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definition module graph
// $Id$
from StdOverloaded import ==
// A rule associating a replacement with a pattern
//:: Rule sym var
// A mapping from variables to nodes (unrooted)
:: Graph sym var
// A node, bearing the contents of a variable
:: Node sym var
:== (sym,[var])
/*
graph.lit - Unrooted graphs
===========================
Description
-----------
This script implements an abstract type for unrooted graphs and useful
functions to manipulate them.
------------------------------------------------------------
Interface
---------
Exported identifiers:
> %export
> compilegraph || Compile graph from list of node definitions
> emptygraph || The empty unrooted graph
> extgraph || Extend a graph with the image of a matching
> foldgraph || Fold up a graph
> graph || Unrooted graphs over functorspace * and nodespace **
> instance || Check whether second graph is instance of first
> instantiate || Matches a pattern in a graph, if possible
> movegraph || Move a graph to a new node domain
> nodecontents || Determine the contents of a node
> nodelist || Determine the preorder list of reachable nodes from a given node
> nodeset || Determine the reachable nodes from a given node
> overwritegraph || Overwrite a graph with a given graph
> paths || List of all paths in the graph
> printgraph || Prints a graph seen from given nodes
> prunegraph || Undefine the contents of a node
> redirectgraph || Redirects all references to nodes in a graph
> refcount || Determines the reference count function of a graph
> restrictgraph || Restricts the graph to certain defined nodes
> showgraph || Text representation of a graph
> updategraph || Update the contents of a node
Required types: none
------------------------------------------------------------
Includes
--------
> %include "basic.lit" || foldlr mapsnd showlist showpair
> %include "pfun.lit" || domres emptypfun extend overwrite pfun postcomp restrict showpfun total
------------------------------------------------------------
Implementation
--------------
> abstype graph * **
> with emptygraph :: graph * **
> updategraph :: ** -> (*,[**]) -> graph * ** -> graph * **
> prunegraph :: ** -> graph * ** -> graph * **
> restrictgraph :: [**] -> graph * ** -> graph * **
> redirectgraph :: (**->**) -> graph * ** -> graph * **
> overwritegraph :: graph * ** -> graph * ** -> graph * **
> showgraph :: (*->[char]) -> (**->[char]) -> graph * ** -> [char]
> nodecontents :: graph * ** -> ** -> (bool,(*,[**]))
> nodeset :: graph * ** -> [**] -> ([**],[**])
> movegraph :: (***->**) -> [***] -> graph * *** -> graph * **
> printgraph :: (*->[char]) -> (**->[char]) -> graph * ** -> [**] -> [[char]]
> refcount :: graph * ** -> [**] -> ** -> num
> graph * ** == pfun ** (*,[**])
> emptygraph = emptypfun
> updategraph = extend
> prunegraph = restrict
> restrictgraph = domres
> redirectgraph = postcomp.mapsnd.map
> overwritegraph = overwrite
> showgraph showfunc shownode = showpfun shownode (showpair showfunc (showlist shownode))
*/
// The empty graph.
emptygraph :: Graph .sym .var
// Assign a node to a variable in a graph.
updategraph :: .var (Node .sym .var) (Graph .sym .var) -> Graph .sym .var
// Unassign a variable in a graph, making it free.
prunegraph :: .var (Graph .sym .var) -> Graph .sym .var
// Restrict a graph to a given domain, i.e.
// make all variables free except those in the domain.
restrictgraph :: !.[var] .(Graph sym var) -> Graph sym var | == var
// Redirect references (node arguments) in a graph
// according to a redirection function
redirectgraph :: (.var->.var) !(Graph .sym .var) -> Graph .sym .var | == var
// Overwrite the variables in the second graph by their contents in the first.
// Keeps the contents of the second graph if free in the first.
overwritegraph :: !(Graph .sym .var) (Graph .sym .var) -> Graph .sym .var
// Movegraph moves a graph to a different variable domain
// Requires a list of bound variables in the graph
movegraph :: (var1->.var2) !.[var1] .(Graph sym var1) -> Graph sym .var2 | == var1
// Varcontents obtains the contents of a variable in a graph
// Returns a boolean determining if it's bound, and
// its contents if the boolean is True.
varcontents :: !(Graph .sym var) var -> (.Bool,Node .sym var) | == var
// Graphvars determines the top-level-bound and free variables in a graph,
// reachable from a given list of variables.
// No duplicates.
graphvars :: .(Graph sym var) !.[var] -> (.[var],.[var]) | == var
// Graphvarlist determines all top level variables in a graph,
// reachable from a given list of variables.
// No duplicates.
varlist :: .(Graph sym var) !.[var] -> .[var] | == var
// Cannot remember what this one does???
prefix :: .(Graph sym var) .[var] !.[var] -> .([var],[var]) | == var
// Do reference counting in a graph for the outer bindings.
// References from case branches are counted once only.
// Initial list of variables is counted too.
refcount :: .(Graph sym var) !.[var] -> (var -> Int) | == var
// Determine whether the second argument is an instance of the first,
// i.e. whether there is a structure preserving mapping from the first to the second.
// Free variables may be mapped to anything.
// Bound variables may not be mapped to free variables.
isinstance
:: (.Graph sym pvar,pvar)
(.Graph sym var,var)
-> Bool
| == sym
& == var
& == pvar
/*
> compilegraph :: [(**,(*,[**]))] -> graph * **
> compilegraph = foldr (uncurry updategraph) emptygraph
------------------------------------------------------------------------
> foldgraph
> :: (**->***->***) ->
> (**->***) ->
> (*->[***]->***) ->
> graph * ** ->
> [**] ->
> [***]
> foldgraph folddef foldref foldcont graph roots
> = foldedroots
> where count = refcount graph roots
> (unused,foldedroots) = foldlm fold ([],roots)
> fold (seen,node)
> = (seen,foldref node), if member seen node
> = (seen'',cond (def&count node>1) (folddef node folded) folded), otherwise
> where (seen'',folded)
> = (seen',foldcont sym foldedargs), if def
> = (node:seen,foldref node), otherwise
> (seen',foldedargs) = foldlm fold (node:seen,args)
> (def,(sym,args)) = nodecontents graph node
> paths :: graph * ** -> ** -> [[**]]
> paths graph node
> = paths' [] node []
> where paths' top node rest
> = rest, if member top node
> = top':cond def (foldr (paths' top') rest args) rest, otherwise
> where (def,(sym,args)) = nodecontents graph node
> top' = node:top
> extgraph :: graph * ** -> graph * *** -> [***] -> pfun *** ** -> graph * ** -> graph * **
> extgraph sgraph pattern pnodes matching graph
> = foldr addnode graph pnodes
> where addnode pnode
> = total id (postcomp addnode' matching) pnode, if fst (nodecontents pattern pnode)
> = id, otherwise
> addnode' snode
> = updategraph snode scont, if sdef
> = id, otherwise
>|| = error "extgraph: closed node mapped to open node", otherwise
> || Could have used id, but let's report error when there is one...
> where (sdef,scont) = nodecontents sgraph snode
*/
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