diff -r f04b33ce250f -r a4dc62a46ee4 intr_elim.ML --- a/intr_elim.ML Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,141 +0,0 @@ -(* Title: HOL/intr_elim.ML - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1994 University of Cambridge - -Introduction/elimination rule module -- for Inductive/Coinductive Definitions -*) - -signature INDUCTIVE_ARG = (** Description of a (co)inductive def **) - sig - val thy : theory (*new theory with inductive defs*) - val monos : thm list (*monotonicity of each M operator*) - val con_defs : thm list (*definitions of the constructors*) - end; - -(*internal items*) -signature INDUCTIVE_I = - sig - val rec_tms : term list (*the recursive sets*) - val intr_tms : term list (*terms for the introduction rules*) - end; - -signature INTR_ELIM = - sig - val thy : theory (*copy of input theory*) - val defs : thm list (*definitions made in thy*) - val mono : thm (*monotonicity for the lfp definition*) - val unfold : thm (*fixed-point equation*) - val intrs : thm list (*introduction rules*) - val elim : thm (*case analysis theorem*) - val raw_induct : thm (*raw induction rule from Fp.induct*) - val mk_cases : thm list -> string -> thm (*generates case theorems*) - val rec_names : string list (*names of recursive sets*) - end; - -(*prove intr/elim rules for a fixedpoint definition*) -functor Intr_elim_Fun - (structure Inductive: sig include INDUCTIVE_ARG INDUCTIVE_I end - and Fp: FP) : INTR_ELIM = -struct -open Logic Inductive Ind_Syntax; - -val rec_names = map (#1 o dest_Const o head_of) rec_tms; -val big_rec_name = space_implode "_" rec_names; - -val _ = deny (big_rec_name mem map ! (stamps_of_thy thy)) - ("Definition " ^ big_rec_name ^ - " would clash with the theory of the same name!"); - -(*fetch fp definitions from the theory*) -val big_rec_def::part_rec_defs = - map (get_def thy) - (case rec_names of [_] => rec_names | _ => big_rec_name::rec_names); - - -val sign = sign_of thy; - -(********) -val _ = writeln " Proving monotonicity..."; - -val Const("==",_) $ _ $ (Const(_,fpT) $ fp_abs) = - big_rec_def |> rep_thm |> #prop |> unvarify; - -(*For the type of the argument of mono*) -val [monoT] = binder_types fpT; - -val mono = - prove_goalw_cterm [] - (cterm_of sign (mk_Trueprop (Const("mono", monoT-->boolT) $ fp_abs))) - (fn _ => - [rtac monoI 1, - REPEAT (ares_tac (basic_monos @ monos) 1)]); - -val unfold = standard (mono RS (big_rec_def RS Fp.Tarski)); - -(********) -val _ = writeln " Proving the introduction rules..."; - -fun intro_tacsf disjIn prems = - [(*insert prems and underlying sets*) - cut_facts_tac prems 1, - rtac (unfold RS ssubst) 1, - REPEAT (resolve_tac [Part_eqI,CollectI] 1), - (*Now 1-2 subgoals: the disjunction, perhaps equality.*) - rtac disjIn 1, - (*Not ares_tac, since refl must be tried before any equality assumptions; - backtracking may occur if the premises have extra variables!*) - DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 ORELSE assume_tac 1)]; - -(*combines disjI1 and disjI2 to access the corresponding nested disjunct...*) -val mk_disj_rls = - let fun f rl = rl RS disjI1 - and g rl = rl RS disjI2 - in accesses_bal(f, g, asm_rl) end; - -val intrs = map (uncurry (prove_goalw_cterm part_rec_defs)) - (map (cterm_of sign) intr_tms ~~ - map intro_tacsf (mk_disj_rls(length intr_tms))); - -(********) -val _ = writeln " Proving the elimination rule..."; - -(*Includes rules for Suc and Pair since they are common constructions*) -val elim_rls = [asm_rl, FalseE, Suc_neq_Zero, Zero_neq_Suc, - make_elim Suc_inject, - refl_thin, conjE, exE, disjE]; - -(*Breaks down logical connectives in the monotonic function*) -val basic_elim_tac = - REPEAT (SOMEGOAL (eresolve_tac (elim_rls@sumprod_free_SEs) - ORELSE' bound_hyp_subst_tac)) - THEN prune_params_tac; - -val elim = rule_by_tactic basic_elim_tac (unfold RS equals_CollectD); - -(*Applies freeness of the given constructors, which *must* be unfolded by - the given defs. Cannot simply use the local con_defs because con_defs=[] - for inference systems. -fun con_elim_tac defs = - rewrite_goals_tac defs THEN basic_elim_tac THEN fold_tac defs; - *) -fun con_elim_tac simps = - let val elim_tac = REPEAT o (eresolve_tac (elim_rls@sumprod_free_SEs)) - in ALLGOALS(EVERY'[elim_tac, - asm_full_simp_tac (nat_ss addsimps simps), - elim_tac, - REPEAT o bound_hyp_subst_tac]) - THEN prune_params_tac - end; - - -(*String s should have the form t:Si where Si is an inductive set*) -fun mk_cases defs s = - rule_by_tactic (con_elim_tac defs) - (assume_read thy s RS elim); - -val defs = big_rec_def::part_rec_defs; - -val raw_induct = standard ([big_rec_def, mono] MRS Fp.induct); -end; -