/usr/share/hol88-2.02.19940316/Library/trs/matching.ml is in hol88-library-source 2.02.19940316-35.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 | % matching.ml (c) R.J.Boulton 1990 %
%----------------------------------------------------------------------------%
% Datatype for a full representation of a theorem %
% The first string is for the theory name. The second is for the theorem %
% name. %
lettype foundthm = thmkind # string # string # thm;;
% Datatype for representing theorem patterns %
% The first seven constructors generate representations for theorem patterns. %
% The rest combine or modify such representations. %
rectype thmpattern_rep = Kind' of thmkind
| Thryname' of namepattern
| Thmname' of namepattern
| Conc' of termpattern
| HypP' of termpattern list
| HypF' of termpattern list
| Side' of side_condition
| Andalso' of thmpattern_rep # thmpattern_rep
| Orelse' of thmpattern_rep # thmpattern_rep
| Not' of thmpattern_rep
| Where' of thmpattern_rep # thmpattern_rep;;
% Abstract datatype for theorem patterns %
% There are two types of theorem pattern clause. %
% There are main clauses, in which tests are performed on a foundthm. All of %
% the constructors are allowed in this type of clause, though in principle, %
% side-condition tests should not be. Side-condition tests within main %
% clauses are re-interpreted as follows: %
% %
% Side <side-condition> %
% %
% is interpreted as %
% %
% (Conc (autotermpattern "conc:bool")) Where (Side <side-condition>) %
% %
% This only makes sense if <side-condition> tests "conc". %
% Only `Side', `Andalso', `Orelse', and `Not' constructors are permitted %
% within a side-condition clause. %
% `Where' is used to link these two types of clause. Its first argument is a %
% main clause. Its second argument is a side-condition clause. Note that %
% `Where' cannot occur within a side-condition clause. %
% All of these constraints are imposed by the abstract datatype, which uses %
% the type `thmpattern_rep' as its representing type. %
abstype thmpattern = thmpattern_rep
with show_thmpattern thmp = rep_thmpattern thmp
% : (thmpattern -> thmpattern_rep) %
and Kind knd = abs_thmpattern (Kind' knd)
% : (thmkind -> thmpattern) %
and Thryname nmp = abs_thmpattern (Thryname' nmp)
% : (namepattern -> thmpattern) %
and Thmname nmp = abs_thmpattern (Thmname' nmp)
% : (namepattern -> thmpattern) %
and Conc patt = abs_thmpattern (Conc' patt)
% : (termpattern -> thmpattern) %
and HypP pattl = abs_thmpattern (HypP' pattl)
% : (termpattern list -> thmpattern) %
and HypF pattl = abs_thmpattern (HypF' pattl)
% : (termpattern list -> thmpattern) %
and Side x = abs_thmpattern (Side' x)
% : (side_condition -> thmpattern) %
and Andalso (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
abs_thmpattern (Andalso' (rep_thmpattern thmp1,rep_thmpattern thmp2))
and Orelse (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
abs_thmpattern (Orelse' (rep_thmpattern thmp1,rep_thmpattern thmp2))
and Not thmp = abs_thmpattern (Not' (rep_thmpattern thmp))
% : (thmpattern -> thmpattern) %
and Where (thmp1,thmp2) =
% : ((thmpattern # thmpattern) -> thmpattern) %
% Function to check that a side-condition clause is legal %
% The function either returns `true' or fails. The failure which %
% occurs in the body of `Where' if `is_legal_sidecond' returns false %
% is therefore unnecessary. %
letrec is_legal_sidecond thmp_rep =
% : (thmpattern_rep -> bool) %
case thmp_rep
of (Kind' _) . failwith `Where -- \`Kind' used in side-condition`
| (Thryname' _) .
failwith `Where -- \`Thryname' used in side-condition`
| (Thmname' _) .
failwith `Where -- \`Thmname' used in side-condition`
| (Conc' _) . failwith `Where -- \`Conc' used in side-condition`
| (HypP' _) . failwith `Where -- \`HypP' used in side-condition`
| (HypF' _) . failwith `Where -- \`HypF' used in side-condition`
| (Side' _) . true
| (Andalso' (thmp_rep1,thmp_rep2)) .
((is_legal_sidecond thmp_rep1) & (is_legal_sidecond thmp_rep2))
| (Orelse' (thmp_rep1,thmp_rep2)) .
((is_legal_sidecond thmp_rep1) & (is_legal_sidecond thmp_rep2))
| (Not' thmp_rep1) . (is_legal_sidecond thmp_rep1)
| (Where' _) . failwith `Where -- \`Where' used in side-condition`
in if (is_legal_sidecond (rep_thmpattern thmp2))
then abs_thmpattern
(Where' (rep_thmpattern thmp1,rep_thmpattern thmp2))
else failwith `Where -- illegal side-condition`
% Function to test a theorem pattern against a foundthm %
% It calls `mainmatch' to attempt the matching. `mainmatch' returns a %
% `result_of_match', which `thmmatch' converts to a Boolean value. %
and thmmatch thmp fthm =
% : (thmpattern -> foundthm -> bool) %
rom_to_bool (mainmatch (rep_thmpattern thmp) fthm ())
% The following auxiliary matching functions are local to the abstract type %
% definition. Hence, they are hidden from the user. %
% `mainmatch' is used for processing main clauses of theorem patterns, given %
% a foundthm to match against. For the first six cases of clause type, %
% auxiliary functions are called. Note that these and `mainmatch' itself are %
% lazy. That is they require a null argument before they actually perform %
% any computation. %
% Side-condition clauses are re-interpreted when they occur within a main %
% clause, as described at the beginning of this abstract type definition. %
% `Andalso' and `Orelse' call `mainmatch' recursively on their two arguments %
% and use subsidiary functions to combine the results. `Not' calls %
% `mainmatch' on its argument and then calls a subsidiary function to %
% process the result. `Where' calls `mainmatch' on its first argument, and %
% then passes the result along with its second argument to a function which %
% deals with the side-condition clause. %
whererec mainmatch thmp_rep fthm () =
% : (thmpattern_rep -> foundthm -> void -> result_of_match) %
case thmp_rep
of (Kind' x) . (kindfn x fthm ())
| (Thryname' x) . (thrynamefn x fthm ())
| (Thmname' x) . (thmnamefn x fthm ())
| (Conc' x) . (concfn x fthm ())
| (HypP' x) . (hypPfn x fthm ())
| (HypF' x) . (hypFfn x fthm ())
| (Side' _) . (mainmatch
(Where' ((Conc' o autotermpattern) "conc:bool",thmp_rep))
fthm
()
)
| (Andalso' (x,y)) . (andalsofn
(mainmatch x fthm)
(mainmatch y fthm)
()
)
| (Orelse' (x,y)) . (approms
(mainmatch x fthm)
(mainmatch y fthm)
()
)
| (Not' x) . (notfn (mainmatch x fthm) ())
| (Where' (x,y)) . (wherefn y (mainmatch x fthm) ())
% `sidematch' is used for processing side-condition clauses, given an %
% environment which consists of a single matching. All side-condition tests %
% within the clause are applied to this matching. %
% Tests on the foundthm itself are prohibited (there is no foundthm %
% available to test). This means that the first six cases for theorem %
% patterns all cause failures. %
% If the side-condition clause is simply a side-condition, the side- %
% condition is applied to the environment. If the test succeeds, the %
% result is passed back up. If not, `Nomatch' is passed back up. %
% `Andalso', `Orelse' and `Not' cause `sidematch' to be called recursively, %
% and the results of these calls are processed further by subsidiary %
% functions. `Where' is prohibited within side-condition clauses. %
% The failures due to illegal constructor use should never occur because %
% the abstract datatype will prevent such constructions. %
and sidematch thmp_rep env () =
% : (thmpattern_rep -> matching -> void -> result_of_match) %
case thmp_rep
of (Kind' _) . (failwith `sidematch -- illegal use of Kind`)
| (Thryname' _) . (failwith `sidematch -- illegal use of Thryname`)
| (Thmname' _) . (failwith `sidematch -- illegal use of Thmname`)
| (Conc' _) . (failwith `sidematch -- illegal use of Conc`)
| (HypP' _) . (failwith `sidematch -- illegal use of HypP`)
| (HypF' _) . (failwith `sidematch -- illegal use of HypF`)
| (Side' x) . ((x env) ??[`no match`] (Nomatch))
| (Andalso' (x,y)) . (andalsofn
(sidematch x env)
(sidematch y env)
()
)
| (Orelse' (x,y)) . (approms
(sidematch x env)
(sidematch y env)
()
)
| (Not' x) . (notfn (sidematch x env) ())
| (Where' _) . (failwith `sidematch -- illegal use of Where`)
% `andalsofn' is used for ANDing two `result_of_matches' together. %
% The first argument is applied to (). If the result is `Nomatch', then the %
% result of the whole evaluation is `Nomatch'. If not, the second argument %
% is treated similarly. If both the arguments contain matchings, the %
% function attempts to join the two `heads'. If this succeeds, the result %
% becomes the `head' of the combined `result_of_match'. If not, the result %
% is discarded. %
% The rest of the `result_of_match' is (when required) obtained by calling %
% `andalsofn' recursively, firstly on the original first argument and the %
% `tail' of the second, and then on the tail of the first and the original %
% second argument. The two resulting `result_of_matches' are appended using %
% `approms'. %
% The overall effect of this is to combine a `list' of n matchings with a %
% `list' of m matchings to form a `list' of all the possible combinations %
% of matchings which can be joined successfully (maximum length n * m). %
and andalsofn rom1fn rom2fn () =
% : ((void -> result_of_match) -> (void -> result_of_match) -> %
% (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Nomatch)
| (Match (m1,romfn1)) .
(case (rom2fn ())
of (Nomatch) . (Nomatch)
| (Match (m2,romfn2)) .
(let rest = (approms
(andalsofn rom1fn romfn2)
(andalsofn romfn1 rom2fn)
)
in ( (Match (join_matchings m1 m2,rest))
??[`no match`] (rest ())
)
)
)
% `notfn' simply negates a `result_of_match', discarding any matchings, %
% since they make no sense when negated. `Not' can therefore be very %
% destructive. %
and notfn rom1fn () =
% : ((void -> result_of_match) -> (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Match_null)
| (Match _) . (Nomatch)
% `wherefn' is used for handling side-condition clauses. %
% It passes each matching in the `result_of_match' it is given to the %
% theorem pattern. The matchings are passed in turn as environments. %
% The evaluation proceeds only as far as is necessary, but the %
% potential to continue it is retained. %
% `sidematch' is used to test the theorem pattern under each of the %
% environments. It returns a `result_of_match'. Only those matchings %
% consistent with the environment should be retained. That is, any %
% wildcard which appears in the environment as well as in the matching %
% should match to the same object in both cases. `andalsofn' is used %
% to perform this checking. %
% The `result_of_matches' generated for each environment are appended %
% using `approms'. %
and wherefn thmp_rep rom1fn () =
% : (thmpattern_rep -> (void -> result_of_match) -> %
% (void -> result_of_match)) %
case (rom1fn ())
of (Nomatch) . (Nomatch)
| (Match (m,romfn)) . (approms
(andalsofn
(\().Match (m,(\().Nomatch)))
(sidematch thmp_rep m))
(wherefn thmp_rep romfn)
()
)
% `kindfn' tests the kind of a found theorem. %
and kindfn knd fthm () =
% : (thmkind -> foundthm -> (void -> result_of_match)) %
bool_to_rom (knd = (fst fthm))
% `thrynamefn' uses a `namepattern' to test the name of the theory to which %
% a found theorem belongs. %
and thrynamefn nmp fthm () =
% : (namepattern -> foundthm -> (void -> result_of_match)) %
bool_to_rom (namematch nmp ((fst o snd) fthm))
% `thmnamefn' uses a `namepattern' to test the name of a found theorem. %
and thmnamefn nmp fthm () =
% : (namepattern -> foundthm -> (void -> result_of_match)) %
bool_to_rom (namematch nmp ((fst o snd o snd) fthm))
% `concfn' tests the conclusion of a found theorem against a termpattern. %
% The conclusion is extracted and then matched against the termpattern. %
% If the match succeeds, the matching is made into a `result_of_match'. %
% Otherwise, `Nomatch' is returned as the `result_of_match'. %
and concfn patt fthm () =
% : (termpattern -> foundthm -> (void -> result_of_match)) %
(Match (make_matching patt ((concl o snd o snd o snd) fthm),(\().Nomatch)))
??[`no match`] Nomatch
% `hypPfn' tests the hypotheses of a found theorem against a list of %
% termpatterns. Not all of the hypotheses need to be matched for the match to %
% succeed. %
% The list of hypotheses is extracted from the found theorem. If there are %
% more termpatterns than hypotheses, `Nomatch' is returned. Otherwise, %
% `hypfn' is used to test the termpatterns against the hypotheses. %
and hypPfn pattl fthm () =
% : (termpattern list -> foundthm -> (void -> result_of_match)) %
let hypl = (hyp o snd o snd o snd) fthm
in if ((length pattl) > (length hypl))
then Nomatch
else hypfn pattl hypl ()
% `hypFfn' tests the hypotheses of a found theorem against a list of %
% termpatterns. All of the hypotheses need to be matched for the match to %
% succeed. %
% The list of hypotheses is extracted from the found theorem. If there are %
% the same number of termpatterns as there are hypotheses, `hypfn' is used to %
% test the termpatterns against the hypotheses. Otherwise, `Nomatch' is %
% returned. %
and hypFfn pattl fthm () =
% : (termpattern list -> foundthm -> (void -> result_of_match)) %
let hypl = (hyp o snd o snd o snd) fthm
in if ((length pattl) = (length hypl))
then hypfn pattl hypl ()
else Nomatch
% `hypfn' tests a list of termpatterns against a list of hypotheses %
% The result is a `result_of_match'. A subsidiary function is used to allow %
% backtracking. %
% `hypmatch' takes four arguments plus a null argument to provide `lazy' %
% evaluation. The first argument is an accumulated matching for the %
% wildcards bound so far. The second argument is a list of hypotheses left %
% unmatched. This has to be remembered while the various ways of matching %
% them are attempted. The third argument is the list of patterns not yet %
% matched. The fourth argument is the list of hypotheses which have not yet %
% been tried against the head of the pattern list. %
% When the pattern list is empty, the accumulated matching is made into a %
% `result_of_match', and returned as result. If the list of hypotheses runs %
% out before the patterns, `Nomatch' is returned. %
% If the head of the pattern list matches the head of the hypothesis list, %
% and the resulting matching is consistent with the accumulated matching, %
% the head of the hypothesis list is removed from the previous level's list %
% and `hypmatch' is called recursively to attempt a new level of match. Any %
% other ways of matching are found as described below, and are appended to %
% the result of this call. %
% Any other ways of matching are found by a recursive call to `hypmatch' %
% with all of the original arguments except that the fourth argument is the %
% tail of the original list. The result of this call becomes the result of %
% the original call if the head of the pattern list did not match the head %
% of the hypothesis list. %
and hypfn pattl hypl () =
% : (termpattern list -> term list -> (void -> result_of_match)) %
letrec hypmatch m prevtl pl terml () =
% : (matching -> term list -> termpattern list -> term list -> %
% (void -> result_of_match)) %
if (null pl)
then Match(m,(\().Nomatch))
else if (null terml)
then Nomatch
else (let rest = hypmatch m prevtl pl (tl terml)
in ((let newm = join_matchings m
(make_matching (hd pl) (hd terml))
in (let newtl = filter (\x. not (x = (hd terml))) prevtl
in approms
(hypmatch newm newtl (tl pl) newtl)
rest
()
)
)
??[`no match`] rest ()
)
)
in hypmatch null_matching hypl pattl hypl ();;
% Infix declarations to make construction of theorem patterns nicer %
ml_paired_infix `Andalso`;;
ml_paired_infix `Orelse`;;
ml_paired_infix `Where`;;
% Function to filter a list of theorems using a theorem pattern %
let thmfilter thmp fthml = filter (thmmatch thmp) fthml;;
% : (thmpattern -> foundthm list -> foundthm list) %
%----------------------------------------------------------------------------%
|