TFL/post.ML
changeset 10769 70b9b0cfe05f
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10768:a7282df327c6 10769:70b9b0cfe05f
       
     1 (*  Title:      TFL/post.ML
       
     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 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 end
       
    98    handle U.ERR _ => false;
       
    99    
       
   100 
       
   101 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
       
   102 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
       
   103 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
       
   104 fun mk_meta_eq r = case concl_of r of
       
   105      Const("==",_)$_$_ => r
       
   106   |   _ $(Const("op =",_)$_$_) => r RS eq_reflection
       
   107   |   _ => r RS P_imp_P_eq_True
       
   108 
       
   109 (*Is this the best way to invoke the simplifier??*)
       
   110 fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
       
   111 
       
   112 fun join_assums th =
       
   113   let val {sign,...} = rep_thm th
       
   114       val tych = cterm_of sign
       
   115       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
       
   116       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
       
   117       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
       
   118       val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
       
   119   in
       
   120     R.GEN_ALL
       
   121       (R.DISCH_ALL
       
   122          (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
       
   123   end
       
   124   val gen_all = S.gen_all
       
   125 in
       
   126 fun proof_stage cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =
       
   127   let
       
   128     val _ = message "Proving induction theorem ..."
       
   129     val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
       
   130     val _ = message "Postprocessing ...";
       
   131     val {rules, induction, nested_tcs} =
       
   132       std_postprocessor cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}
       
   133   in
       
   134   case nested_tcs
       
   135   of [] => {induction=induction, rules=rules,tcs=[]}
       
   136   | L  => let val dummy = message "Simplifying nested TCs ..."
       
   137               val (solved,simplified,stubborn) =
       
   138                U.itlist (fn th => fn (So,Si,St) =>
       
   139                      if (id_thm th) then (So, Si, th::St) else
       
   140                      if (solved th) then (th::So, Si, St)
       
   141                      else (So, th::Si, St)) nested_tcs ([],[],[])
       
   142               val simplified' = map join_assums simplified
       
   143               val rewr = full_simplify (ss addsimps (solved @ simplified'));
       
   144               val induction' = rewr induction
       
   145               and rules'     = rewr rules
       
   146           in
       
   147           {induction = induction',
       
   148                rules = rules',
       
   149                  tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
       
   150                            (simplified@stubborn)}
       
   151           end
       
   152   end;
       
   153 
       
   154 
       
   155 (*lcp: curry the predicate of the induction rule*)
       
   156 fun curry_rule rl = split_rule_var
       
   157                         (head_of (HOLogic.dest_Trueprop (concl_of rl)),
       
   158                          rl);
       
   159 
       
   160 (*lcp: put a theorem into Isabelle form, using meta-level connectives*)
       
   161 val meta_outer =
       
   162     curry_rule o standard o
       
   163     rule_by_tactic (REPEAT
       
   164                     (FIRSTGOAL (resolve_tac [allI, impI, conjI]
       
   165                                 ORELSE' etac conjE)));
       
   166 
       
   167 (*Strip off the outer !P*)
       
   168 val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
       
   169 
       
   170 fun simplify_defn thy cs ss congs wfs id pats def0 =
       
   171    let val def = freezeT def0 RS meta_eq_to_obj_eq
       
   172        val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats))
       
   173        val {lhs=f,rhs} = S.dest_eq (concl def)
       
   174        val (_,[R,_]) = S.strip_comb rhs
       
   175        val {induction, rules, tcs} =
       
   176              proof_stage cs ss wfs theory
       
   177                {f = f, R = R, rules = rules,
       
   178                 full_pats_TCs = full_pats_TCs,
       
   179                 TCs = TCs}
       
   180        val rules' = map (standard o Rulify.rulify_no_asm) (R.CONJUNCTS rules)
       
   181    in  {induct = meta_outer (Rulify.rulify_no_asm (induction RS spec')),
       
   182         rules = ListPair.zip(rules', rows),
       
   183         tcs = (termination_goals rules') @ tcs}
       
   184    end
       
   185   handle U.ERR {mesg,func,module} =>
       
   186                error (mesg ^
       
   187                       "\n    (In TFL function " ^ module ^ "." ^ func ^ ")");
       
   188 
       
   189 (*---------------------------------------------------------------------------
       
   190  * Defining a function with an associated termination relation.
       
   191  *---------------------------------------------------------------------------*)
       
   192 fun define_i thy cs ss congs wfs fid R eqs =
       
   193   let val {functional,pats} = Prim.mk_functional thy eqs
       
   194       val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional
       
   195   in (thy, simplify_defn thy cs ss congs wfs fid pats def) end;
       
   196 
       
   197 fun define thy cs ss congs wfs fid R seqs =
       
   198   define_i thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)
       
   199     handle U.ERR {mesg,...} => error mesg;
       
   200 
       
   201 
       
   202 (*---------------------------------------------------------------------------
       
   203  *
       
   204  *     Definitions with synthesized termination relation
       
   205  *
       
   206  *---------------------------------------------------------------------------*)
       
   207 
       
   208 fun func_of_cond_eqn tm =
       
   209   #1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm)))))));
       
   210 
       
   211 fun defer_i thy congs fid eqs =
       
   212  let val {rules,R,theory,full_pats_TCs,SV,...} =
       
   213              Prim.lazyR_def thy (Sign.base_name fid) congs eqs
       
   214      val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules));
       
   215      val dummy = message "Proving induction theorem ...";
       
   216      val induction = Prim.mk_induction theory
       
   217                         {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
       
   218  in (theory,
       
   219      (*return the conjoined induction rule and recursion equations,
       
   220        with assumptions remaining to discharge*)
       
   221      standard (induction RS (rules RS conjI)))
       
   222  end
       
   223 
       
   224 fun defer thy congs fid seqs =
       
   225   defer_i thy congs fid (map (read_term thy) seqs)
       
   226     handle U.ERR {mesg,...} => error mesg;
       
   227 end;
       
   228 
       
   229 end;