1 (* Title: HOL/Tools/TFL/tfl.ML
2 Author: Konrad Slind, Cambridge University Computer Laboratory
4 First part of main module.
9 val trace: bool Unsynchronized.ref
10 val trace_thms: string -> thm list -> unit
11 val trace_cterm: string -> cterm -> unit
13 val mk_functional: theory -> term list -> {functional: term, pats: pattern list}
14 val wfrec_definition0: theory -> string -> term -> term -> theory * thm
15 val post_definition: thm list -> theory * (thm * pattern list) ->
19 full_pats_TCs: (term * term list) list}
20 val wfrec_eqns: theory -> xstring -> thm list -> term list ->
24 extracta: (thm * term list) list,
26 val lazyR_def: theory -> xstring -> thm list -> term list ->
31 full_pats_TCs: (term * term list) list,
32 patterns : pattern list}
33 val mk_induction: theory ->
34 {fconst: term, R: term, SV: term list, pat_TCs_list: (term * term list) list} -> thm
35 val postprocess: bool -> {wf_tac: tactic, terminator: tactic, simplifier: cterm -> thm}
36 -> theory -> {rules: thm, induction: thm, TCs: term list list}
37 -> {rules: thm, induction: thm, nested_tcs: thm list}
40 structure Prim: PRIM =
43 val trace = Unsynchronized.ref false;
46 fun TFL_ERR func mesg = Utils.ERR {module = "Tfl", func = func, mesg = mesg};
48 val concl = #2 o Rules.dest_thm;
49 val hyp = #1 o Rules.dest_thm;
51 val list_mk_type = Utils.end_itlist (curry (op -->));
53 fun front_last [] = raise TFL_ERR "front_last" "empty list"
54 | front_last [x] = ([],x)
56 let val (pref,x) = front_last t
62 (*---------------------------------------------------------------------------
63 * The next function is common to pattern-match translation and
64 * proof of completeness of cases for the induction theorem.
66 * The curried function "gvvariant" returns a function to generate distinct
67 * variables that are guaranteed not to be in names. The names of
68 * the variables go u, v, ..., z, aa, ..., az, ... The returned
69 * function contains embedded refs!
70 *---------------------------------------------------------------------------*)
72 let val slist = Unsynchronized.ref names
73 val vname = Unsynchronized.ref "u"
75 if member (op =) (!slist) (!vname)
76 then (vname := Symbol.bump_string (!vname); new())
77 else (slist := !vname :: !slist; !vname)
79 fn ty => Free(new(), ty)
83 (*---------------------------------------------------------------------------
84 * Used in induction theorem production. This is the simple case of
85 * partitioning up pattern rows by the leading constructor.
86 *---------------------------------------------------------------------------*)
87 fun ipartition gv (constructors,rows) =
88 let fun pfail s = raise TFL_ERR "partition.part" s
89 fun part {constrs = [], rows = [], A} = rev A
90 | part {constrs = [], rows = _::_, A} = pfail"extra cases in defn"
91 | part {constrs = _::_, rows = [], A} = pfail"cases missing in defn"
92 | part {constrs = c::crst, rows, A} =
93 let val (c, T) = dest_Const c
94 val L = binder_types T
95 val (in_group, not_in_group) =
96 fold_rev (fn (row as (p::rst, rhs)) =>
97 fn (in_group,not_in_group) =>
98 let val (pc,args) = USyntax.strip_comb p
99 in if (#1(dest_Const pc) = c)
100 then ((args@rst, rhs)::in_group, not_in_group)
101 else (in_group, row::not_in_group)
103 val col_types = Utils.take type_of (length L, #1(hd in_group))
105 part{constrs = crst, rows = not_in_group,
106 A = {constructor = c,
107 new_formals = map gv col_types,
108 group = in_group}::A}
110 in part{constrs = constructors, rows = rows, A = []}
115 (*---------------------------------------------------------------------------
116 * Each pattern carries with it a tag (i,b) where
117 * i is the clause it came from and
118 * b=true indicates that clause was given by the user
119 * (or is an instantiation of a user supplied pattern)
121 *---------------------------------------------------------------------------*)
123 type pattern = term * (int * bool)
125 fun pattern_map f (tm,x) = (f tm, x);
127 fun pattern_subst theta = pattern_map (subst_free theta);
130 fun row_of_pat x = fst (snd x);
131 fun given x = snd (snd x);
133 (*---------------------------------------------------------------------------
134 * Produce an instance of a constructor, plus genvars for its arguments.
135 *---------------------------------------------------------------------------*)
136 fun fresh_constr ty_match colty gv c =
137 let val (_,Ty) = dest_Const c
138 val L = binder_types Ty
139 and ty = body_type Ty
140 val ty_theta = ty_match ty colty
141 val c' = USyntax.inst ty_theta c
142 val gvars = map (USyntax.inst ty_theta o gv) L
147 (*---------------------------------------------------------------------------
148 * Goes through a list of rows and picks out the ones beginning with a
149 * pattern with constructor = name.
150 *---------------------------------------------------------------------------*)
151 fun mk_group name rows =
152 fold_rev (fn (row as ((prfx, p::rst), rhs)) =>
153 fn (in_group,not_in_group) =>
154 let val (pc,args) = USyntax.strip_comb p
155 in if ((#1 (Term.dest_Const pc) = name) handle TERM _ => false)
156 then (((prfx,args@rst), rhs)::in_group, not_in_group)
157 else (in_group, row::not_in_group) end)
160 (*---------------------------------------------------------------------------
161 * Partition the rows. Not efficient: we should use hashing.
162 *---------------------------------------------------------------------------*)
163 fun partition _ _ (_,_,_,[]) = raise TFL_ERR "partition" "no rows"
164 | partition gv ty_match
165 (constructors, colty, res_ty, rows as (((prfx,_),_)::_)) =
166 let val fresh = fresh_constr ty_match colty gv
167 fun part {constrs = [], rows, A} = rev A
168 | part {constrs = c::crst, rows, A} =
169 let val (c',gvars) = fresh c
170 val (in_group, not_in_group) = mk_group (#1 (dest_Const c')) rows
172 if (null in_group) (* Constructor not given *)
173 then [((prfx, #2(fresh c)), (USyntax.ARB res_ty, (~1,false)))]
178 A = {constructor = c',
180 group = in_group'}::A}
182 in part{constrs=constructors, rows=rows, A=[]}
185 (*---------------------------------------------------------------------------
186 * Misc. routines used in mk_case
187 *---------------------------------------------------------------------------*)
190 let val L = length (binder_types (type_of c))
191 fun build (prfx,tag,plist) =
192 let val (args, plist') = chop L plist
193 in (prfx,tag,list_comb(c,args)::plist') end
196 fun v_to_prfx (prfx, v::pats) = (v::prfx,pats)
197 | v_to_prfx _ = raise TFL_ERR "mk_case" "v_to_prfx";
199 fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats)
200 | v_to_pats _ = raise TFL_ERR "mk_case" "v_to_pats";
203 (*----------------------------------------------------------------------------
204 * Translation of pattern terms into nested case expressions.
206 * This performs the translation and also builds the full set of patterns.
207 * Thus it supports the construction of induction theorems even when an
208 * incomplete set of patterns is given.
209 *---------------------------------------------------------------------------*)
211 fun mk_case ty_info ty_match usednames range_ty =
213 fun mk_case_fail s = raise TFL_ERR "mk_case" s
214 val fresh_var = gvvariant usednames
215 val divide = partition fresh_var ty_match
216 fun expand constructors ty ((_,[]), _) = mk_case_fail"expand_var_row"
217 | expand constructors ty (row as ((prfx, p::rst), rhs)) =
219 then let val fresh = fresh_constr ty_match ty fresh_var
221 let val capp = list_comb(c,gvs)
222 in ((prfx, capp::rst), pattern_subst[(p,capp)] rhs)
224 in map expnd (map fresh constructors) end
226 fun mk{rows=[],...} = mk_case_fail"no rows"
227 | mk{path=[], rows = ((prfx, []), (tm,tag))::_} = (* Done *)
228 ([(prfx,tag,[])], tm)
229 | mk{path=[], rows = _::_} = mk_case_fail"blunder"
230 | mk{path as u::rstp, rows as ((prfx, []), rhs)::rst} =
232 rows = ((prfx, [fresh_var(type_of u)]), rhs)::rst}
233 | mk{path = u::rstp, rows as ((_, p::_), _)::_} =
234 let val (pat_rectangle,rights) = ListPair.unzip rows
235 val col0 = map(hd o #2) pat_rectangle
237 if (forall is_Free col0)
238 then let val rights' = map (fn(v,e) => pattern_subst[(v,u)] e)
239 (ListPair.zip (col0, rights))
240 val pat_rectangle' = map v_to_prfx pat_rectangle
241 val (pref_patl,tm) = mk{path = rstp,
242 rows = ListPair.zip (pat_rectangle',
244 in (map v_to_pats pref_patl, tm)
247 let val pty as Type (ty_name,_) = type_of p
249 case (ty_info ty_name)
250 of NONE => mk_case_fail("Not a known datatype: "^ty_name)
251 | SOME{case_const,constructors} =>
253 val case_const_name = #1(dest_Const case_const)
254 val nrows = maps (expand constructors pty) rows
255 val subproblems = divide(constructors, pty, range_ty, nrows)
256 val groups = map #group subproblems
257 and new_formals = map #new_formals subproblems
258 and constructors' = map #constructor subproblems
259 val news = map (fn (nf,rows) => {path = nf@rstp, rows=rows})
260 (ListPair.zip (new_formals, groups))
261 val rec_calls = map mk news
262 val (pat_rect,dtrees) = ListPair.unzip rec_calls
263 val case_functions = map USyntax.list_mk_abs
264 (ListPair.zip (new_formals, dtrees))
265 val types = map type_of (case_functions@[u]) @ [range_ty]
266 val case_const' = Const(case_const_name, list_mk_type types)
267 val tree = list_comb(case_const', case_functions@[u])
268 val pat_rect1 = flat (ListPair.map mk_pat (constructors', pat_rect))
276 (* Repeated variable occurrences in a pattern are not allowed. *)
278 case (USyntax.dest_term tm)
279 of USyntax.VAR{Name = c, Ty = T} => [Free(c, T)]
280 | USyntax.CONST _ => []
281 | USyntax.COMB{Rator, Rand} => FV_multiset Rator @ FV_multiset Rand
282 | USyntax.LAMB _ => raise TFL_ERR "FV_multiset" "lambda";
284 fun no_repeat_vars thy pat =
285 let fun check [] = true
287 if member (op aconv) rst v then
288 raise TFL_ERR "no_repeat_vars"
289 (quote (#1 (dest_Free v)) ^
290 " occurs repeatedly in the pattern " ^
291 quote (Syntax.string_of_term_global thy pat))
293 in check (FV_multiset pat)
296 fun dest_atom (Free p) = p
297 | dest_atom (Const p) = p
298 | dest_atom _ = raise TFL_ERR "dest_atom" "function name not an identifier";
300 fun same_name (p,q) = #1(dest_atom p) = #1(dest_atom q);
302 local fun mk_functional_err s = raise TFL_ERR "mk_functional" s
304 mk_functional_err "recdef does not allow currying"
307 (*multiple function names?*)
308 if length (distinct same_name fs) < length fs
309 then mk_functional_err
310 "The function being declared appears with multiple types"
311 else mk_functional_err
312 (string_of_int (length fs) ^
313 " distinct function names being declared")
315 fun mk_functional thy clauses =
316 let val (L,R) = ListPair.unzip (map HOLogic.dest_eq clauses
317 handle TERM _ => raise TFL_ERR "mk_functional"
318 "recursion equations must use the = relation")
319 val (funcs,pats) = ListPair.unzip (map (fn (t$u) =>(t,u)) L)
320 val atom = single (distinct (op aconv) funcs)
321 val (fname,ftype) = dest_atom atom
322 val dummy = map (no_repeat_vars thy) pats
323 val rows = ListPair.zip (map (fn x => ([]:term list,[x])) pats,
324 map_index (fn (i, t) => (t,(i,true))) R)
325 val names = List.foldr OldTerm.add_term_names [] R
326 val atype = type_of(hd pats)
327 and aname = Name.variant names "a"
328 val a = Free(aname,atype)
329 val ty_info = Thry.match_info thy
330 val ty_match = Thry.match_type thy
331 val range_ty = type_of (hd R)
332 val (patts, case_tm) = mk_case ty_info ty_match (aname::names) range_ty
333 {path=[a], rows=rows}
334 val patts1 = map (fn (_,tag,[pat]) => (pat,tag)) patts
335 handle Match => mk_functional_err "error in pattern-match translation"
336 val patts2 = Library.sort (Library.int_ord o Library.pairself row_of_pat) patts1
337 val finals = map row_of_pat patts2
338 val originals = map (row_of_pat o #2) rows
339 val dummy = case (subtract (op =) finals originals)
341 | L => mk_functional_err
342 ("The following clauses are redundant (covered by preceding clauses): " ^
343 commas (map (fn i => string_of_int (i + 1)) L))
344 in {functional = Abs(Long_Name.base_name fname, ftype,
346 absfree(aname,atype, case_tm))),
351 (*----------------------------------------------------------------------------
353 * PRINCIPLES OF DEFINITION
355 *---------------------------------------------------------------------------*)
358 (*For Isabelle, the lhs of a definition must be a constant.*)
359 fun const_def sign (c, Ty, rhs) =
360 singleton (Syntax.check_terms (Proof_Context.init_global sign))
361 (Const("==",dummyT) $ Const(c,Ty) $ rhs);
363 (*Make all TVars available for instantiation by adding a ? to the front*)
364 fun poly_tvars (Type(a,Ts)) = Type(a, map (poly_tvars) Ts)
365 | poly_tvars (TFree (a,sort)) = TVar (("?" ^ a, 0), sort)
366 | poly_tvars (TVar ((a,i),sort)) = TVar (("?" ^ a, i+1), sort);
368 local val f_eq_wfrec_R_M =
369 #ant(USyntax.dest_imp(#2(USyntax.strip_forall (concl Thms.WFREC_COROLLARY))))
370 val {lhs=f, rhs} = USyntax.dest_eq f_eq_wfrec_R_M
371 val (fname,_) = dest_Free f
372 val (wfrec,_) = USyntax.strip_comb rhs
374 fun wfrec_definition0 thy fid R (functional as Abs(x, Ty, _)) =
375 let val def_name = Long_Name.base_name fid ^ "_def"
376 val wfrec_R_M = map_types poly_tvars
377 (wfrec $ map_types poly_tvars R)
379 val def_term = const_def thy (fid, Ty, wfrec_R_M)
381 Global_Theory.add_defs false [Thm.no_attributes (Binding.name def_name, def_term)] thy
387 (*---------------------------------------------------------------------------
388 * This structure keeps track of congruence rules that aren't derived
389 * from a datatype definition.
390 *---------------------------------------------------------------------------*)
391 fun extraction_thms thy =
392 let val {case_rewrites,case_congs} = Thry.extract_info thy
393 in (case_rewrites, case_congs)
397 (*---------------------------------------------------------------------------
398 * Pair patterns with termination conditions. The full list of patterns for
399 * a definition is merged with the TCs arising from the user-given clauses.
400 * There can be fewer clauses than the full list, if the user omitted some
401 * cases. This routine is used to prepare input for mk_induction.
402 *---------------------------------------------------------------------------*)
403 fun merge full_pats TCs =
404 let fun insert (p,TCs) =
405 let fun insrt ((x as (h,[]))::rst) =
406 if (p aconv h) then (p,TCs)::rst else x::insrt rst
407 | insrt (x::rst) = x::insrt rst
408 | insrt[] = raise TFL_ERR "merge.insert" "pattern not found"
410 fun pass ([],ptcl_final) = ptcl_final
411 | pass (ptcs::tcl, ptcl) = pass(tcl, insert ptcs ptcl)
413 pass (TCs, map (fn p => (p,[])) full_pats)
417 fun givens pats = map pat_of (filter given pats);
419 fun post_definition meta_tflCongs (theory, (def, pats)) =
420 let val tych = Thry.typecheck theory
421 val f = #lhs(USyntax.dest_eq(concl def))
422 val corollary = Rules.MATCH_MP Thms.WFREC_COROLLARY def
423 val pats' = filter given pats
424 val given_pats = map pat_of pats'
425 val rows = map row_of_pat pats'
426 val WFR = #ant(USyntax.dest_imp(concl corollary))
427 val R = #Rand(USyntax.dest_comb WFR)
428 val corollary' = Rules.UNDISCH corollary (* put WF R on assums *)
429 val corollaries = map (fn pat => Rules.SPEC (tych pat) corollary')
431 val (case_rewrites,context_congs) = extraction_thms theory
432 (*case_ss causes minimal simplification: bodies of case expressions are
433 not simplified. Otherwise large examples (Red-Black trees) are too
435 val case_ss = Simplifier.global_context theory
436 (HOL_basic_ss addcongs
437 (map (#weak_case_cong o snd) o Symtab.dest o Datatype.get_all) theory addsimps case_rewrites)
438 val corollaries' = map (Simplifier.simplify case_ss) corollaries
439 val extract = Rules.CONTEXT_REWRITE_RULE
440 (f, [R], @{thm cut_apply}, meta_tflCongs@context_congs)
441 val (rules, TCs) = ListPair.unzip (map extract corollaries')
442 val rules0 = map (rewrite_rule [Thms.CUT_DEF]) rules
443 val mk_cond_rule = Rules.FILTER_DISCH_ALL(not o curry (op aconv) WFR)
444 val rules1 = Rules.LIST_CONJ(map mk_cond_rule rules0)
448 full_pats_TCs = merge (map pat_of pats) (ListPair.zip (given_pats, TCs)),
453 (*---------------------------------------------------------------------------
454 * Perform the extraction without making the definition. Definition and
455 * extraction commute for the non-nested case. (Deferred recdefs)
457 * The purpose of wfrec_eqns is merely to instantiate the recursion theorem
458 * and extract termination conditions: no definition is made.
459 *---------------------------------------------------------------------------*)
461 fun wfrec_eqns thy fid tflCongs eqns =
462 let val {lhs,rhs} = USyntax.dest_eq (hd eqns)
463 val (f,args) = USyntax.strip_comb lhs
464 val (fname,fty) = dest_atom f
465 val (SV,a) = front_last args (* SV = schematic variables *)
466 val g = list_comb(f,SV)
467 val h = Free(fname,type_of g)
468 val eqns1 = map (subst_free[(g,h)]) eqns
469 val {functional as Abs(x, Ty, _), pats} = mk_functional thy eqns1
470 val given_pats = givens pats
471 (* val f = Free(x,Ty) *)
472 val Type("fun", [f_dty, f_rty]) = Ty
473 val dummy = if x<>fid then
474 raise TFL_ERR "wfrec_eqns"
475 ("Expected a definition of " ^
476 quote fid ^ " but found one of " ^
479 val (case_rewrites,context_congs) = extraction_thms thy
480 val tych = Thry.typecheck thy
481 val WFREC_THM0 = Rules.ISPEC (tych functional) Thms.WFREC_COROLLARY
482 val Const(@{const_name All},_) $ Abs(Rname,Rtype,_) = concl WFREC_THM0
483 val R = Free (Name.variant (List.foldr OldTerm.add_term_names [] eqns) Rname,
485 val WFREC_THM = Rules.ISPECL [tych R, tych g] WFREC_THM0
486 val ([proto_def, WFR],_) = USyntax.strip_imp(concl WFREC_THM)
489 writeln ("ORIGINAL PROTO_DEF: " ^
490 Syntax.string_of_term_global thy proto_def)
492 val R1 = USyntax.rand WFR
493 val corollary' = Rules.UNDISCH (Rules.UNDISCH WFREC_THM)
494 val corollaries = map (fn pat => Rules.SPEC (tych pat) corollary') given_pats
495 val corollaries' = map (rewrite_rule case_rewrites) corollaries
496 fun extract X = Rules.CONTEXT_REWRITE_RULE
497 (f, R1::SV, @{thm cut_apply}, tflCongs@context_congs) X
498 in {proto_def = proto_def,
502 extracta = map extract corollaries'}
506 (*---------------------------------------------------------------------------
507 * Define the constant after extracting the termination conditions. The
508 * wellfounded relation used in the definition is computed by using the
509 * choice operator on the extracted conditions (plus the condition that
510 * such a relation must be wellfounded).
511 *---------------------------------------------------------------------------*)
513 fun lazyR_def thy fid tflCongs eqns =
514 let val {proto_def,WFR,pats,extracta,SV} =
515 wfrec_eqns thy fid tflCongs eqns
516 val R1 = USyntax.rand WFR
517 val f = #lhs(USyntax.dest_eq proto_def)
518 val (extractants,TCl) = ListPair.unzip extracta
519 val dummy = if !trace
520 then writeln (cat_lines ("Extractants =" ::
521 map (Display.string_of_thm_global thy) extractants))
523 val TCs = fold_rev (union (op aconv)) TCl []
524 val full_rqt = WFR::TCs
525 val R' = USyntax.mk_select{Bvar=R1, Body=USyntax.list_mk_conj full_rqt}
526 val R'abs = USyntax.rand R'
527 val proto_def' = subst_free[(R1,R')] proto_def
528 val dummy = if !trace then writeln ("proto_def' = " ^
529 Syntax.string_of_term_global
532 val {lhs,rhs} = USyntax.dest_eq proto_def'
533 val (c,args) = USyntax.strip_comb lhs
534 val (name,Ty) = dest_atom c
535 val defn = const_def thy (name, Ty, USyntax.list_mk_abs (args,rhs))
536 val ([def0], theory) =
538 |> Global_Theory.add_defs false
539 [Thm.no_attributes (Binding.name (fid ^ "_def"), defn)]
540 val def = Thm.unvarify_global def0;
542 if !trace then writeln ("DEF = " ^ Display.string_of_thm_global theory def)
544 (* val fconst = #lhs(USyntax.dest_eq(concl def)) *)
545 val tych = Thry.typecheck theory
546 val full_rqt_prop = map (Dcterm.mk_prop o tych) full_rqt
547 (*lcp: a lot of object-logic inference to remove*)
548 val baz = Rules.DISCH_ALL
549 (fold_rev Rules.DISCH full_rqt_prop
550 (Rules.LIST_CONJ extractants))
551 val dum = if !trace then writeln ("baz = " ^ Display.string_of_thm_global theory baz)
553 val f_free = Free (fid, fastype_of f) (*'cos f is a Const*)
554 val SV' = map tych SV;
555 val SVrefls = map Thm.reflexive SV'
556 val def0 = (fold (fn x => fn th => Rules.rbeta(Thm.combination th x))
559 val def' = Rules.MP (Rules.SPEC (tych R') (Rules.GEN (tych R1) baz)) def0
560 val body_th = Rules.LIST_CONJ (map Rules.ASSUME full_rqt_prop)
561 val SELECT_AX = (*in this way we hope to avoid a STATIC dependence upon
562 theory Hilbert_Choice*)
563 ML_Context.thm "Hilbert_Choice.tfl_some"
564 handle ERROR msg => cat_error msg
565 "defer_recdef requires theory Main or at least Hilbert_Choice as parent"
566 val bar = Rules.MP (Rules.ISPECL[tych R'abs, tych R1] SELECT_AX) body_th
567 in {theory = theory, R=R1, SV=SV,
568 rules = fold (Utils.C Rules.MP) (Rules.CONJUNCTS bar) def',
569 full_pats_TCs = merge (map pat_of pats) (ListPair.zip (givens pats, TCl)),
575 (*----------------------------------------------------------------------------
579 *---------------------------------------------------------------------------*)
582 (*------------------------ Miscellaneous function --------------------------
584 * [x_1,...,x_n] ?v_1...v_n. M[v_1,...,v_n]
585 * -----------------------------------------------------------
586 * ( M[x_1,...,x_n], [(x_i,?v_1...v_n. M[v_1,...,v_n]),
588 * (x_j,?v_n. M[x_1,...,x_(n-1),v_n])] )
590 * This function is totally ad hoc. Used in the production of the induction
591 * theorem. The nchotomy theorem can have clauses that look like
593 * ?v1..vn. z = C vn..v1
595 * in which the order of quantification is not the order of occurrence of the
596 * quantified variables as arguments to C. Since we have no control over this
597 * aspect of the nchotomy theorem, we make the correspondence explicit by
598 * pairing the incoming new variable with the term it gets beta-reduced into.
599 *---------------------------------------------------------------------------*)
601 fun alpha_ex_unroll (xlist, tm) =
602 let val (qvars,body) = USyntax.strip_exists tm
603 val vlist = #2 (USyntax.strip_comb (USyntax.rhs body))
604 val plist = ListPair.zip (vlist, xlist)
605 val args = map (the o AList.lookup (op aconv) plist) qvars
606 handle Option => raise Fail "TFL.alpha_ex_unroll: no correspondence"
608 | build (_$rex) (v::rst) =
609 let val ex1 = Term.betapply(rex, v)
610 in ex1 :: build ex1 rst
612 val (nex::exl) = rev (tm::build tm args)
614 (nex, ListPair.zip (args, rev exl))
619 (*----------------------------------------------------------------------------
621 * PROVING COMPLETENESS OF PATTERNS
623 *---------------------------------------------------------------------------*)
625 fun mk_case ty_info usednames thy =
627 val divide = ipartition (gvvariant usednames)
628 val tych = Thry.typecheck thy
629 fun tych_binding(x,y) = (tych x, tych y)
630 fun fail s = raise TFL_ERR "mk_case" s
631 fun mk{rows=[],...} = fail"no rows"
632 | mk{path=[], rows = [([], (thm, bindings))]} =
633 Rules.IT_EXISTS (map tych_binding bindings) thm
634 | mk{path = u::rstp, rows as (p::_, _)::_} =
635 let val (pat_rectangle,rights) = ListPair.unzip rows
636 val col0 = map hd pat_rectangle
637 val pat_rectangle' = map tl pat_rectangle
639 if (forall is_Free col0) (* column 0 is all variables *)
640 then let val rights' = map (fn ((thm,theta),v) => (thm,theta@[(u,v)]))
641 (ListPair.zip (rights, col0))
642 in mk{path = rstp, rows = ListPair.zip (pat_rectangle', rights')}
644 else (* column 0 is all constructors *)
645 let val Type (ty_name,_) = type_of p
647 case (ty_info ty_name)
648 of NONE => fail("Not a known datatype: "^ty_name)
649 | SOME{constructors,nchotomy} =>
650 let val thm' = Rules.ISPEC (tych u) nchotomy
651 val disjuncts = USyntax.strip_disj (concl thm')
652 val subproblems = divide(constructors, rows)
653 val groups = map #group subproblems
654 and new_formals = map #new_formals subproblems
655 val existentials = ListPair.map alpha_ex_unroll
656 (new_formals, disjuncts)
657 val constraints = map #1 existentials
658 val vexl = map #2 existentials
659 fun expnd tm (pats,(th,b)) = (pats, (Rules.SUBS [Rules.ASSUME (tych tm)] th, b))
660 val news = map (fn (nf,rows,c) => {path = nf@rstp,
661 rows = map (expnd c) rows})
662 (Utils.zip3 new_formals groups constraints)
663 val recursive_thms = map mk news
664 val build_exists = Library.foldr
666 Rules.CHOOSE (tych x, Rules.ASSUME (tych t)) th)
667 val thms' = ListPair.map build_exists (vexl, recursive_thms)
668 val same_concls = Rules.EVEN_ORS thms'
669 in Rules.DISJ_CASESL thm' same_concls
676 fun complete_cases thy =
677 let val tych = Thry.typecheck thy
678 val ty_info = Thry.induct_info thy
680 let val names = List.foldr OldTerm.add_term_names [] pats
681 val T = type_of (hd pats)
682 val aname = Name.variant names "a"
683 val vname = Name.variant (aname::names) "v"
684 val a = Free (aname, T)
685 val v = Free (vname, T)
686 val a_eq_v = HOLogic.mk_eq(a,v)
687 val ex_th0 = Rules.EXISTS (tych (USyntax.mk_exists{Bvar=v,Body=a_eq_v}), tych a)
688 (Rules.REFL (tych a))
689 val th0 = Rules.ASSUME (tych a_eq_v)
690 val rows = map (fn x => ([x], (th0,[]))) pats
694 (Rules.CHOOSE(tych v, ex_th0)
695 (mk_case ty_info (vname::aname::names)
696 thy {path=[v], rows=rows})))
700 (*---------------------------------------------------------------------------
701 * Constructing induction hypotheses: one for each recursive call.
703 * Note. R will never occur as a variable in the ind_clause, because
704 * to do so, it would have to be from a nested definition, and we don't
705 * allow nested defns to have R variable.
707 * Note. When the context is empty, there can be no local variables.
708 *---------------------------------------------------------------------------*)
711 fun (tm1 ==> tm2) = USyntax.mk_imp{ant = tm1, conseq = tm2}
713 fun build_ih f P (pat,TCs) =
714 let val globals = USyntax.free_vars_lr pat
715 fun nested tm = is_some (USyntax.find_term (curry (op aconv) f) tm)
717 let val (cntxt,R_y_pat) = USyntax.strip_imp(#2(USyntax.strip_forall tm))
718 val (R,y,_) = USyntax.dest_relation R_y_pat
719 val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
721 of [] => (P_y, (tm,[]))
723 val imp = USyntax.list_mk_conj cntxt ==> P_y
724 val lvs = gen_rems (op aconv) (USyntax.free_vars_lr imp, globals)
725 val locals = #2(Utils.pluck (curry (op aconv) P) lvs) handle Utils.ERR _ => lvs
726 in (USyntax.list_mk_forall(locals,imp), (tm,locals)) end
729 of [] => (USyntax.list_mk_forall(globals, P$pat), [])
730 | _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs)
731 val ind_clause = USyntax.list_mk_conj ihs ==> P$pat
732 in (USyntax.list_mk_forall(globals,ind_clause), TCs_locals)
739 fun (tm1 ==> tm2) = USyntax.mk_imp{ant = tm1, conseq = tm2}
741 fun build_ih f (P,SV) (pat,TCs) =
742 let val pat_vars = USyntax.free_vars_lr pat
743 val globals = pat_vars@SV
744 fun nested tm = is_some (USyntax.find_term (curry (op aconv) f) tm)
746 let val (cntxt,R_y_pat) = USyntax.strip_imp(#2(USyntax.strip_forall tm))
747 val (R,y,_) = USyntax.dest_relation R_y_pat
748 val P_y = if (nested tm) then R_y_pat ==> P$y else P$y
750 of [] => (P_y, (tm,[]))
752 val imp = USyntax.list_mk_conj cntxt ==> P_y
753 val lvs = subtract (op aconv) globals (USyntax.free_vars_lr imp)
754 val locals = #2(Utils.pluck (curry (op aconv) P) lvs) handle Utils.ERR _ => lvs
755 in (USyntax.list_mk_forall(locals,imp), (tm,locals)) end
758 of [] => (USyntax.list_mk_forall(pat_vars, P$pat), [])
759 | _ => let val (ihs, TCs_locals) = ListPair.unzip(map dest_TC TCs)
760 val ind_clause = USyntax.list_mk_conj ihs ==> P$pat
761 in (USyntax.list_mk_forall(pat_vars,ind_clause), TCs_locals)
766 (*---------------------------------------------------------------------------
767 * This function makes good on the promise made in "build_ih".
769 * Input is tm = "(!y. R y pat ==> P y) ==> P pat",
770 * TCs = TC_1[pat] ... TC_n[pat]
771 * thm = ih1 /\ ... /\ ih_n |- ih[pat]
772 *---------------------------------------------------------------------------*)
773 fun prove_case f thy (tm,TCs_locals,thm) =
774 let val tych = Thry.typecheck thy
775 val antc = tych(#ant(USyntax.dest_imp tm))
776 val thm' = Rules.SPEC_ALL thm
777 fun nested tm = is_some (USyntax.find_term (curry (op aconv) f) tm)
778 fun get_cntxt TC = tych(#ant(USyntax.dest_imp(#2(USyntax.strip_forall(concl TC)))))
779 fun mk_ih ((TC,locals),th2,nested) =
780 Rules.GENL (map tych locals)
781 (if nested then Rules.DISCH (get_cntxt TC) th2 handle Utils.ERR _ => th2
782 else if USyntax.is_imp (concl TC) then Rules.IMP_TRANS TC th2
783 else Rules.MP th2 TC)
786 (if USyntax.is_imp(concl thm') (* recursive calls in this clause *)
787 then let val th1 = Rules.ASSUME antc
788 val TCs = map #1 TCs_locals
789 val ylist = map (#2 o USyntax.dest_relation o #2 o USyntax.strip_imp o
790 #2 o USyntax.strip_forall) TCs
791 val TClist = map (fn(TC,lvs) => (Rules.SPEC_ALL(Rules.ASSUME(tych TC)),lvs))
793 val th2list = map (Utils.C Rules.SPEC th1 o tych) ylist
794 val nlist = map nested TCs
795 val triples = Utils.zip3 TClist th2list nlist
796 val Pylist = map mk_ih triples
797 in Rules.MP thm' (Rules.LIST_CONJ Pylist) end
802 (*---------------------------------------------------------------------------
804 * x = (v1,...,vn) |- M[x]
805 * ---------------------------------------------
806 * ?v1 ... vn. x = (v1,...,vn) |- M[x]
808 *---------------------------------------------------------------------------*)
809 fun LEFT_ABS_VSTRUCT tych thm =
810 let fun CHOOSER v (tm,thm) =
811 let val ex_tm = USyntax.mk_exists{Bvar=v,Body=tm}
812 in (ex_tm, Rules.CHOOSE(tych v, Rules.ASSUME (tych ex_tm)) thm)
814 val [veq] = filter (can USyntax.dest_eq) (#1 (Rules.dest_thm thm))
815 val {lhs,rhs} = USyntax.dest_eq veq
816 val L = USyntax.free_vars_lr rhs
817 in #2 (fold_rev CHOOSER L (veq,thm)) end;
820 (*----------------------------------------------------------------------------
821 * Input : f, R, and [(pat1,TCs1),..., (patn,TCsn)]
823 * Instantiates WF_INDUCTION_THM, getting Sinduct and then tries to prove
824 * recursion induction (Rinduct) by proving the antecedent of Sinduct from
825 * the antecedent of Rinduct.
826 *---------------------------------------------------------------------------*)
827 fun mk_induction thy {fconst, R, SV, pat_TCs_list} =
828 let val tych = Thry.typecheck thy
829 val Sinduction = Rules.UNDISCH (Rules.ISPEC (tych R) Thms.WF_INDUCTION_THM)
830 val (pats,TCsl) = ListPair.unzip pat_TCs_list
831 val case_thm = complete_cases thy pats
832 val domain = (type_of o hd) pats
833 val Pname = Name.variant (List.foldr (Library.foldr OldTerm.add_term_names)
835 val P = Free(Pname, domain --> HOLogic.boolT)
836 val Sinduct = Rules.SPEC (tych P) Sinduction
837 val Sinduct_assumf = USyntax.rand ((#ant o USyntax.dest_imp o concl) Sinduct)
838 val Rassums_TCl' = map (build_ih fconst (P,SV)) pat_TCs_list
839 val (Rassums,TCl') = ListPair.unzip Rassums_TCl'
840 val Rinduct_assum = Rules.ASSUME (tych (USyntax.list_mk_conj Rassums))
841 val cases = map (fn pat => Term.betapply (Sinduct_assumf, pat)) pats
842 val tasks = Utils.zip3 cases TCl' (Rules.CONJUNCTS Rinduct_assum)
843 val proved_cases = map (prove_case fconst thy) tasks
844 val v = Free (Name.variant (List.foldr OldTerm.add_term_names [] (map concl proved_cases))
848 val substs = map (Rules.SYM o Rules.ASSUME o tych o (curry HOLogic.mk_eq v)) pats
849 val proved_cases1 = ListPair.map (fn (th,th') => Rules.SUBS[th]th')
850 (substs, proved_cases)
851 val abs_cases = map (LEFT_ABS_VSTRUCT tych) proved_cases1
852 val dant = Rules.GEN vtyped (Rules.DISJ_CASESL (Rules.ISPEC vtyped case_thm) abs_cases)
853 val dc = Rules.MP Sinduct dant
854 val Parg_ty = type_of(#Bvar(USyntax.dest_forall(concl dc)))
855 val vars = map (gvvariant[Pname]) (USyntax.strip_prod_type Parg_ty)
856 val dc' = fold_rev (Rules.GEN o tych) vars
857 (Rules.SPEC (tych(USyntax.mk_vstruct Parg_ty vars)) dc)
859 Rules.GEN (tych P) (Rules.DISCH (tych(concl Rinduct_assum)) dc')
861 handle Utils.ERR _ => raise TFL_ERR "mk_induction" "failed derivation";
866 (*---------------------------------------------------------------------------
870 *---------------------------------------------------------------------------*)
873 fun simplify_induction thy hth ind =
874 let val tych = Thry.typecheck thy
875 val (asl,_) = Rules.dest_thm ind
876 val (_,tc_eq_tc') = Rules.dest_thm hth
877 val tc = USyntax.lhs tc_eq_tc'
880 if (can (Thry.match_term thy asm) tc)
883 (Rules.MATCH_MP Thms.simp_thm (Rules.DISCH (tych asm) ind))
890 (*---------------------------------------------------------------------------
891 * The termination condition is an antecedent to the rule, and an
892 * assumption to the theorem.
893 *---------------------------------------------------------------------------*)
894 fun elim_tc tcthm (rule,induction) =
895 (Rules.MP rule tcthm, Rules.PROVE_HYP tcthm induction)
899 if !trace then writeln (cat_lines (s :: map Display.string_of_thm_without_context L))
902 fun trace_cterm s ct =
904 writeln (cat_lines [s, Syntax.string_of_term_global (Thm.theory_of_cterm ct) (Thm.term_of ct)])
908 fun postprocess strict {wf_tac, terminator, simplifier} theory {rules,induction,TCs} =
909 let val tych = Thry.typecheck theory
910 val prove = Rules.prove strict;
912 (*---------------------------------------------------------------------
913 * Attempt to eliminate WF condition. It's the only assumption of rules
914 *---------------------------------------------------------------------*)
915 val (rules1,induction1) =
916 let val thm = prove(tych(HOLogic.mk_Trueprop
917 (hd(#1(Rules.dest_thm rules)))),
919 in (Rules.PROVE_HYP thm rules, Rules.PROVE_HYP thm induction)
920 end handle Utils.ERR _ => (rules,induction);
922 (*----------------------------------------------------------------------
923 * The termination condition (tc) is simplified to |- tc = tc' (there
924 * might not be a change!) and then 3 attempts are made:
926 * 1. if |- tc = T, then eliminate it with eqT; otherwise,
927 * 2. apply the terminator to tc'. If |- tc' = T then eliminate; else
928 * 3. replace tc by tc' in both the rules and the induction theorem.
929 *---------------------------------------------------------------------*)
931 fun simplify_tc tc (r,ind) =
932 let val tc1 = tych tc
933 val _ = trace_cterm "TC before simplification: " tc1
934 val tc_eq = simplifier tc1
935 val _ = trace_thms "result: " [tc_eq]
937 elim_tc (Rules.MATCH_MP Thms.eqT tc_eq) (r,ind)
938 handle Utils.ERR _ =>
939 (elim_tc (Rules.MATCH_MP(Rules.MATCH_MP Thms.rev_eq_mp tc_eq)
940 (prove(tych(HOLogic.mk_Trueprop(USyntax.rhs(concl tc_eq))),
943 handle Utils.ERR _ =>
944 (Rules.UNDISCH(Rules.MATCH_MP (Rules.MATCH_MP Thms.simp_thm r) tc_eq),
945 simplify_induction theory tc_eq ind))
948 (*----------------------------------------------------------------------
949 * Nested termination conditions are harder to get at, since they are
950 * left embedded in the body of the function (and in induction
951 * theorem hypotheses). Our "solution" is to simplify them, and try to
952 * prove termination, but leave the application of the resulting theorem
953 * to a higher level. So things go much as in "simplify_tc": the
954 * termination condition (tc) is simplified to |- tc = tc' (there might
955 * not be a change) and then 2 attempts are made:
957 * 1. if |- tc = T, then return |- tc; otherwise,
958 * 2. apply the terminator to tc'. If |- tc' = T then return |- tc; else
959 * 3. return |- tc = tc'
960 *---------------------------------------------------------------------*)
961 fun simplify_nested_tc tc =
962 let val tc_eq = simplifier (tych (#2 (USyntax.strip_forall tc)))
965 (Rules.MATCH_MP Thms.eqT tc_eq
966 handle Utils.ERR _ =>
967 (Rules.MATCH_MP(Rules.MATCH_MP Thms.rev_eq_mp tc_eq)
968 (prove(tych(HOLogic.mk_Trueprop (USyntax.rhs(concl tc_eq))),
970 handle Utils.ERR _ => tc_eq))
973 (*-------------------------------------------------------------------
974 * Attempt to simplify the termination conditions in each rule and
975 * in the induction theorem.
976 *-------------------------------------------------------------------*)
977 fun strip_imp tm = if USyntax.is_neg tm then ([],tm) else USyntax.strip_imp tm
978 fun loop ([],extras,R,ind) = (rev R, ind, extras)
979 | loop ((r,ftcs)::rst, nthms, R, ind) =
980 let val tcs = #1(strip_imp (concl r))
981 val extra_tcs = subtract (op aconv) tcs ftcs
982 val extra_tc_thms = map simplify_nested_tc extra_tcs
983 val (r1,ind1) = fold simplify_tc tcs (r,ind)
984 val r2 = Rules.FILTER_DISCH_ALL(not o USyntax.is_WFR) r1
985 in loop(rst, nthms@extra_tc_thms, r2::R, ind1)
987 val rules_tcs = ListPair.zip (Rules.CONJUNCTS rules1, TCs)
988 val (rules2,ind2,extras) = loop(rules_tcs,[],[],induction1)
990 {induction = ind2, rules = Rules.LIST_CONJ rules2, nested_tcs = extras}