TFL/post.sml
author wenzelm
Mon Sep 11 18:00:47 2000 +0200 (2000-09-11)
changeset 9924 3370f6aa3200
parent 9904 09253f667beb
child 10015 8c16ec5ba62b
permissions -rw-r--r--
updated;
     1 (*  Title:      TFL/post.sml
     2     ID:         $Id$
     3     Author:     Konrad Slind, Cambridge University Computer Laboratory
     4     Copyright   1997  University of Cambridge
     5 
     6 Second part of main module (postprocessing of TFL definitions).
     7 *)
     8 
     9 signature TFL =
    10 sig
    11   val trace: bool ref
    12   val quiet_mode: bool ref
    13   val message: string -> unit
    14   val tgoalw: theory -> thm list -> thm list -> thm list
    15   val tgoal: theory -> thm list -> thm list
    16   val std_postprocessor: claset -> simpset -> thm list -> theory ->
    17     {induction: thm, rules: thm, TCs: term list list} ->
    18     {induction: thm, rules: thm, nested_tcs: thm list}
    19   val define_i: theory -> claset -> simpset -> thm list -> thm list -> xstring ->
    20     term -> term list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
    21   val define: theory -> claset -> simpset -> thm list -> thm list -> xstring ->
    22     string -> string list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
    23   val defer_i: theory -> thm list -> xstring -> term list -> theory * thm
    24   val defer: theory -> thm list -> xstring -> string list -> theory * thm
    25 end;
    26 
    27 structure Tfl: TFL =
    28 struct
    29 
    30 structure S = USyntax
    31 
    32 
    33 (* messages *)
    34 
    35 val trace = Prim.trace
    36 
    37 val quiet_mode = ref false;
    38 fun message s = if ! quiet_mode then () else writeln s;
    39 
    40 
    41 (* misc *)
    42 
    43 fun read_term thy = Sign.simple_read_term (Theory.sign_of thy) HOLogic.termT;
    44 
    45 
    46 (*---------------------------------------------------------------------------
    47  * Extract termination goals so that they can be put it into a goalstack, or
    48  * have a tactic directly applied to them.
    49  *--------------------------------------------------------------------------*)
    50 fun termination_goals rules =
    51     map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)
    52       (foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
    53 
    54 (*---------------------------------------------------------------------------
    55  * Finds the termination conditions in (highly massaged) definition and
    56  * puts them into a goalstack.
    57  *--------------------------------------------------------------------------*)
    58 fun tgoalw thy defs rules =
    59   case termination_goals rules of
    60       [] => error "tgoalw: no termination conditions to prove"
    61     | L  => goalw_cterm defs
    62               (Thm.cterm_of (Theory.sign_of thy)
    63                         (HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));
    64 
    65 fun tgoal thy = tgoalw thy [];
    66 
    67 (*---------------------------------------------------------------------------
    68  * Three postprocessors are applied to the definition.  It
    69  * attempts to prove wellfoundedness of the given relation, simplifies the
    70  * non-proved termination conditions, and finally attempts to prove the
    71  * simplified termination conditions.
    72  *--------------------------------------------------------------------------*)
    73 fun std_postprocessor cs ss wfs =
    74   Prim.postprocess
    75    {wf_tac     = REPEAT (ares_tac wfs 1),
    76     terminator = asm_simp_tac ss 1
    77                  THEN TRY (fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1),
    78     simplifier = Rules.simpl_conv ss []};
    79 
    80 
    81 
    82 val concl = #2 o Rules.dest_thm;
    83 
    84 (*---------------------------------------------------------------------------
    85  * Postprocess a definition made by "define". This is a separate stage of
    86  * processing from the definition stage.
    87  *---------------------------------------------------------------------------*)
    88 local
    89 structure R = Rules
    90 structure U = Utils
    91 
    92 (* The rest of these local definitions are for the tricky nested case *)
    93 val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl
    94 
    95 fun id_thm th =
    96    let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th))))
    97    in lhs aconv rhs
    98    end handle _ => false
    99 
   100 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
   101 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
   102 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
   103 fun mk_meta_eq r = case concl_of r of
   104      Const("==",_)$_$_ => r
   105   |   _ $(Const("op =",_)$_$_) => r RS eq_reflection
   106   |   _ => r RS P_imp_P_eq_True
   107 
   108 (*Is this the best way to invoke the simplifier??*)
   109 fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
   110 
   111 fun join_assums th =
   112   let val {sign,...} = rep_thm th
   113       val tych = cterm_of sign
   114       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
   115       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
   116       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
   117       val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
   118   in
   119     R.GEN_ALL
   120       (R.DISCH_ALL
   121          (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
   122   end
   123   val gen_all = S.gen_all
   124 in
   125 fun proof_stage cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =
   126   let
   127     val _ = message "Proving induction theorem ..."
   128     val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
   129     val _ = message "Postprocessing ...";
   130     val {rules, induction, nested_tcs} =
   131       std_postprocessor cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}
   132   in
   133   case nested_tcs
   134   of [] => {induction=induction, rules=rules,tcs=[]}
   135   | L  => let val dummy = message "Simplifying nested TCs ..."
   136               val (solved,simplified,stubborn) =
   137                U.itlist (fn th => fn (So,Si,St) =>
   138                      if (id_thm th) then (So, Si, th::St) else
   139                      if (solved th) then (th::So, Si, St)
   140                      else (So, th::Si, St)) nested_tcs ([],[],[])
   141               val simplified' = map join_assums simplified
   142               val rewr = full_simplify (ss addsimps (solved @ simplified'));
   143               val induction' = rewr induction
   144               and rules'     = rewr rules
   145           in
   146           {induction = induction',
   147                rules = rules',
   148                  tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
   149                            (simplified@stubborn)}
   150           end
   151   end;
   152 
   153 
   154 (*lcp: curry the predicate of the induction rule*)
   155 fun curry_rule rl = split_rule_var
   156                         (head_of (HOLogic.dest_Trueprop (concl_of rl)),
   157                          rl);
   158 
   159 (*lcp: put a theorem into Isabelle form, using meta-level connectives*)
   160 val meta_outer =
   161     curry_rule o standard o
   162     rule_by_tactic (REPEAT
   163                     (FIRSTGOAL (resolve_tac [allI, impI, conjI]
   164                                 ORELSE' etac conjE)));
   165 
   166 (*Strip off the outer !P*)
   167 val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
   168 
   169 fun simplify_defn thy cs ss congs wfs id pats def0 =
   170    let val def = freezeT def0 RS meta_eq_to_obj_eq
   171        val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats))
   172        val {lhs=f,rhs} = S.dest_eq (concl def)
   173        val (_,[R,_]) = S.strip_comb rhs
   174        val {induction, rules, tcs} =
   175              proof_stage cs ss wfs theory
   176                {f = f, R = R, rules = rules,
   177                 full_pats_TCs = full_pats_TCs,
   178                 TCs = TCs}
   179        val rules' = map (standard o Rulify.rulify_no_asm) (R.CONJUNCTS rules)
   180    in  {induct = meta_outer (Rulify.rulify_no_asm (induction RS spec')),
   181         rules = ListPair.zip(rules', rows),
   182         tcs = (termination_goals rules') @ tcs}
   183    end
   184   handle Utils.ERR {mesg,func,module} =>
   185                error (mesg ^
   186                       "\n    (In TFL function " ^ module ^ "." ^ func ^ ")");
   187 
   188 (*---------------------------------------------------------------------------
   189  * Defining a function with an associated termination relation.
   190  *---------------------------------------------------------------------------*)
   191 fun define_i thy cs ss congs wfs fid R eqs =
   192   let val {functional,pats} = Prim.mk_functional thy eqs
   193       val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional
   194   in (thy, simplify_defn thy cs ss congs wfs fid pats def) end;
   195 
   196 fun define thy cs ss congs wfs fid R seqs =
   197   define_i thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)
   198     handle Utils.ERR {mesg,...} => error mesg;
   199 
   200 
   201 (*---------------------------------------------------------------------------
   202  *
   203  *     Definitions with synthesized termination relation
   204  *
   205  *---------------------------------------------------------------------------*)
   206 
   207 local open USyntax
   208 in
   209 fun func_of_cond_eqn tm =
   210   #1(strip_comb(#lhs(dest_eq(#2 (strip_forall(#2(strip_imp tm)))))))
   211 end;
   212 
   213 fun defer_i thy congs fid eqs =
   214  let val {rules,R,theory,full_pats_TCs,SV,...} =
   215              Prim.lazyR_def thy (Sign.base_name fid) congs eqs
   216      val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules))
   217      val dummy = message "Proving induction theorem ...";
   218      val induction = Prim.mk_induction theory
   219                         {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
   220  in (theory,
   221      (*return the conjoined induction rule and recursion equations,
   222        with assumptions remaining to discharge*)
   223      standard (induction RS (rules RS conjI)))
   224  end
   225 
   226 fun defer thy congs fid seqs =
   227   defer_i thy congs fid (map (read_term thy) seqs)
   228     handle Utils.ERR {mesg,...} => error mesg;
   229 end;
   230 
   231 end;