TFL/post.sml
author paulson
Fri, 23 Apr 1999 12:23:21 +0200
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Now for recdefs that omit the WF relation; removed the separation between draft and theory modes
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(*  Title:      TFL/post
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    ID:         $Id$
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    Author:     Konrad Slind, Cambridge University Computer Laboratory
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    Copyright   1997  University of Cambridge
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Postprocessing of TFL definitions
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*)
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signature TFL = 
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  sig
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   structure Prim : TFL_sig
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   val tgoalw : theory -> thm list -> thm list -> thm list
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   val tgoal: theory -> thm list -> thm list
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   val std_postprocessor : simpset -> theory 
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                           -> {induction:thm, rules:thm, TCs:term list list} 
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                           -> {induction:thm, rules:thm, nested_tcs:thm list}
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   val define_i : theory -> xstring -> term -> term list
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                  -> theory * Prim.pattern list
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   val define   : theory -> xstring -> string -> string list 
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                  -> theory * Prim.pattern list
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   val function_i : theory -> xstring 
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                  -> thm list (* congruence rules *)
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                  -> term list -> theory * thm
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   val function : theory -> xstring 
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                  -> thm list 
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                  -> string list -> theory * thm
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   val simplify_defn : simpset * thm list 
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                        -> theory * (string * Prim.pattern list)
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                        -> {rules:thm list, induct:thm, tcs:term list}
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  end;
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structure Tfl: TFL =
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struct
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 structure Prim = Prim
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 structure S = USyntax
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 val trace = Prim.trace
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 (*---------------------------------------------------------------------------
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  * Extract termination goals so that they can be put it into a goalstack, or 
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  * have a tactic directly applied to them.
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  *--------------------------------------------------------------------------*)
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 fun termination_goals rules = 
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     map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)
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       (foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
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 (*---------------------------------------------------------------------------
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  * Finds the termination conditions in (highly massaged) definition and 
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  * puts them into a goalstack.
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  *--------------------------------------------------------------------------*)
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 fun tgoalw thy defs rules = 
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   case termination_goals rules of
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       [] => error "tgoalw: no termination conditions to prove"
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     | L  => goalw_cterm defs 
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	       (Thm.cterm_of (Theory.sign_of thy) 
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			 (HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));
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 fun tgoal thy = tgoalw thy [];
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 (*---------------------------------------------------------------------------
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 * Three postprocessors are applied to the definition.  It
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 * attempts to prove wellfoundedness of the given relation, simplifies the
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 * non-proved termination conditions, and finally attempts to prove the 
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 * simplified termination conditions.
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 *--------------------------------------------------------------------------*)
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 fun std_postprocessor ss =
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   Prim.postprocess
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    {WFtac      = REPEAT (ares_tac [wf_empty, wf_pred_nat, 
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				    wf_measure, wf_inv_image, 
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				    wf_lex_prod, wf_less_than, wf_trancl] 1),
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     terminator = asm_simp_tac ss 1
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		  THEN TRY(CLASET' (fn cs => best_tac
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			   (cs addSDs [not0_implies_Suc] addss ss)) 1),
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     simplifier = Rules.simpl_conv ss []};
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 val concl = #2 o Rules.dest_thm;
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 (*---------------------------------------------------------------------------
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  * Defining a function with an associated termination relation. 
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  *---------------------------------------------------------------------------*)
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 fun define_i thy fid R eqs = 
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   let val {functional,pats} = Prim.mk_functional thy eqs
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   in (Prim.wfrec_definition0 thy (Sign.base_name fid) R functional, pats)
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   end;
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 fun define thy fid R eqs = 
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   let fun read thy = readtm (Theory.sign_of thy) (TVar(("DUMMY",0),[])) 
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   in  define_i thy fid (read thy R) (map (read thy) eqs)  end
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   handle Utils.ERR {mesg,...} => error mesg;
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(*---------------------------------------------------------------------------
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 * Postprocess a definition made by "define". This is a separate stage of 
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 * processing from the definition stage.
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 *---------------------------------------------------------------------------*)
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 local 
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 structure R = Rules
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 structure U = Utils
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 (* The rest of these local definitions are for the tricky nested case *)
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 val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl
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 fun id_thm th = 
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    let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th))))
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    in lhs aconv rhs
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    end handle _ => false
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 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
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 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
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 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
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 fun mk_meta_eq r = case concl_of r of
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      Const("==",_)$_$_ => r
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   |   _ $(Const("op =",_)$_$_) => r RS eq_reflection
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   |   _ => r RS P_imp_P_eq_True
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 (*Is this the best way to invoke the simplifier??*)
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 fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
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 fun join_assums th = 
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   let val {sign,...} = rep_thm th
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       val tych = cterm_of sign
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       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
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       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
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       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
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       val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
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   in 
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     R.GEN_ALL 
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       (R.DISCH_ALL 
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	  (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
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   end
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   val gen_all = S.gen_all
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 in
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 fun proof_stage ss theory {f, R, rules, full_pats_TCs, TCs} =
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   let val dummy = writeln "Proving induction theorem..  "
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       val ind = Prim.mk_induction theory 
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                    {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
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       val dummy = writeln "Proved induction theorem.\nPostprocessing..  "
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       val {rules, induction, nested_tcs} = 
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	   std_postprocessor ss theory {rules=rules, induction=ind, TCs=TCs}
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   in
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   case nested_tcs
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   of [] => (writeln "Postprocessing done.";
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	     {induction=induction, rules=rules,tcs=[]})
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   | L  => let val dummy = writeln "Simplifying nested TCs..  "
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	       val (solved,simplified,stubborn) =
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		U.itlist (fn th => fn (So,Si,St) =>
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		      if (id_thm th) then (So, Si, th::St) else
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		      if (solved th) then (th::So, Si, St) 
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		      else (So, th::Si, St)) nested_tcs ([],[],[])
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	       val simplified' = map join_assums simplified
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	       val rewr = full_simplify (ss addsimps (solved @ simplified'));
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	       val induction' = rewr induction
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	       and rules'     = rewr rules
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	       val dummy = writeln "Postprocessing done."
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	   in
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	   {induction = induction',
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		rules = rules',
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		  tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
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			    (simplified@stubborn)}
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	   end
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   end;
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 (*lcp: curry the predicate of the induction rule*)
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 fun curry_rule rl = split_rule_var
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			 (head_of (HOLogic.dest_Trueprop (concl_of rl)), 
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			  rl);
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 (*lcp: put a theorem into Isabelle form, using meta-level connectives*)
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 val meta_outer = 
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     curry_rule o standard o 
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     rule_by_tactic (REPEAT 
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		     (FIRSTGOAL (resolve_tac [allI, impI, conjI]
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				 ORELSE' etac conjE)));
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 (*Strip off the outer !P*)
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 val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
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 val wf_rel_defs = [lex_prod_def, measure_def, inv_image_def];
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 (*Convert conclusion from = to ==*)
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 val eq_reflect_list = map (fn th => (th RS eq_reflection) handle _ => th);
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 (*---------------------------------------------------------------------------
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  * Install the basic context notions. Others (for nat and list and prod) 
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  * have already been added in thry.sml
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  *---------------------------------------------------------------------------*)
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 fun simplify_defn (ss, tflCongs) (thy,(id,pats)) =
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    let val dummy = deny (id mem (Sign.stamp_names_of (Theory.sign_of thy)))
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			 ("Recursive definition " ^ id ^ 
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			  " would clash with the theory of the same name!")
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	val def = freezeT(get_def thy id)   RS   meta_eq_to_obj_eq
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	val {theory,rules,TCs,full_pats_TCs,patterns} = 
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		 Prim.post_definition (Prim.congs tflCongs)
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		    (thy, (def,pats))
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	val {lhs=f,rhs} = S.dest_eq(concl def)
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	val (_,[R,_]) = S.strip_comb rhs
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	val ss' = ss addsimps Prim.default_simps
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	val {induction, rules, tcs} = 
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	      proof_stage ss' theory 
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		{f = f, R = R, rules = rules,
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		 full_pats_TCs = full_pats_TCs,
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		 TCs = TCs}
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	val rules' = map (standard o normalize_thm [RSmp]) (R.CONJUNCTS rules)
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    in  {induct = meta_outer
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		   (normalize_thm [RSspec,RSmp] (induction RS spec')), 
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	 rules = rules', 
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	 tcs = (termination_goals rules') @ tcs}
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    end
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   handle Utils.ERR {mesg,func,module} => 
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		error (mesg ^ 
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		       "\n    (In TFL function " ^ module ^ "." ^ func ^ ")");
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(*---------------------------------------------------------------------------
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 *
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 *     Definitions with synthesized termination relation
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 *
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 *---------------------------------------------------------------------------*)
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 local open USyntax
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 in 
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 fun func_of_cond_eqn tm =
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   #1(strip_comb(#lhs(dest_eq(#2 (strip_forall(#2(strip_imp tm)))))))
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 end;
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 fun function_i thy fid congs eqs = 
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  let val dum = Theory.requires thy "WF_Rel" "recursive function definitions"
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      val {rules,R,theory,full_pats_TCs,SV,...} = 
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	      Prim.lazyR_def thy fid congs eqs
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      val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules))
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      val dummy = writeln "Definition made.\nProving induction theorem..  "
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      val induction = Prim.mk_induction theory 
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                         {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
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      val dummy = writeln "Induction theorem proved."
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  in (theory, 
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      (*return the conjoined induction rule and recursion equations, 
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	with assumptions remaining to discharge*)
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      standard (induction RS (rules RS conjI)))
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  end
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 fun function thy fid congs seqs = 
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   let val _ =  writeln ("Deferred recursive function " ^ fid)
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       fun read thy = readtm (Theory.sign_of thy) (TVar(("DUMMY",0),[])) 
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   in  function_i thy fid congs (map (read thy) seqs)  end
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   handle Utils.ERR {mesg,...} => error mesg;
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 end;
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end;