1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
|
definition module graph
// $Id$
from pfun import Pfun
from StdOverloaded import ==
from cleanversion import String
from StdString import toString
// 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
// 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
// Determine a multiline representation of a graph with multiple roots
printgraph :: .(Graph sym var) .[var] -> .[String] | toString sym & toString var & == var
printgraphBy :: (sym->String) (var->String) .(Graph sym var) .[var] -> .[String] | == 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
*/
compilegraph :: ![(var,Node sym var)] -> Graph sym var
/*
------------------------------------------------------------------------
> 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
*/
extgraph :: (Graph sym var) (Graph sym pvar) [pvar] (Pfun pvar var) (Graph sym var) -> Graph sym var | == var & == pvar
instance == (Graph sym var) | == sym & == var
instantiate ::
(Graph sym pvar,Graph sym var)
(pvar,var)
([(pvar,var)],[(pvar,var)],[(pvar,var)])
-> ([(pvar,var)],[(pvar,var)],[(pvar,var)])
| == sym
& == var
& == pvar
|
