summaryrefslogtreecommitdiff
path: root/src/termination.sml
blob: f0b21d999c9b8cadbac3a35e323456eaadf4ba6e (plain)
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
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
(* Copyright (c) 2008, Adam Chlipala
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * - Redistributions of source code must retain the above copyright notice,
 *   this list of conditions and the following disclaimer.
 * - Redistributions in binary form must reproduce the above copyright notice,
 *   this list of conditions and the following disclaimer in the documentation
 *   and/or other materials provided with the distribution.
 * - The names of contributors may not be used to endorse or promote products
 *   derived from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *)

structure Termination :> TERMINATION = struct

open Elab

structure E = ElabEnv
structure IM = IntBinaryMap
structure IS = IntBinarySet

datatype pedigree =
         Func of int
       | Arg of int * int * con
       | Subarg of int * int * con
       | Rabble

fun p2s p =
    case p of
        Func i => "Func" ^ Int.toString i
      | Arg (i, j, _) => "Arg" ^ Int.toString i ^ "," ^ Int.toString j
      | Subarg (i, j, _) => "Subarg" ^ Int.toString i ^ "," ^ Int.toString j
      | Rabble => "Rabble"

fun declOk' env (d, loc) =
    case d of
        DValRec vis =>
        let
            val nfns = length vis

            val fenv = ListUtil.foldli (fn (i, (_, j, _, _), fenv) => IM.insert (fenv, j, i)) IM.empty vis

            fun namesEq ((c1, _), (c2, _)) =
                case (c1, c2) of
                    (CName s1, CName s2) => s1 = s2
                  | (CRel n1, CRel n2) => n1 = n2
                  | (CNamed n1, CNamed n2) => n1 = n2
                  | (CModProj n1, CModProj n2) => n1 = n2
                  | _ => false

            fun patCon pc =
                let
                    fun unravel (t, _) =
                        case t of
                            TCFun (_, _, _, t) => unravel t
                          | TFun (dom, _) => dom
                          | _ => raise Fail "Termination: Unexpected constructor type"
                in
                    case pc of
                        PConVar i =>
                        let
                            val (_, t) = E.lookupENamed env i
                        in
                            unravel t
                        end
                      | PConProj (m1, ms, x) =>
                        let
                            val (str, sgn) = E.chaseMpath env (m1, ms)
                        in
                            case E.projectVal env {str = str, sgn = sgn, field = x} of
                                NONE => raise Fail "Termination: Bad constructor projection"
                              | SOME t => unravel t
                        end
                end

            fun pat penv (p, (pt, _)) =
                let
                    fun con (i, j, pc, pt') = pat penv (Subarg (i, j, patCon pc), pt')

                    fun record (i, j, t, xps) =
                        case t of
                            (TRecord (CRecord (_, xts), _), _) =>
                            foldl (fn ((x, pt', _), penv) =>
                                      let
                                          val p' =
                                              case List.find (fn (x', _) =>
                                                                 namesEq ((CName x, ErrorMsg.dummySpan), x')) xts of
                                                  NONE => Rabble
                                                | SOME (_, t) => Subarg (i, j, t)
                                      in
                                          pat penv (p', pt')
                                      end) penv xps
                          | _ => foldl (fn ((_, pt', _), penv) => pat penv (Rabble, pt')) penv xps
                in
                    case (p, pt) of
                        (_, PWild) => penv
                      | (_, PVar _) => p :: penv
                      | (_, PPrim _) => penv
                      | (_, PCon (_, _, _, NONE)) => penv
                      | (Arg (i, j, _), PCon (_, pc, _, SOME pt')) => con (i, j, pc, pt')
                      | (Subarg (i, j, _), PCon (_, pc, _, SOME pt')) => con (i, j, pc, pt')
                      | (_, PCon (_, _, _, SOME pt')) => pat penv (Rabble, pt')
                      | (Arg (i, j, t), PRecord xps) => record (i, j, t, xps)
                      | (Subarg (i, j, t), PRecord xps) => record (i, j, t, xps)
                      | (_, PRecord xps) => foldl (fn ((_, pt', _), penv) => pat penv (Rabble, pt')) penv xps
                end

            fun exp parent (penv, calls) e =
                let
                    val default = (Rabble, calls)

                    fun apps () =
                        let
                            fun combiner calls e =
                                case #1 e of
                                    EApp ((ECApp (
                                           (ECApp (
                                            (ECApp (
                                             (ECApp (
                                              (ECApp (
                                               (ECApp (
                                                (ECApp (
                                                 (ECApp (
                                                  (EModProj (m, [], "tag"), _),
                                                  _), _),
                                                 _), _),
                                                _), _),
                                               _), _),
                                              _), _),
                                             _), _),
                                            _), _),
                                           _), _),
                                          (ERecord xets, _)) =>
                                    let
                                        val checkName =
                                            case E.lookupStrNamed env m of
                                                  ("Basis", _) => (fn x : con => case #1 x of
                                                                                     CName s => s = "Link"
                                                                                                orelse s = "Action"
                                                                                   | _ => false)
                                                | _ => (fn _ => false)

                                        val calls = foldl (fn ((x, e, _), calls) =>
                                                              if checkName x then
                                                                  calls
                                                              else
                                                                  #2 (exp parent (penv, calls) e)) calls xets
                                    in
                                        (Rabble, [Rabble], calls)
                                    end

                                  | EApp (e1, e2) =>
                                    let
                                        val (p1, ps, calls) = combiner calls e1
                                        val (p2, calls) = exp parent (penv, calls) e2

                                        val p = case p1 of
                                                    Rabble => Rabble
                                                  | Arg _ => Rabble
                                                  | Subarg (i, j, (TFun (_, ran), _)) => Subarg (i, j, ran)
                                                  | Subarg _ => Rabble
                                                  | Func _ => Rabble
                                    in
                                        (p, ps @ [p2], calls)
                                    end
                                  | ECApp (e, _) =>
                                    let
                                        val (p, ps, calls) = combiner calls e

                                        val p = case p of
                                                    Rabble => Rabble
                                                  | Arg _ => Rabble
                                                  | Subarg (i, j, (TCFun (_, _, _, ran), _)) => Subarg (i, j, ran)
                                                  | Subarg _ => Rabble
                                                  | Func _ => Rabble
                                    in
                                        (p, ps, calls)
                                    end
                                  | EKApp (e, _) => combiner calls e
                                  | _ =>
                                    let
                                        val (p, calls) = exp parent (penv, calls) e
                                    in
                                        (*Print.prefaces "Head" [("e", ElabPrint.p_exp env e)];
                                        print (p2s p ^ "\n");*)
                                        (p, [p], calls)
                                    end

                            val (p, ps, calls) = combiner calls e

                            val calls =
                                case ps of
                                    [] => raise Fail "Termination: Empty ps"
                                  | f :: ps =>
                                    case f of
                                        Func i => (parent, i, ps) :: calls
                                      | _ => calls
                        in
                            (p, calls)
                        end
                in
                    case #1 e of
                        EPrim _ => default
                      | ERel n => (List.nth (penv, n), calls)
                      | ENamed n =>
                        let
                            val p = case IM.find (fenv, n) of
                                        NONE => Rabble
                                      | SOME n' => Func n'
                        in
                            (p, calls)
                        end
                      | EModProj _ => default

                      | EApp _ => apps ()
                      | EAbs (_, _, _, e) => 
                        let
                            val (_, calls) = exp parent (Rabble :: penv, calls) e
                        in
                            (Rabble, calls)
                        end
                      | ECApp _ => apps ()
                      | ECAbs (_, _, _, e) =>
                        let
                            val (_, calls) = exp parent (penv, calls) e
                        in
                            (Rabble, calls)
                        end
                      | EKApp _ => apps ()
                      | EKAbs (_, e) =>
                        let
                            val (_, calls) = exp parent (penv, calls) e
                        in
                            (Rabble, calls)
                        end

                      | ERecord xets =>
                        let
                            val calls = foldl (fn ((_, e, _), calls) => #2 (exp parent (penv, calls) e)) calls xets
                        in
                            (Rabble, calls)
                        end
                      | EField (e, x, _) =>
                        let
                            val (p, calls) = exp parent (penv, calls) e
                            val p =
                                case p of
                                    Subarg (i, j, (TRecord (CRecord (_, xts), _), _)) =>
                                    (case List.find (fn (x', _) => namesEq (x, x')) xts of
                                         NONE => Rabble
                                       | SOME (_, t) => Subarg (i, j, t))
                                  | _ => Rabble
                        in
                            (p, calls)
                        end
                      | ECut (e, _, _) =>
                        let
                            val (_, calls) = exp parent (penv, calls) e
                        in
                            (Rabble, calls)
                        end
                      | ECutMulti (e, _, _) =>
                        let
                            val (_, calls) = exp parent (penv, calls) e
                        in
                            (Rabble, calls)
                        end
                      | EConcat (e1, _, e2, _) =>
                        let
                            val (_, calls) = exp parent (penv, calls) e1
                            val (_, calls) = exp parent (penv, calls) e2
                        in
                            (Rabble, calls)
                        end

                      | ECase (e, pes, _) =>
                        let
                            val (p, calls) = exp parent (penv, calls) e

                            val calls = foldl (fn ((pt, e), calls) =>
                                                  let
                                                      val penv = pat penv (p, pt)
                                                      val (_, calls) = exp parent (penv, calls) e
                                                  in
                                                      calls
                                                  end) calls pes
                        in
                            (Rabble, calls)
                        end

                      | EError => (Rabble, calls)
                      | EUnif (ref (SOME e)) => exp parent (penv, calls) e
                      | EUnif (ref NONE) => (Rabble, calls)

                      | ELet (eds, e, _) =>
                        let
                            fun extPenv ((ed, _), penv) =
                                case ed of
                                    EDVal _ => Rabble :: penv
                                  | EDValRec vis => foldl (fn (_, penv) => Rabble :: penv) penv vis
                        in
                            exp parent (foldl extPenv penv eds, calls) e
                        end
                end

            fun doVali (i, (_, f, _, e), calls) =
                let
                    fun unravel (e, j, penv) =
                        case #1 e of
                            EAbs (_, t, _, e) =>
                            unravel (e, j + 1, Arg (i, j, t) :: penv)
                          | ECAbs (_, _, _, e) =>
                            unravel (e, j, penv)
                          | _ => (j, #2 (exp f (penv, calls) e))
                in
                    unravel (e, 0, [])
                end

            val (ns, calls) = ListUtil.foldliMap doVali [] vis

            fun isRecursive (from, to, _) =
                let
                    fun search (at, soFar) =
                        at = from
                        orelse List.exists (fn (from', to', _) =>
                                               from' = at
                                               andalso not (IS.member (soFar, to'))
                                               andalso search (to', IS.add (soFar, to')))
                                           calls
                in
                    search (to, IS.empty)
                end

            val calls = List.filter isRecursive calls

            fun search (ns, choices) =
                case ns of
                    [] =>
                    let
                        val choices = rev choices
                    in
                        List.all (fn (_, f, args) =>
                                     let
                                         val recArg = List.nth (choices, f)
                                                      
                                         fun isDatatype (t, _) =
                                             case t of
                                                 CNamed _ => true
                                               | CModProj _ => true
                                               | CApp (t, _) => isDatatype t
                                               | _ => false
                                     in
                                         length args > recArg andalso
                                         case List.nth (args, recArg) of
                                             Subarg (i, j, t) => isDatatype t andalso j = List.nth (choices, i)
                                           | _ => false
                                     end) calls
                    end
                  | n :: ns' =>
                    let
                        fun search' i =
                            i < n andalso (search (ns', i :: choices) orelse search' (i + 1))
                    in
                        search' 0
                    end
        in
            if search (ns, []) then
                ()
            else
                ErrorMsg.errorAt loc "Can't prove termination of recursive function(s)"
        end

      | DStr (_, _, _, (StrConst ds, _)) => ignore (foldl declOk env ds)

      | _ => ()

and declOk (d, env) =
    (declOk' env d;
     E.declBinds env d)

fun check ds = ignore (foldl declOk E.empty ds)

end