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
|
(*
* This module performs low-level flow insensitive points-to
* analysis for type-safe languages.
*)
structure PointsTo : POINTS_TO =
struct
datatype edgekind = PI | DOM | RAN | RECORD | MARK
structure C = CellsBasis
datatype cell =
LINK of cell ref
| SREF of C.cell * (edgekind * int * cell ref) list ref
| WREF of C.cell * (edgekind * int * cell ref) list ref
| SCELL of C.cell * (edgekind * int * cell ref) list ref
| WCELL of C.cell * (edgekind * int * cell ref) list ref
| TOP of {mutable:bool, id:C.cell, name:string}
(* a collapsed node *)
type region = cell ref
type edges = (edgekind * int * region) list
fun error msg = MLRiscErrorMsg.error("PointsTo",msg)
(* PI > DOM > RAN > RECORD *)
fun greaterKind(PI,_) = false
| greaterKind(DOM,PI) = false
| greaterKind(RAN,(PI | DOM)) = false
| greaterKind(RECORD,(PI | DOM | RAN)) = false
| greaterKind(MARK,(PI | DOM | RAN | RECORD)) = false
| greaterKind _ = true
fun less(k,i,k',i') = k=k' andalso i > i' orelse greaterKind(k,k')
val sort : (edgekind * int * region) list ->
(edgekind * int * region) list =
ListMergeSort.sort (fn ((k,i,_),(k',i',_)) => less(k,i,k',i'))
val newMem = ref(fn _ => error "newMem") : (unit -> C.cell) ref
fun reset f = newMem := f
fun newSRef() = ref(SREF(!newMem(),ref []))
fun newWRef() = ref(WREF(!newMem(),ref []))
fun newSCell() = ref(SCELL(!newMem(),ref []))
fun newWCell() = ref(WCELL(!newMem(),ref []))
fun newTop{name,mutable} =
ref(TOP{mutable=mutable, id= !newMem(), name=name})
fun find(ref(LINK x)) = find x
| find x = x
fun mut(ref(LINK x)) = mut x
| mut(r as ref(TOP{mutable=false, id, name})) =
(r := TOP{mutable=true, id=id, name=name})
| mut(r as ref(SCELL x)) = r := SREF x
| mut(r as ref(WCELL x)) = r := WREF x
| mut _ = ()
and weak(ref(LINK x)) = weak x
| weak(ref(TOP _)) = ()
| weak(r as ref(SCELL x)) = (r := WCELL x; mergePis x)
| weak(r as ref(SREF x)) = (r := WREF x; mergePis x)
| weak _ = ()
and mergePis(_,edges) =
let val x = newSCell()
fun merge([],es') = es'
| merge((PI,_,y)::es,es') = (unify(x,y); merge(es, es'))
| merge(e::es,es') = merge(es,e::es')
in edges := (PI,0,x)::merge(!edges, []) end
and getIth(k,i,ref(LINK x)) = getIth(k,i,x)
| getIth(k,i,r as ref(TOP _)) = r
| getIth(k,i,ref(SREF(_,edges))) = getIth'(k,i,edges)
| getIth(k,i,ref(WREF(_,edges))) = getIth'(k,i,edges)
| getIth(k,i,ref(SCELL(_,edges))) = getIth'(k,i,edges)
| getIth(k,i,ref(WCELL(_,edges))) = getIth'(k,i,edges)
and getIth'(k,i,edges) =
let fun search((k',i',x)::es) =
if k = k' andalso i = i' then find x else search es
| search [] =
let val x = newSCell()
in edges := (k,i,x) :: !edges; x end
in search(!edges) end
and unify(x,y) =
let val x = find x
val y = find y
fun linkImmut(edges,x,y) = (x := LINK y; collapseAll(!edges,y))
fun linkMut(edges,x,y) = (x := LINK y; mut y; collapseAll(!edges,y))
fun linky(ex,ey,x,y) = (x := LINK y; ey := unifyList(!ex,!ey))
fun linkx(ex,ey,x,y) = (y := LINK x; ex := unifyList(!ex,!ey))
fun linkWREF(ex,ey,id,x,y) =
let val ey = unifyList(!ex,!ey)
val n = WREF(id,ref ey)
in x := LINK y; y := n end
in if x = y then () else
case (!x,!y) of
(TOP{mutable=false,...},TOP{mutable=false, ...}) => (x := LINK y)
| (TOP _, TOP _) => (x := LINK y; mut y)
| (SREF(_,edges), TOP _) => linkMut(edges,x,y)
| (WREF(_,edges), TOP _) => linkMut(edges,x,y)
| (SCELL(_,edges), TOP _) => linkImmut(edges,x,y)
| (WCELL(_,edges), TOP _) => linkImmut(edges,x,y)
| (TOP _, SREF(_,edges)) => linkMut(edges,y,x)
| (TOP _, WREF(_,edges)) => linkMut(edges,y,x)
| (TOP _, SCELL(_,edges)) => linkImmut(edges,y,x)
| (TOP _, WCELL(_,edges)) => linkImmut(edges,y,x)
| (WREF(_,e1), WREF(_,e2)) => linky(e1,e2,x,y)
| (SREF(_,e1), WREF(_,e2)) => linky(e1,e2,x,y)
| (WCELL(_,e1),WREF(_,e2)) => linky(e1,e2,x,y)
| (SCELL(_,e1),WREF(_,e2)) => linky(e1,e2,x,y)
| (WREF(_,e1), SREF(_,e2)) => linkx(e1,e2,x,y)
| (SREF(_,e1), SREF(_,e2)) => linkx(e1,e2,x,y)
| (WCELL(_,e1),SREF(id,e2)) => linkWREF(e1,e2,id,x,y)
| (SCELL(_,e1),SREF(_,e2)) => linky(e1,e2,x,y)
| (WREF(_,e1), WCELL(_,e2)) => linkx(e1,e2,x,y)
| (SREF(_,e1), WCELL(id,e2)) => linkWREF(e1,e2,id,x,y)
| (WCELL(_,e1),WCELL(_,e2)) => linkx(e1,e2,x,y)
| (SCELL(_,e1),WCELL(_,e2)) => linky(e1,e2,x,y)
| (WREF(_,e1), SCELL(_,e2)) => linkx(e1,e2,x,y)
| (SREF(_,e1), SCELL(_,e2)) => linkx(e1,e2,x,y)
| (WCELL(_,e1),SCELL(_,e2)) => linkx(e1,e2,x,y)
| (SCELL(_,e1),SCELL(_,e2)) => linkx(e1,e2,x,y)
| _ => error "unify"
end
and collapseAll([],_) = ()
| collapseAll((_,_,x)::xs,y) = (unify(x,y); collapseAll(xs,y))
and unifyList(l1,l2) =
let fun merge([],l) = l
| merge(l,[]) = l
| merge(a as (c as (k,i,x))::u,b as (d as (k',i',y))::v) =
if k=k' andalso i=i' then (unify(x,y); c::merge(u,v))
else if less(k,i,k',i') then d::merge(a,v) else c::merge(u,b)
in merge(sort l1,sort l2) end
fun pi(x,i) = getIth(PI,i,x)
fun dom(x,i) = getIth(DOM,i,x)
fun ran(x,i) = getIth(RAN,i,x)
fun sub(x,i) = let val m = getIth(PI,i,x) in mut m; m end
fun offset(x,i) = (unify(x,newTop{mutable=false,name=""}); find x)
and unifyAll(x,[]) = ()
| unifyAll(x,(_,_,y)::l) = (unify(x,y); unifyAll(x,l))
fun mkHeader(NONE,es) = es
| mkHeader(SOME h,es) = (PI,~1,h)::es
fun mkAlloc(header, xs) =
let fun collect(_,[],l) = l
| collect(i,x::xs,l) = collect(i+1,xs,(PI,i,x)::l)
in (!newMem(), ref(mkHeader(header,collect(0,xs,[])))) end
fun mkRecord(header,xs) = ref(SCELL(mkAlloc(header, xs)))
fun mkRef(header,x) = ref(SREF(mkAlloc(header, [x])))
fun mkArray(header,xs) = ref(SREF(mkAlloc(header, xs)))
fun mkVector(header,xs) = ref(SCELL(mkAlloc(header, xs)))
fun mkLambda(xs) =
let fun collect(_,[],l) = l
| collect(i,x::xs,l) = collect(i+1,xs,(DOM,i,x)::l)
in ref(SCELL(!newMem(), ref(collect(0,xs,[])))) end
fun app(f,xs) =
let fun loop(_,[]) = ()
| loop(i,x::xs) = (unify(dom(f,i),x); loop(i+1,xs))
in loop(0,xs) end
fun ret(f,xs) =
let fun loop(_,[]) = ()
| loop(i,x::xs) = (unify(ran(f,i),x); loop(i+1,xs))
in loop(0,xs) end
fun strongUpdate(a,i,x) = unify(sub(a,i),x)
fun strongSubscript(a,i) = sub(a,i)
fun weakUpdate(a,x) =
let val elem = sub(a, 0)
in weak elem; unify(elem, x) end
fun weakSubscript(a) =
let val elem = sub(a, 0)
in weak elem; elem end
fun interfere(x,y) = find x = find y
val maxLevels = MLRiscControl.mkInt ("points-to-show-max-levels",
"max # of level to show in pointsTo")
val _ = maxLevels := 3
fun toString r = show(!r, !maxLevels)
and show(LINK x, lvl) = show(!x, lvl)
| show(SREF(id,es), lvl) = "sref"^C.toString id^edges(es, lvl)
| show(WREF(id,es), lvl) = "wref"^C.toString id^edges(es, lvl)
| show(SCELL(id,es), lvl) = "s"^C.toString id^edges(es, lvl)
| show(WCELL(id,es), lvl) = "w"^C.toString id^edges(es, lvl)
| show(TOP{name="",mutable=true,id,...}, _) = "var"^C.toString id
| show(TOP{name="",mutable=false,id,...}, _) = "const"^C.toString id
| show(TOP{name,...}, _) = name
and edges(es, ~1) = ""
| edges(es, lvl) =
let fun prInt i = if i < 0 then "-"^Int.toString(~i) else Int.toString i
fun add(a,"") = a
| add(a,b) = a^","^b
fun cnv((PI,i,x),s) = add(prInt i^"->"^show(!x, lvl-1),s)
| cnv(_,s) = s
in case foldr cnv "" (!es) of
"" => ""
| t => if lvl = 0 then "..." else "["^t^"]"
end
end
|
