Fix problem with Project Dependencies that are defined before the project is used.

//
// Copyright (c) XSharp B.V.  All Rights Reserved.
// Licensed under the Apache License, Version 2.0.
// See License.txt in the project root for license information.
//

USING System.Collections.Generic
USING System.Xml

CLASS SolutionConverter
	PROTECT cSource   AS STRING
	PROTECT cTarget   AS STRING
	PROTECT aGuids	  AS Dictionary<STRING, STRING>
	PROTECT aFiles    AS List<STRING>
    PROTECT aOthers   AS List<STRING>
	PROTECT cPath	  AS STRING
	PROTECT oProgress AS IProgress
    protect lAdjustReferences as LOGIC
	PROPERTY Target AS STRING GET cTarget
	PROPERTY Source AS STRING GET cSource
	CONSTRUCTOR(cName AS STRING, loProgress AS IProgress, lAdjust as LOGIC)
		cSource := cName
		cPath     := System.IO.Path.GetDirectoryName(cSource)
		IF ! cPath:EndsWith("\")
			cPath += "\"
		ENDIF
		cTarget := cPath+System.IO.Path.GetFileNameWithoutExtension(cSource)+"-XS.SLN"
		aFiles := List<STRING> {}
        aOthers:= List<STRING> {}
		aGuids := Dictionary<STRING, STRING>{}
		oProgress := loProgress
        lAdjustReferences := lAdjust
	METHOD Start() AS LOGIC
		LOCAL oReader AS System.IO.TextReader
		LOCAL oWriter AS System.IO.TextWriter
		LOCAL lChanged := FALSE AS LOGIC
		oProgress:WriteLine("Processing..."+cSource)
		oReader := System.IO.StreamReader{cSource}
		oWriter := System.IO.StreamWriter{cTarget}
		DO WHILE oReader:Peek() >= 0
			LOCAL cLine AS STRING
			cLine := oReader:ReadLine()
			IF cLine:Trim():StartsWith("Project(", StringComparison.OrdinalIgnoreCase)
                // VULCANGUID == {5891B814-A2E0-4E64-9A2F-2C2ECAB940FE}
				// Project
				// Line looks like this:
				// Project("VULCANGUID") = "Name", "Filename.vnproj", "PROJECTGUID"
				// We can split the line based on the double quote
				// then we get
				// a[1] = Project(
				// a[2] = VULCANGUID
				// a[3] = ) =
				// a[4] = Name
				// a[5] = ,
				// a[6] = Filename.vnproj
				// a[7] = ,
				// a[8] = PROJECTGUID
				// a[9] = <empty>
				// We can then convert the vnproj file and change it to xsproj
				// and replace VULCANGUID with XSHUID
				// RelativePath with changed extension
				// ProjectGUID with new GUID
				LOCAL aElements AS STRING[]
				aElements := cLine:Split(e"\"":ToCharArray(), StringSplitOptions.None)
    			IF aElements:Length == 9
    				IF aElements[2]:ToUpper() == "{5891B814-A2E0-4E64-9A2F-2C2ECAB940FE}"
						LOCAL cNewFile AS STRING
						LOCAL oPrjConverter AS ProjectConverter
						oPrjConverter := ProjectConverter{oProgress}
						aElements[2] := "{AA6C8D78-22FF-423A-9C7C-5F2393824E04}"	// XS Guid
						cNewFile := System.IO.Path.ChangeExtension(aElements[6], "."+EXTENSION)
						oPrjConverter:ConvertProjectFile(cPath+aElements[6], cPath+cNewFile)
						aFiles:Add(cPath+cNewFile)
                        // add old file to the list too
                        IF SELF:lAdjustReferences
                            VAR cOldFile := System.IO.Path.GetFilename(aElements[6])
						    IF ! aGuids:ContainsKey(cOldFile)
							    aGuids:Add(cOldFile,System.IO.Path.GetFilename(cNewFile))
						    ENDIF
                        ENDIF
						aElements[6] := cNewFile
						IF ! aGuids:ContainsKey(aElements[8])
							aGuids:Add(aElements[8], oPrjConverter:Guid)
						ENDIF
						aElements[8] := oPrjConverter:Guid

						cLine := ""
						FOREACH VAR cElement IN aElements
							IF !String.IsNullOrEmpty(cLine)
								cLine += e"\""
							ENDIF
							cLine += cElement
						NEXT
                    ELSE
                        aOthers:Add(cPath+aElements[6])
				    ENDIF
				ELSE
					// Something wrong
					oProgress:WriteLine( "Incorrect line in Solution: "+ cLine)
				ENDIF
			ELSE
				FOREACH VAR item IN aGuids
                    lChanged := FALSE
                    cLine := Replace(cLine , Item:Key, Item:Value, ref lChanged)
				NEXT
			ENDIF
			oWriter:WriteLine(cLine)
		ENDDO
		oReader:Close()
		oWriter:Close()
		// Now read the file again and replace all 'forward' references
		VAR sContents := System.IO.File.ReadAllText(cTarget)
		FOREACH VAR sItem IN aGuids
            sContents := Replace(sContents, sItem:Key, sItem:Value, ref lChanged)
		NEXT
		if lChanged
			System.IO.File.WriteAllText(cTarget, sContents)
		endif

		// Now update project references in all xsprj files
		FOREACH VAR sFile IN aFiles
			lChanged := FALSE
			if System.IO.File.Exists(sFile)
				sContents := System.IO.File.ReadAllText(sFile)
				FOREACH VAR sItem IN aGuids
                    sContents := Replace(sContents, sItem:Key, sItem:Value, ref lChanged)
				NEXT
				IF lChanged
					System.IO.File.WriteAllText(sFile, sContents)
				ENDIF
			ENDIF
		NEXT
        if self:lAdjustReferences
		    FOREACH VAR sFile IN aOthers
			    lChanged := FALSE
			    if System.IO.File.Exists(sFile)
				    sContents := System.IO.File.ReadAllText(sFile)
				    FOREACH VAR sItem IN aGuids
                        sContents := Replace(sContents, sItem:Key, sItem:Value, ref lChanged)
				    NEXT
				    IF lChanged
                        oProgress:WriteLine("Adjusted "+sFile)
                        System.IO.File.Copy(sFile, sFile+".BAK",true)
					    System.IO.File.WriteAllText(sFile, sContents)
				    ENDIF
			    ENDIF
		    NEXT
        endif
		RETURN TRUE

STATIC METHOD Convert(cFile AS STRING, oProgress AS IProgress, lAdjustReferences as LOGIC) AS VOID
	LOCAL oSolutionConverter AS SolutionConverter
	oSolutionConverter := SolutionConverter{cFile, oProgress, lAdjustReferences}
	IF oSolutionConverter:Start()
		oProgress:WriteLine( "Created " +oSolutionConverter:Target)
		oProgress:WriteLine( "Done")
	ELSE
		oProgress:WriteLine( "Error converting "+cFile)
	ENDIF

STATIC METHOD Replace(sSource as STRING, sKey as STRING, sValue as STRING, lChanged REF LOGIC) AS STRING
    sKey := sKey:ToLower()
    VAR pos := sSource:ToLower():IndexOf(sKey)
    DO WHILE pos >= 0
        VAR sLeft := sSource:Substring(0, pos)
        var sRight := sSource:Substring(pos+sKey:Length)
        sSource := sLeft + sValue+sRight
        lChanged := TRUE
        pos := sSource:ToLower():IndexOf(sKey)
    ENDDO
    RETURN sSource

END CLASS

//
// Copyright (c) XSharp B.V.  All Rights Reserved.
// Licensed under the Apache License, Version 2.0.
// See License.txt in the project root for license information.
//

USING System.Collections.Generic
USING System.Xml

CLASS SolutionConverter
	PROTECT cSource   AS STRING
	PROTECT cTarget   AS STRING
	PROTECT aGuids	  AS Dictionary<STRING, STRING>
	PROTECT aFiles    AS List<STRING>
    PROTECT aOthers   AS List<STRING>
	PROTECT cPath	  AS STRING
	PROTECT oProgress AS IProgress
    protect lAdjustReferences as LOGIC
	PROPERTY Target AS STRING GET cTarget
	PROPERTY Source AS STRING GET cSource
	CONSTRUCTOR(cName AS STRING, loProgress AS IProgress, lAdjust as LOGIC)
		cSource := cName
		cPath     := System.IO.Path.GetDirectoryName(cSource)
		IF ! cPath:EndsWith("\")
			cPath += "\"
		ENDIF
		cTarget := cPath+System.IO.Path.GetFileNameWithoutExtension(cSource)+"-XS.SLN"
		aFiles := List<STRING> {}
        aOthers:= List<STRING> {}
		aGuids := Dictionary<STRING, STRING>{}
		oProgress := loProgress
        lAdjustReferences := lAdjust
	METHOD Start() AS LOGIC
		LOCAL oReader AS System.IO.TextReader
		LOCAL oWriter AS System.IO.TextWriter
		oProgress:WriteLine("Processing..."+cSource)
		oReader := System.IO.StreamReader{cSource}
		oWriter := System.IO.StreamWriter{cTarget}
		DO WHILE oReader:Peek() >= 0
			LOCAL cLine AS STRING
			cLine := oReader:ReadLine()
			IF cLine:Trim():StartsWith("Project(", StringComparison.OrdinalIgnoreCase)
                // VULCANGUID == {5891B814-A2E0-4E64-9A2F-2C2ECAB940FE}
				// Project
				// Line looks like this:
				// Project("VULCANGUID") = "Name", "Filename.vnproj", "PROJECTGUID"
				// We can split the line based on the double quote
				// then we get
				// a[1] = Project(
				// a[2] = VULCANGUID
				// a[3] = ) =
				// a[4] = Name
				// a[5] = ,
				// a[6] = Filename.vnproj
				// a[7] = ,
				// a[8] = PROJECTGUID
				// a[9] = <empty>
				// We can then convert the vnproj file and change it to xsproj
				// and replace VULCANGUID with XSHUID
				// RelativePath with changed extension
				// ProjectGUID with new GUID
				LOCAL aElements AS STRING[]
				aElements := cLine:Split(e"\"":ToCharArray(), StringSplitOptions.None)
    			IF aElements:Length == 9
    				IF aElements[2]:ToUpper() == "{5891B814-A2E0-4E64-9A2F-2C2ECAB940FE}"
						LOCAL cNewFile AS STRING
						LOCAL oPrjConverter AS ProjectConverter
						oPrjConverter := ProjectConverter{oProgress}
						aElements[2] := "{AA6C8D78-22FF-423A-9C7C-5F2393824E04}"	// XS Guid
						cNewFile := System.IO.Path.ChangeExtension(aElements[6], "."+EXTENSION)
						oPrjConverter:ConvertProjectFile(cPath+aElements[6], cPath+cNewFile)
						aFiles:Add(cPath+cNewFile)
                        // add old file to the list too
                        IF SELF:lAdjustReferences
                            VAR cOldFile := System.IO.Path.GetFilename(aElements[6])
						    IF ! aGuids:ContainsKey(cOldFile)
							    aGuids:Add(cOldFile,System.IO.Path.GetFilename(cNewFile))
						    ENDIF
                        ENDIF
						aElements[6] := cNewFile
						IF ! aGuids:ContainsKey(aElements[8])
							aGuids:Add(aElements[8], oPrjConverter:Guid)
						ENDIF
						aElements[8] := oPrjConverter:Guid

						cLine := ""
						FOREACH VAR cElement IN aElements
							IF !String.IsNullOrEmpty(cLine)
								cLine += e"\""
							ENDIF
							cLine += cElement
						NEXT
                    ELSE
                        aOthers:Add(cPath+aElements[6])
				    ENDIF
				ELSE
					// Something wrong
					oProgress:WriteLine( "Incorrect line in Solution: "+ cLine)
				ENDIF
			ELSE
				FOREACH VAR item IN aGuids
                    local lChanged := FALSE as LOGIC
                    cLine := Replace(cLine , Item:Key, Item:Value, ref lChanged)
				NEXT
			ENDIF
			oWriter:WriteLine(cLine)
		ENDDO
		oReader:Close()
		oWriter:Close()
		// Now update project references in all xsprj files
		FOREACH VAR sFile IN aFiles
			LOCAL sContents AS STRING
			LOCAL lChanged := FALSE AS LOGIC
			if System.IO.File.Exists(sFile)
				sContents := System.IO.File.ReadAllText(sFile)
				FOREACH VAR sItem IN aGuids
                    sContents := Replace(sContents, sItem:Key, sItem:Value, ref lChanged)
				NEXT
				IF lChanged
					System.IO.File.WriteAllText(sFile, sContents)
				ENDIF
			ENDIF
		NEXT
        if self:lAdjustReferences
		    FOREACH VAR sFile IN aOthers
			    LOCAL sContents AS STRING
			    LOCAL lChanged := FALSE AS LOGIC
			    if System.IO.File.Exists(sFile)
				    sContents := System.IO.File.ReadAllText(sFile)
				    FOREACH VAR sItem IN aGuids
                        sContents := Replace(sContents, sItem:Key, sItem:Value, ref lChanged)
				    NEXT
				    IF lChanged
                        oProgress:WriteLine("Adjusted "+sFile)
                        System.IO.File.Copy(sFile, sFile+".BAK",true)
					    System.IO.File.WriteAllText(sFile, sContents)
				    ENDIF
			    ENDIF
		    NEXT
        endif
		RETURN TRUE

STATIC METHOD Convert(cFile AS STRING, oProgress AS IProgress, lAdjustReferences as LOGIC) AS VOID
	LOCAL oSolutionConverter AS SolutionConverter
	oSolutionConverter := SolutionConverter{cFile, oProgress, lAdjustReferences}
	IF oSolutionConverter:Start()
		oProgress:WriteLine( "Created " +oSolutionConverter:Target)
		oProgress:WriteLine( "Done")
	ELSE
		oProgress:WriteLine( "Error converting "+cFile)
	ENDIF

STATIC METHOD Replace(sSource as STRING, sKey as STRING, sValue as STRING, lChanged REF LOGIC) AS STRING
    sKey := sKey:ToLower()
    VAR pos := sSource:ToLower():IndexOf(sKey)
    DO WHILE pos >= 0
        VAR sLeft := sSource:Substring(0, pos)
        var sRight := sSource:Substring(pos+sKey:Length)
        sSource := sLeft + sValue+sRight
        lChanged := TRUE
        pos := sSource:ToLower():IndexOf(sKey)
    ENDDO
    RETURN sSource

END CLASS


add contexts

add contexts

-- 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 "../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 :: (k ~> *) ~> * where
  Var :: tf a -> LC tf
  App :: LC tf -> LC tf -> LC tf
  Lam :: tf a -> LC tf -> LC tf
  LetRec :: tf a -> LC tf -> LC tf -> LC 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)

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

data DeBrujnContext :: (value ~> *) ~> Dict Nat value ~> * where
  DeBrujnEmpty :: DeBrujnContext value {}dict
  DeBrujnExtend :: DeBrujnContext value dict -> value v -> DeBrujnContext value {dict; {dictSize dict} = v}dict
 deriving LeftList(dtx)