUNC_STATIC( QQUICKWIDGET_DELETE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    delete obj;
    obj = NULL;
    PHB_ITEM self = hb_stackSelfItem();
    PHB_ITEM ptr = hb_itemPutPtr( NULL, NULL );
    hb_objSendMsg( self, "_pointer", 1, ptr );
    hb_itemRelease( ptr );
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QUrl source() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_SOURCE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QUrl * ptr = new QUrl( obj->source () );
      _qt5xhb_createReturnClass ( ptr, "QURL", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setSource(const QUrl&)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETSOURCE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISQURL(1) )
    {
      obj->setSource ( *PQURL(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QQmlEngine* engine() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ENGINE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQmlEngine * ptr = obj->engine ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQMLENGINE" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QQmlContext* rootContext() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ROOTCONTEXT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQmlContext * ptr = obj->rootContext ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQMLCONTEXT" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QQuickItem *rootObject() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ROOTOBJECT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QQuickItem * ptr = obj->rootObject ();
      _qt5xhb_createReturnQObjectClass ( ptr, "QQUICKITEM" );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
ResizeMode resizeMode() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_RESIZEMODE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      RENUM( obj->resizeMode () );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setResizeMode(ResizeMode)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETRESIZEMODE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISNUM(1) )
    {
      obj->setResizeMode ( (QQuickWidget::ResizeMode) hb_parni(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
Status status() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_STATUS )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      RENUM( obj->status () );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QList<QQmlError> errors() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_ERRORS )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QList<QQmlError> list = obj->errors ();
      PHB_DYNS pDynSym = hb_dynsymFindName( "QQMLERROR" );
      PHB_ITEM pArray = hb_itemArrayNew(0);
      int i;
      for(i=0;i<list.count();i++)
      {
        if( pDynSym )
        {
          hb_vmPushDynSym( pDynSym );
          hb_vmPushNil();
          hb_vmDo( 0 );
          PHB_ITEM pObject = hb_itemNew( NULL );
          hb_itemCopy( pObject, hb_stackReturnItem() );
          PHB_ITEM pItem = hb_itemNew( NULL );
          hb_itemPutPtr( pItem, (QQmlError *) new QQmlError ( list[i] ) );
          hb_objSendMsg( pObject, "_POINTER", 1, pItem );
          hb_itemRelease( pItem );
          PHB_ITEM pDestroy = hb_itemNew( NULL );
          hb_itemPutL( pDestroy, true );
          hb_objSendMsg( pObject, "_SELF_DESTRUCTION", 1, pDestroy );
          hb_itemRelease( pDestroy );
          hb_arrayAddForward( pArray, pObject );
          hb_itemRelease( pObject );
        }
        else
        {
          hb_errRT_BASE( EG_NOFUNC, 1001, NULL, "QQMLERROR", HB_ERR_ARGS_BASEPARAMS );
        }
      }
      hb_itemReturnRelease(pArray);
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QSize sizeHint() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_SIZEHINT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSize * ptr = new QSize( obj->sizeHint () );
      _qt5xhb_createReturnClass ( ptr, "QSIZE", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
QSize initialSize() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_INITIALSIZE )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSize * ptr = new QSize( obj->initialSize () );
      _qt5xhb_createReturnClass ( ptr, "QSIZE", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setContent(const QUrl& url, QQmlComponent *component, QObject *item)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETCONTENT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(3) && ISQURL(1) && ISQQMLCOMPONENT(2) && ISQOBJECT(3) )
    {
      obj->setContent ( *PQURL(1), PQQMLCOMPONENT(2), PQOBJECT(3) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

/*
QSurfaceFormat format() const
*/
HB_FUNC_STATIC( QQUICKWIDGET_FORMAT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(0) )
    {
      QSurfaceFormat * ptr = new QSurfaceFormat( obj->format () );
      _qt5xhb_createReturnClass ( ptr, "QSURFACEFORMAT", true );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }
#endif
}

/*
void setFormat(const QSurfaceFormat &format)
*/
HB_FUNC_STATIC( QQUICKWIDGET_SETFORMAT )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidget * obj = (QQuickWidget *) _qt5xhb_itemGetPtrStackSelfItem();

  if( obj )
  {
    if( ISNUMPAR(1) && ISQSURFACEFORMAT(1) )
    {
      obj->setFormat ( *PQSURFACEFORMAT(1) );
    }
    else
    {
      hb_errRT_BASE( EG_ARG, 3012, NULL, HB_ERR_FUNCNAME, HB_ERR_ARGS_BASEPARAMS );
    }
  }

  hb_itemReturn( hb_stackSelfItem() );
#endif
}

void QQuickWidgetSlots_connect_signal ( const QString & signal, const QString & slot );

HB_FUNC_STATIC( QQUICKWIDGET_ONSTATUSCHANGED )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidgetSlots_connect_signal( "statusChanged(QQuickWidget::Status)", "statusChanged(QQuickWidget::Status)" );
#else
  hb_retl( false );
#endif
}

HB_FUNC_STATIC( QQUICKWIDGET_ONSCENEGRAPHERROR )
{
#if (QT_VERSION >= QT_VERSION_CHECK(5,3,0))
  QQuickWidgetSlots_connect_signal( "sceneGraphError(QQuickWindow::SceneGraphError,QString)", "sceneGraphError(QQuickWindow::SceneGraphError,QString)" );
#else
  hb_retl( false );
#endif
}

#pragma ENDDUMP