wenzelm@10769: (*  Title:      TFL/post.ML
wenzelm@10769:     ID:         $Id$
wenzelm@10769:     Author:     Konrad Slind, Cambridge University Computer Laboratory
wenzelm@10769:     Copyright   1997  University of Cambridge
wenzelm@10769: 
wenzelm@10769: Second part of main module (postprocessing of TFL definitions).
wenzelm@10769: *)
wenzelm@10769: 
wenzelm@10769: signature TFL =
wenzelm@10769: sig
wenzelm@10769:   val trace: bool ref
wenzelm@10769:   val quiet_mode: bool ref
wenzelm@10769:   val message: string -> unit
wenzelm@10769:   val tgoalw: theory -> thm list -> thm list -> thm list
wenzelm@10769:   val tgoal: theory -> thm list -> thm list
wenzelm@11632:   val define_i: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring ->
wenzelm@10769:     term -> term list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
wenzelm@11632:   val define: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring ->
wenzelm@10769:     string -> string list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
wenzelm@10769:   val defer_i: theory -> thm list -> xstring -> term list -> theory * thm
wenzelm@10769:   val defer: theory -> thm list -> xstring -> string list -> theory * thm
wenzelm@10769: end;
wenzelm@10769: 
wenzelm@10769: structure Tfl: TFL =
wenzelm@10769: struct
wenzelm@10769: 
wenzelm@10769: structure S = USyntax
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: (* messages *)
wenzelm@10769: 
wenzelm@10769: val trace = Prim.trace
wenzelm@10769: 
wenzelm@10769: val quiet_mode = ref false;
wenzelm@10769: fun message s = if ! quiet_mode then () else writeln s;
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: (* misc *)
wenzelm@10769: 
wenzelm@12341: val read_term = Thm.term_of oo (HOLogic.read_cterm o Theory.sign_of);
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  * Extract termination goals so that they can be put it into a goalstack, or
wenzelm@10769:  * have a tactic directly applied to them.
wenzelm@10769:  *--------------------------------------------------------------------------*)
wenzelm@10769: fun termination_goals rules =
wenzelm@10769:     map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)
wenzelm@10769:       (foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  * Finds the termination conditions in (highly massaged) definition and
wenzelm@10769:  * puts them into a goalstack.
wenzelm@10769:  *--------------------------------------------------------------------------*)
wenzelm@10769: fun tgoalw thy defs rules =
wenzelm@10769:   case termination_goals rules of
wenzelm@10769:       [] => error "tgoalw: no termination conditions to prove"
wenzelm@10769:     | L  => goalw_cterm defs
wenzelm@10769:               (Thm.cterm_of (Theory.sign_of thy)
wenzelm@10769:                         (HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));
wenzelm@10769: 
wenzelm@10769: fun tgoal thy = tgoalw thy [];
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  * Three postprocessors are applied to the definition.  It
wenzelm@10769:  * attempts to prove wellfoundedness of the given relation, simplifies the
wenzelm@10769:  * non-proved termination conditions, and finally attempts to prove the
wenzelm@10769:  * simplified termination conditions.
wenzelm@10769:  *--------------------------------------------------------------------------*)
wenzelm@11632: fun std_postprocessor strict cs ss wfs =
wenzelm@11632:   Prim.postprocess strict
wenzelm@10769:    {wf_tac     = REPEAT (ares_tac wfs 1),
wenzelm@10769:     terminator = asm_simp_tac ss 1
nipkow@12488:                  THEN TRY (arith_tac 1 ORELSE
nipkow@12488:                            fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1),
wenzelm@10769:     simplifier = Rules.simpl_conv ss []};
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: val concl = #2 o Rules.dest_thm;
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  * Postprocess a definition made by "define". This is a separate stage of
wenzelm@10769:  * processing from the definition stage.
wenzelm@10769:  *---------------------------------------------------------------------------*)
wenzelm@10769: local
wenzelm@10769: structure R = Rules
wenzelm@10769: structure U = Utils
wenzelm@10769: 
wenzelm@10769: (* The rest of these local definitions are for the tricky nested case *)
wenzelm@10769: val solved = not o can S.dest_eq o #2 o S.strip_forall o concl
wenzelm@10769: 
wenzelm@10769: fun id_thm th =
wenzelm@10769:    let val {lhs,rhs} = S.dest_eq (#2 (S.strip_forall (#2 (R.dest_thm th))));
wenzelm@10769:    in lhs aconv rhs end
wenzelm@10769:    handle U.ERR _ => false;
wenzelm@10769:    
wenzelm@10769: 
wenzelm@10769: fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
wenzelm@10769: val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
wenzelm@10769: val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
wenzelm@10769: fun mk_meta_eq r = case concl_of r of
wenzelm@10769:      Const("==",_)$_$_ => r
wenzelm@10769:   |   _ $(Const("op =",_)$_$_) => r RS eq_reflection
wenzelm@10769:   |   _ => r RS P_imp_P_eq_True
wenzelm@10769: 
wenzelm@10769: (*Is this the best way to invoke the simplifier??*)
wenzelm@10769: fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
wenzelm@10769: 
wenzelm@10769: fun join_assums th =
wenzelm@10769:   let val {sign,...} = rep_thm th
wenzelm@10769:       val tych = cterm_of sign
wenzelm@10769:       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
wenzelm@10769:       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
wenzelm@10769:       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
wenzelm@10769:       val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
wenzelm@10769:   in
wenzelm@10769:     R.GEN_ALL
wenzelm@10769:       (R.DISCH_ALL
wenzelm@10769:          (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
wenzelm@10769:   end
wenzelm@10769:   val gen_all = S.gen_all
wenzelm@10769: in
wenzelm@11632: fun proof_stage strict cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =
wenzelm@10769:   let
wenzelm@10769:     val _ = message "Proving induction theorem ..."
wenzelm@10769:     val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
wenzelm@10769:     val _ = message "Postprocessing ...";
wenzelm@10769:     val {rules, induction, nested_tcs} =
wenzelm@11632:       std_postprocessor strict cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}
wenzelm@10769:   in
wenzelm@10769:   case nested_tcs
wenzelm@10769:   of [] => {induction=induction, rules=rules,tcs=[]}
wenzelm@10769:   | L  => let val dummy = message "Simplifying nested TCs ..."
wenzelm@10769:               val (solved,simplified,stubborn) =
wenzelm@10769:                U.itlist (fn th => fn (So,Si,St) =>
wenzelm@10769:                      if (id_thm th) then (So, Si, th::St) else
wenzelm@10769:                      if (solved th) then (th::So, Si, St)
wenzelm@10769:                      else (So, th::Si, St)) nested_tcs ([],[],[])
wenzelm@10769:               val simplified' = map join_assums simplified
wenzelm@10769:               val rewr = full_simplify (ss addsimps (solved @ simplified'));
wenzelm@10769:               val induction' = rewr induction
wenzelm@10769:               and rules'     = rewr rules
wenzelm@10769:           in
wenzelm@10769:           {induction = induction',
wenzelm@10769:                rules = rules',
wenzelm@10769:                  tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
wenzelm@10769:                            (simplified@stubborn)}
wenzelm@10769:           end
wenzelm@10769:   end;
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: (*lcp: curry the predicate of the induction rule*)
wenzelm@11038: fun curry_rule rl =
wenzelm@11038:   SplitRule.split_rule_var (Term.head_of (HOLogic.dest_Trueprop (concl_of rl)), rl);
wenzelm@10769: 
wenzelm@10769: (*lcp: put a theorem into Isabelle form, using meta-level connectives*)
wenzelm@10769: val meta_outer =
wenzelm@11038:   curry_rule o standard o
wenzelm@11038:   rule_by_tactic (REPEAT (FIRSTGOAL (resolve_tac [allI, impI, conjI] ORELSE' etac conjE)));
wenzelm@10769: 
wenzelm@10769: (*Strip off the outer !P*)
wenzelm@10769: val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
wenzelm@10769: 
wenzelm@11632: fun simplify_defn strict thy cs ss congs wfs id pats def0 =
wenzelm@10769:    let val def = freezeT def0 RS meta_eq_to_obj_eq
wenzelm@10769:        val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats))
wenzelm@10769:        val {lhs=f,rhs} = S.dest_eq (concl def)
wenzelm@10769:        val (_,[R,_]) = S.strip_comb rhs
wenzelm@10769:        val {induction, rules, tcs} =
wenzelm@11632:              proof_stage strict cs ss wfs theory
wenzelm@10769:                {f = f, R = R, rules = rules,
wenzelm@10769:                 full_pats_TCs = full_pats_TCs,
wenzelm@10769:                 TCs = TCs}
wenzelm@11771:        val rules' = map (standard o ObjectLogic.rulify_no_asm) (R.CONJUNCTS rules)
wenzelm@11771:    in  {induct = meta_outer (ObjectLogic.rulify_no_asm (induction RS spec')),
wenzelm@10769:         rules = ListPair.zip(rules', rows),
wenzelm@10769:         tcs = (termination_goals rules') @ tcs}
wenzelm@10769:    end
wenzelm@10769:   handle U.ERR {mesg,func,module} =>
wenzelm@10769:                error (mesg ^
wenzelm@10769:                       "\n    (In TFL function " ^ module ^ "." ^ func ^ ")");
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  * Defining a function with an associated termination relation.
wenzelm@10769:  *---------------------------------------------------------------------------*)
wenzelm@11632: fun define_i strict thy cs ss congs wfs fid R eqs =
wenzelm@10769:   let val {functional,pats} = Prim.mk_functional thy eqs
wenzelm@10769:       val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional
wenzelm@11632:   in (thy, simplify_defn strict thy cs ss congs wfs fid pats def) end;
wenzelm@10769: 
wenzelm@11632: fun define strict thy cs ss congs wfs fid R seqs =
wenzelm@11632:   define_i strict thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)
wenzelm@10769:     handle U.ERR {mesg,...} => error mesg;
wenzelm@10769: 
wenzelm@10769: 
wenzelm@10769: (*---------------------------------------------------------------------------
wenzelm@10769:  *
wenzelm@10769:  *     Definitions with synthesized termination relation
wenzelm@10769:  *
wenzelm@10769:  *---------------------------------------------------------------------------*)
wenzelm@10769: 
wenzelm@10769: fun func_of_cond_eqn tm =
wenzelm@10769:   #1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm)))))));
wenzelm@10769: 
wenzelm@10769: fun defer_i thy congs fid eqs =
wenzelm@10769:  let val {rules,R,theory,full_pats_TCs,SV,...} =
wenzelm@10769:              Prim.lazyR_def thy (Sign.base_name fid) congs eqs
wenzelm@10769:      val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules));
wenzelm@10769:      val dummy = message "Proving induction theorem ...";
wenzelm@10769:      val induction = Prim.mk_induction theory
wenzelm@10769:                         {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
wenzelm@10769:  in (theory,
wenzelm@10769:      (*return the conjoined induction rule and recursion equations,
wenzelm@10769:        with assumptions remaining to discharge*)
wenzelm@10769:      standard (induction RS (rules RS conjI)))
wenzelm@10769:  end
wenzelm@10769: 
wenzelm@10769: fun defer thy congs fid seqs =
wenzelm@10769:   defer_i thy congs fid (map (read_term thy) seqs)
wenzelm@10769:     handle U.ERR {mesg,...} => error mesg;
wenzelm@10769: end;
wenzelm@10769: 
wenzelm@10769: end;