--- a/src/ZF/intr_elim.ML Mon Dec 28 16:58:11 1998 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,165 +0,0 @@
-(* Title: ZF/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*)
- val type_intrs : thm list (*type-checking intro rules*)
- val type_elims : thm list (*type-checking elim rules*)
- end;
-
-
-signature INDUCTIVE_I = (** Terms read from the theory section **)
- sig
- val rec_tms : term list (*the recursive sets*)
- val dom_sum : term (*their common domain*)
- 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 bnd_mono : thm (*monotonicity for the lfp definition*)
- val dom_subset : thm (*inclusion of recursive set in dom*)
- val intrs : thm list (*introduction rules*)
- val elim : thm (*case analysis theorem*)
- val mk_cases : thm list -> string -> thm (*generates case theorems*)
- end;
-
-signature INTR_ELIM_AUX = (** Used to make induction rules **)
- sig
- val raw_induct : thm (*raw induction rule from Fp.induct*)
- 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 and Pr : PR and Su : SU)
- : sig include INTR_ELIM INTR_ELIM_AUX end =
-let
-
-val rec_names = map (#1 o dest_Const o head_of) Inductive.rec_tms;
-val big_rec_base_name = space_implode "_" (map Sign.base_name rec_names);
-
-val _ = deny (big_rec_base_name mem (Sign.stamp_names_of (sign_of Inductive.thy)))
- ("Definition " ^ big_rec_base_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 Inductive.thy)
- (case rec_names of [_] => rec_names | _ => big_rec_base_name::rec_names);
-
-
-val sign = sign_of Inductive.thy;
-
-(********)
-val _ = writeln " Proving monotonicity...";
-
-val Const("==",_) $ _ $ (_ $ dom_sum $ fp_abs) =
- big_rec_def |> rep_thm |> #prop |> Logic.unvarify;
-
-val bnd_mono =
- prove_goalw_cterm []
- (cterm_of sign (FOLogic.mk_Trueprop (Fp.bnd_mono $ dom_sum $ fp_abs)))
- (fn _ =>
- [rtac (Collect_subset RS bnd_monoI) 1,
- REPEAT (ares_tac (basic_monos @ Inductive.monos) 1)]);
-
-val dom_subset = standard (big_rec_def RS Fp.subs);
-
-val unfold = standard ([big_rec_def, bnd_mono] MRS Fp.Tarski);
-
-(********)
-val _ = writeln " Proving the introduction rules...";
-
-(*Mutual recursion? Helps to derive subset rules for the individual sets.*)
-val Part_trans =
- case rec_names of
- [_] => asm_rl
- | _ => standard (Part_subset RS subset_trans);
-
-(*To type-check recursive occurrences of the inductive sets, possibly
- enclosed in some monotonic operator M.*)
-val rec_typechecks =
- [dom_subset] RL (asm_rl :: ([Part_trans] RL Inductive.monos)) RL [subsetD];
-
-(*Type-checking is hardest aspect of proof;
- disjIn selects the correct disjunct after unfolding*)
-fun intro_tacsf disjIn prems =
- [(*insert prems and underlying sets*)
- cut_facts_tac prems 1,
- DETERM (stac unfold 1),
- REPEAT (resolve_tac [Part_eqI,CollectI] 1),
- (*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*)
- rtac disjIn 2,
- (*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] 2 APPEND assume_tac 2),
- (*Now solve the equations like Tcons(a,f) = Inl(?b4)*)
- rewrite_goals_tac Inductive.con_defs,
- REPEAT (rtac refl 2),
- (*Typechecking; this can fail*)
- REPEAT (FIRSTGOAL ( dresolve_tac rec_typechecks
- ORELSE' eresolve_tac (asm_rl::PartE::SigmaE2::
- Inductive.type_elims)
- ORELSE' hyp_subst_tac)),
- DEPTH_SOLVE (swap_res_tac (SigmaI::subsetI::Inductive.type_intrs) 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 = ListPair.map (uncurry (prove_goalw_cterm part_rec_defs))
- (map (cterm_of sign) Inductive.intr_tms,
- map intro_tacsf (mk_disj_rls(length Inductive.intr_tms)));
-
-(********)
-val _ = writeln " Proving the elimination rule...";
-
-(*Breaks down logical connectives in the monotonic function*)
-val basic_elim_tac =
- REPEAT (SOMEGOAL (eresolve_tac (Ind_Syntax.elim_rls @ Su.free_SEs)
- ORELSE' bound_hyp_subst_tac))
- THEN prune_params_tac
- (*Mutual recursion: collapse references to Part(D,h)*)
- THEN fold_tac part_rec_defs;
-
-in
- struct
- val thy = Inductive.thy
- and defs = big_rec_def :: part_rec_defs
- and bnd_mono = bnd_mono
- and dom_subset = dom_subset
- and intrs = intrs;
-
- val elim = rule_by_tactic basic_elim_tac
- (unfold RS Ind_Syntax.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.
- String s should have the form t:Si where Si is an inductive set*)
- fun mk_cases defs s =
- rule_by_tactic (rewrite_goals_tac defs THEN
- basic_elim_tac THEN
- fold_tac defs)
- (assume_read Inductive.thy s RS elim)
- |> standard;
-
- val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct)
- and rec_names = rec_names
- end
-end;
-