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
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
|
module FixpointSolver
open Ast
open AstUtils
open Resolver
open Utils
/////////////
type UnifDirection = LTR | RTL
exception CannotUnify
let rec SelectiveUnifyImplies okToUnifyFunc lhs rhs dir unifs =
///
let __AddOrNone unifs name e =
if okToUnifyFunc name then
Some(unifs |> Utils.MapAddNew name e)
else
None
///
let __UnifLists lstL lstR =
if List.length lstL = List.length lstR then
try
let unifs2 = List.fold2 (fun acc elL elR -> match SelectiveUnifyImplies okToUnifyFunc elL elR dir acc with
| Some(u) -> u
| None -> raise CannotUnify) unifs lstL lstR
Some(unifs2)
with
| CannotUnify -> None
else
None
///
let __ApplyUnifs unifs exprList =
exprList |> List.fold (fun acc e ->
let e' = e |> Rewrite (fun e ->
match e with
| VarLiteral(id) when Map.containsKey id unifs -> Some(unifs |> Map.find id)
| _ -> None)
acc |> Set.add e'
) Set.empty
if lhs = FalseLiteral || rhs = TrueLiteral then
Some(unifs)
else
try
let l,r = match dir with
| LTR -> lhs,rhs
| RTL -> rhs,lhs
match l, r with
| VarLiteral(vname), rhs -> __AddOrNone unifs vname rhs
| IntLiteral(nL), IntLiteral(nR) when nL = nR ->
Some(unifs)
| BoolLiteral(bL), BoolLiteral(bR) when bL = bR ->
Some(unifs)
| SetExpr(elistL), SetExpr(elistR) ->
let s1 = elistL |> __ApplyUnifs unifs
let s2 = elistR |> Set.ofList
if (s1 = s2) then
Some(unifs)
else
__UnifLists elistL elistR
| SequenceExpr(elistL), SequenceExpr(elistR) when List.length elistL = List.length elistR ->
__UnifLists elistL elistR
| _ when l = r ->
Some(unifs)
| _ ->
let __TryUnifyPair x1 a1 x2 a2 unifs =
let builder = new Utils.CascadingBuilder<_>(None)
builder {
let! unifsLhs = SelectiveUnifyImplies okToUnifyFunc x1 a1 dir unifs
let! unifsRhs = SelectiveUnifyImplies okToUnifyFunc x2 a2 dir unifsLhs
return Some(unifsRhs)
}
// target implies candidate!
let rec ___f2 consequence premise unifs =
match consequence, premise with
// same operators + commutative -> try both
| BinaryExpr(_, opT, lhsT, rhsT), BinaryExpr(_, opC, lhsC, rhsC) when opT = opC && IsCommutativeOp opT ->
match __TryUnifyPair lhsC lhsT rhsC rhsT unifs with
| Some(x) -> Some(x)
| None -> __TryUnifyPair lhsC rhsT rhsC lhsT unifs
// operators are the same
| BinaryExpr(_, opT, lhsT, rhsT), BinaryExpr(_, opC, lhsC, rhsC) when opC = opT ->
__TryUnifyPair lhsC lhsT rhsC rhsT unifs
// operators are exactly the invers of one another
| BinaryExpr(_, opT, lhsT, rhsT), BinaryExpr(_, opC, lhsC, rhsC) when AreInverseOps opC opT ->
__TryUnifyPair lhsC rhsT rhsC lhsT unifs
//
| BinaryExpr(_, opT, lhsT, rhsT), BinaryExpr(_, opC, lhsC, rhsC) when DoesImplyOp opC opT ->
__TryUnifyPair lhsC lhsT rhsC rhsT unifs
| UnaryExpr(opC, subC), UnaryExpr(opP, subP) when opC = opP ->
SelectiveUnifyImplies okToUnifyFunc subP subC dir unifs
| SelectExpr(lstC, idxC), SelectExpr(lstP, idxP) ->
__TryUnifyPair lstP lstC idxP idxC unifs
| SeqLength(lstC), SeqLength(lstP) ->
SelectiveUnifyImplies okToUnifyFunc lstP lstC dir unifs
| Dot(exprC, fldNameC), Dot(exprP, fldNameP) when fldNameC = fldNameP ->
SelectiveUnifyImplies okToUnifyFunc exprP exprC dir unifs
| _ -> None
let rec ___f1 targetLst candidateLst unifs =
match targetLst, candidateLst with
| targetExpr :: targetRest, candExpr :: candRest ->
// trying to find a unification for "targetExpr"
let uOpt = match ___f2 targetExpr candExpr unifs with
// found -> just return
| Some(unifs2) -> Some(unifs2)
// not found -> keep looking in the rest of the candidate expressions
| None -> ___f1 [targetExpr] candRest unifs
match uOpt with
// found -> try find for the rest of the target expressions
| Some(unifs2) -> ___f1 targetRest candidateLst unifs2
// not found -> fail
| None -> None
| targetExpr :: _, [] ->
// no more candidates for unification for this targetExpr -> fail
None
| [], _ ->
// we've found unifications for all target expressions -> return the current unifications map
Some(unifs)
let __HasSetExpr e = DescendExpr2 (fun ex acc -> if acc then true else match ex with SetExpr(_) -> true | _ -> false) e false
let __PreprocSplitSort e = e |> DesugarAndRemove |> DistributeNegation |> SplitIntoConjunts |> List.sortBy (fun e -> if __HasSetExpr e then 1 else 0)
let lhsConjs = lhs |> __PreprocSplitSort
let rhsConjs = rhs |> __PreprocSplitSort
___f1 rhsConjs lhsConjs unifs
with
| CannotUnify
| KeyAlreadyExists -> None
let UnifyImplies lhs rhs dir unifs = SelectiveUnifyImplies (fun e -> true) lhs rhs dir unifs
////////////////////////////////////////////
let rec ComputeClosure heapInst expandExprFunc premises =
let bogusExpr = VarLiteral("!@#$%^&*()")
let ApplyUnifs unifs expr =
Rewrite (function
| VarLiteral(id) when unifs |> Map.containsKey id ->
Some(unifs |> Map.find id)
| _ -> None
) expr
let FindMatches expr except premises =
let okToUnifyFunc = fun (varName: string) -> varName.StartsWith("$")
premises |> Set.toList
|> List.choose (function BinaryExpr(_,"=",lhs,rhs) ->
if lhs = expr && not (rhs = except) then
Some(rhs)
elif rhs = expr && not (lhs = except) then
Some(lhs)
else
match SelectiveUnifyImplies okToUnifyFunc lhs expr LTR Map.empty with
| Some(unifs) -> Some(ApplyUnifs unifs rhs)
| None ->
match SelectiveUnifyImplies okToUnifyFunc rhs expr LTR Map.empty with
| Some(unifs) -> Some(ApplyUnifs unifs lhs)
| None -> None
| _ -> None)
let MySetAdd expr set =
let x = Printer.PrintExpr 0 expr
if x.Contains("$") then
set
else
match expr with
| BinaryExpr(p,op,lhs,rhs) when IsCommutativeOp op && Set.contains (BinaryExpr(p,op,rhs,lhs)) set -> set
| BinaryExpr(p,op,lhs,rhs) when IsCommutativeOp op && rhs = lhs -> set
| _ -> Set.add expr set
let SelectExprCombinerFunc lst idx =
// distribute the indexing operation if possible
let rec __fff lst idx =
let selExpr = SelectExpr(lst, idx)
match lst with
| BinaryExpr(_,"+",lhs,rhs) ->
let idxVal = EvalFull heapInst idx |> Expr2Int
let lhsVal = EvalFull heapInst lhs |> Expr2List
let rhsVal = EvalFull heapInst rhs |> Expr2List
if idxVal < List.length lhsVal then
__fff lhs idx
else
__fff rhs (BinarySub idx (IntLiteral(List.length lhsVal)))
| SequenceExpr(elist) ->
let idxVal = EvalFull heapInst idx |> Expr2Int
[elist.[idxVal]]
| _ -> [selExpr]
__fff lst idx
let SeqLenCombinerFunc lst =
// distribute the SeqLength operation if possible
let rec __fff lst =
let lenExpr = SeqLength(lst)
match lst with
| BinaryExpr(_,"+",lhs,rhs) ->
BinaryAdd (__fff lhs) (__fff rhs)
| SequenceExpr(elist) ->
IntLiteral(List.length elist)
| _ -> lenExpr
[__fff lst]
let BinaryInCombiner lhs rhs =
// distribute the "in" operation if possible
let rec __fff lhs rhs =
let binInExpr = BinaryIn lhs rhs
match rhs with
| BinaryExpr(_,"+",BinaryExpr(_,"+",SetExpr(_), Dot(_)), Dot(_)) -> Logger.Trace ""
| _ -> ()//TODO: remove
match rhs with
| BinaryExpr(_,"+",l,r) ->
// let lhsVal = EvalFull heapInst lhs
// let lVal = EvalFull heapInst l
// let rVal = EvalFull heapInst r
// match lVal,rVal with
// | SequenceExpr(elist), _ | _, SequenceExpr(elist)
// | SetExpr(elist), _ | _, SetExpr(elist) ->
// if elist |> Utils.ListContains lhsVal then
// __fff lhs l
// else
// __fff lhs r
// | _ -> [binInExpr]
[BinaryOr (BinaryIn lhs l) (BinaryIn lhs r)]
| SequenceExpr(elist) ->
let len = elist |> List.length
if len = 0 then
[FalseLiteral]
elif len = 1 then
[BinaryEq lhs elist.[0]]
else
let lhsVal = EvalFull heapInst lhs
let lst0Val = EvalFull heapInst elist.[0]
if lhsVal = lst0Val then
[BinaryEq lhs elist.[0]]
else
[BinaryIn lhs (SequenceExpr(elist |> List.tail))]
| _ -> [binInExpr]
__fff lhs rhs
let BinaryNotInCombiner lhs rhs =
// distribute the "!in" operation if possible
let rec __fff lhs rhs =
let binNotInExpr = BinaryNotIn lhs rhs
match rhs with
| BinaryExpr(_,"+",l,r) ->
// let lhsVal = EvalFull heapInst lhs
// let lVal = EvalFull heapInst l
// let rVal = EvalFull heapInst r
// match lVal,rVal with
// | SequenceExpr(elistL), SequenceExpr(elistR)
// | SetExpr(elistL), SetExpr(elistR) ->
// (__fff lhs l) @
// (__fff lhs r)
// | _ -> [binNotInExpr]
__fff lhs l @ __fff lhs r
| SequenceExpr(elist) ->
let len = elist |> List.length
if len = 0 then
[TrueLiteral]
elif len = 1 then
[BinaryNeq lhs elist.[0]]
else
let lhsVal = EvalFull heapInst lhs
let lst0Val = EvalFull heapInst elist.[0]
[BinaryNeq lhs elist.[0]] @
[BinaryNotIn lhs (SequenceExpr(elist |> List.tail))]
| _ -> [binNotInExpr]
__fff lhs rhs
let rec __CombineAllMatches expr premises =
let lst0 = FindMatches expr bogusExpr premises
let lstCombined =
match expr with
| BinaryExpr(p,op,lhs,rhs) ->
let lhsMatches = __CombineAllMatches lhs premises
let rhsMatches = __CombineAllMatches rhs premises
let lst1 = Utils.ListCombine (fun e1 e2 -> BinaryExpr(p,op,e1,e2)) lhsMatches rhsMatches
let lst2 =
if op = "in" then
Utils.ListCombineMult BinaryInCombiner lhsMatches rhsMatches
elif op = "!in" then
Utils.ListCombineMult BinaryNotInCombiner lhsMatches rhsMatches
else
[]
lst1 @ lst2
| UnaryExpr(op,sub) ->
__CombineAllMatches sub premises |> List.map (fun e -> UnaryExpr(op,e))
| SelectExpr(lst,idx) ->
let lstMatches = __CombineAllMatches lst premises
let idxMatches = __CombineAllMatches idx premises
Utils.ListCombineMult SelectExprCombinerFunc lstMatches idxMatches
| SeqLength(lst) ->
__CombineAllMatches lst premises |> List.map SeqLenCombinerFunc |> List.concat
// TODO: other cases
| _ -> []
expr :: (lst0 @ lstCombined)
let rec __ExpandPremise expr premises =
let __AddToPremisses exprLst premises = exprLst |> List.fold (fun acc e -> MySetAdd e acc) premises
let allMatches = lazy(__CombineAllMatches expr premises)
match expr with
| BinaryExpr(p,op,lhs,rhs) when IsRelationalOp op ->
let x = allMatches.Force()
__AddToPremisses x premises
| SelectExpr(lst, idx) ->
let x = allMatches.Force()
__AddToPremisses x premises
| _ -> premises
let rec __Iter exprLst premises =
match exprLst with
| expr :: rest ->
let newPremises =
if expandExprFunc expr then
__ExpandPremise expr premises
else
premises
__Iter rest newPremises
| [] -> premises
(* --- function body starts here --- *)
let premises' = __Iter (premises |> Set.toList) premises
if premises' = premises then
premises'
else
//Logger.TraceLine "-----------------------"
//premises' |> Set.iter (fun e -> Logger.TraceLine (Printer.PrintExpr 0 e))
ComputeClosure heapInst expandExprFunc premises'
|