--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/intr_elim.ML Fri Mar 03 12:02:25 1995 +0100
@@ -0,0 +1,141 @@
+(* 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;
+