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
|
implementation module trd
// $Id$
import rule
import graph
import basic
from general import --->
import StdEnv
/*
trd.lit - Type rule derivation
==============================
Description
-----------
This module defines the derivation of a type rule from a given rule.
------------------------------------------------------------
Interface
---------
Exported identifiers:
> %export
> ruletype || Derive a type rule from a rule
------------------------------------------------------------
Includes
--------
> %include "basic.lit"
> %include "pfun.lit"
> %include "graph.lit"
> %include "rule.lit"
Naming conventions:
* - symbol (sym)
** - node (node)
*** - type symbol (tsym)
**** - type node in type rule to build (tnode)
***** - type node in given type rules (trnode)
------------------------------------------------------------
Implementation
--------------
`Ruletype' determines the type of a rule.
First, for every closed node, its type rule is copied into a global
(initially unconnected) type graph, and for every open node, a distinct
type node is allocated in the same type graph. Then for every closed
node n and argument n-i, the result type of n-i is unified with the i-th
argument type of n.
> ruletype
> :: [****] ->
> ((*,[**])->rule *** *****) ->
> rule * ** ->
> rule *** ****
> ruletype theap typerule rule
> = foldr (buildtype typerule graph) bcont nodes theap emptygraph []
> where args = lhs rule; root = rhs rule; graph = rulegraph rule
> nodes = nodelist graph (root:args)
> bcont theap tgraph assignment
> = foldr sharepair spcont pairs id tgraph assignment
> where pairs = mkpairs assignment
> spcont redirection tgraph assignment
> = mkrule (map lookup args) (lookup root) tgraph
> where lookup = redirection.foldmap id notype assignment
> notype = error "ruletype: no type node assigned to node"
*/
ruletype
:: .[tvar]
((Node sym var) -> Rule tsym trvar)
(Rule sym var)
-> .Rule tsym tvar
| == var
& == tsym
& == tvar
& == trvar
ruletype theap typerule rule
= foldr (buildtype typerule graph) bcont nodes theap emptygraph []
where args = arguments rule
root = ruleroot rule
graph = rulegraph rule
nodes = varlist graph [root:args]
bcont theap tgraph assignment
= foldr sharepair spcont pairs id tgraph assignment
where pairs = mkpairs assignment
spcont redirection tgraph assignment
= mkrule (map lookup args) (lookup root) tgraph
where lookup = redirection o (foldmap id notype assignment)
notype = abort "ruletype: no type node assigned to node"
/*
`Buildtype' builds the part of the global type graph corresponding to a
node. For a closed node, the type rule is copied; for an open node, a
single type node is allocated. Track is kept of which type nodes have
been assigned to the node and its arguments.
*/
buildtype
:: .((Node sym var) -> Rule tsym trvar) // Assignement of type rules to symbols
.(Graph sym var) // Graph to which to apply typing
var // ???
.([tvar] -> .(u:(Graph tsym tvar) -> .(v:[w:(var,tvar)] -> .result))) // Continuation
.[tvar] // Type heap
u:(Graph tsym tvar) // Type graph build so far
x:[y:(var,tvar)] // Assignment of type variables to variables
-> .result // Final result
| == var
& == trvar
, [x<=v,v y<=w,x<=y]
buildtype typerule graph node bcont theap tgraph assignment
| def
= bcont theap` tgraph` assignment`
= bcont (tl theap) tgraph [(node,hd theap):assignment]
where (def,cont) = varcontents graph node
(_,args) = cont
trule = typerule cont
trargs = arguments trule; trroot = ruleroot trule; trgraph = rulegraph trule
trnodes = varlist trgraph [trroot:trargs]
(tnodes,theap`) = (claim--->"basic.claim begins from trd.buildtype") trnodes theap
matching = zip2 trnodes tnodes
tgraph` = foldr addnode tgraph matching
addnode (trnode,tnode)
| trdef
= updategraph tnode (mapsnd (map match) trcont)
= id
where (trdef,trcont) = varcontents trgraph trnode
match = foldmap id nomatch matching
nomatch = abort "buildtype: no match from type rule node to type node"
assignment` = zip2 [node:args] (map match [trroot:trargs])++assignment
sharepair
:: (.var,.var) // Variables to share
w:((.var->var2) -> v:((Graph sym var2) -> .result)) // Continuation
(.var->var2) // Redirection
(Graph sym var2) // Graph before redirection
-> .result // Final result
| == sym
& == var2
, [v<=w]
sharepair lrnode spcont redirection graph
= share (mappair redirection redirection lrnode) spcont redirection graph
/*
`Share' shares two nodes in a graph by redirecting all references from
one to the other, and sharing the arguments recursively. The resulting
redirection function is also returned.
*/
/*
share ::
(var,var) // Variables to share
((var->var) (Graph sym var) -> result) // Continuation
(var->var) // Redirection
(Graph sym var) // Graph before redirection
-> result | == sym & == var // Final result
*/
share lrnode scont redirect graph
| lnode==rnode
= scont redirect graph
| ldef && rdef
= foldr share scont lrargs redirect` graph`
= scont redirect` graph`
where (lnode,rnode) = lrnode
(ldef,(lsym,largs)) = varcontents graph lnode
(rdef,(rsym,rargs)) = varcontents graph rnode
lrargs
| lsym<>rsym
= abort "share: incompatible symbols"
| not (eqlen largs rargs)
= abort "share: incompatible arities"
= zip2 (redargs largs) (redargs rargs)
redargs = map adjustone
redirect` = adjustone o redirect
adjustone
| ldef
= adjust rnode lnode id
= adjust lnode rnode id
graph` = redirectgraph adjustone graph
/*
mkpairs :: [(var1,var2)] -> [(var2,var2)] | == var1
*/
mkpairs pairs
= f (map snd (partition fst snd pairs))
where f [[x1,x2:xs]:xss] = [(x1,x2):f [[x2:xs]:xss]]
f [xs:xss] = f xss
f [] = []
|
