TFL/post.ML
author wenzelm
Fri Oct 12 12:08:04 2001 +0200 (2001-10-12)
changeset 11729 a7da2e8b5762
parent 11632 6fc8de600f58
child 11771 b7b100a2de1d
permissions -rw-r--r--
removed read_inst', no longer export insts';
     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 define_i: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring ->
    17     term -> term list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
    18   val define: bool -> theory -> claset -> simpset -> thm list -> thm list -> xstring ->
    19     string -> string list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
    20   val defer_i: theory -> thm list -> xstring -> term list -> theory * thm
    21   val defer: theory -> thm list -> xstring -> string list -> theory * thm
    22 end;
    23 
    24 structure Tfl: TFL =
    25 struct
    26 
    27 structure S = USyntax
    28 
    29 
    30 (* messages *)
    31 
    32 val trace = Prim.trace
    33 
    34 val quiet_mode = ref false;
    35 fun message s = if ! quiet_mode then () else writeln s;
    36 
    37 
    38 (* misc *)
    39 
    40 fun read_term thy = Sign.simple_read_term (Theory.sign_of thy) HOLogic.termT;
    41 
    42 
    43 (*---------------------------------------------------------------------------
    44  * Extract termination goals so that they can be put it into a goalstack, or
    45  * have a tactic directly applied to them.
    46  *--------------------------------------------------------------------------*)
    47 fun termination_goals rules =
    48     map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)
    49       (foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
    50 
    51 (*---------------------------------------------------------------------------
    52  * Finds the termination conditions in (highly massaged) definition and
    53  * puts them into a goalstack.
    54  *--------------------------------------------------------------------------*)
    55 fun tgoalw thy defs rules =
    56   case termination_goals rules of
    57       [] => error "tgoalw: no termination conditions to prove"
    58     | L  => goalw_cterm defs
    59               (Thm.cterm_of (Theory.sign_of thy)
    60                         (HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));
    61 
    62 fun tgoal thy = tgoalw thy [];
    63 
    64 (*---------------------------------------------------------------------------
    65  * Three postprocessors are applied to the definition.  It
    66  * attempts to prove wellfoundedness of the given relation, simplifies the
    67  * non-proved termination conditions, and finally attempts to prove the
    68  * simplified termination conditions.
    69  *--------------------------------------------------------------------------*)
    70 fun std_postprocessor strict cs ss wfs =
    71   Prim.postprocess strict
    72    {wf_tac     = REPEAT (ares_tac wfs 1),
    73     terminator = asm_simp_tac ss 1
    74                  THEN TRY (fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1),
    75     simplifier = Rules.simpl_conv ss []};
    76 
    77 
    78 
    79 val concl = #2 o Rules.dest_thm;
    80 
    81 (*---------------------------------------------------------------------------
    82  * Postprocess a definition made by "define". This is a separate stage of
    83  * processing from the definition stage.
    84  *---------------------------------------------------------------------------*)
    85 local
    86 structure R = Rules
    87 structure U = Utils
    88 
    89 (* The rest of these local definitions are for the tricky nested case *)
    90 val solved = not o can S.dest_eq o #2 o S.strip_forall o concl
    91 
    92 fun id_thm th =
    93    let val {lhs,rhs} = S.dest_eq (#2 (S.strip_forall (#2 (R.dest_thm th))));
    94    in lhs aconv rhs end
    95    handle U.ERR _ => false;
    96    
    97 
    98 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
    99 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
   100 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
   101 fun mk_meta_eq r = case concl_of r of
   102      Const("==",_)$_$_ => r
   103   |   _ $(Const("op =",_)$_$_) => r RS eq_reflection
   104   |   _ => r RS P_imp_P_eq_True
   105 
   106 (*Is this the best way to invoke the simplifier??*)
   107 fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
   108 
   109 fun join_assums th =
   110   let val {sign,...} = rep_thm th
   111       val tych = cterm_of sign
   112       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
   113       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
   114       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
   115       val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
   116   in
   117     R.GEN_ALL
   118       (R.DISCH_ALL
   119          (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
   120   end
   121   val gen_all = S.gen_all
   122 in
   123 fun proof_stage strict cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =
   124   let
   125     val _ = message "Proving induction theorem ..."
   126     val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
   127     val _ = message "Postprocessing ...";
   128     val {rules, induction, nested_tcs} =
   129       std_postprocessor strict cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}
   130   in
   131   case nested_tcs
   132   of [] => {induction=induction, rules=rules,tcs=[]}
   133   | L  => let val dummy = message "Simplifying nested TCs ..."
   134               val (solved,simplified,stubborn) =
   135                U.itlist (fn th => fn (So,Si,St) =>
   136                      if (id_thm th) then (So, Si, th::St) else
   137                      if (solved th) then (th::So, Si, St)
   138                      else (So, th::Si, St)) nested_tcs ([],[],[])
   139               val simplified' = map join_assums simplified
   140               val rewr = full_simplify (ss addsimps (solved @ simplified'));
   141               val induction' = rewr induction
   142               and rules'     = rewr rules
   143           in
   144           {induction = induction',
   145                rules = rules',
   146                  tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
   147                            (simplified@stubborn)}
   148           end
   149   end;
   150 
   151 
   152 (*lcp: curry the predicate of the induction rule*)
   153 fun curry_rule rl =
   154   SplitRule.split_rule_var (Term.head_of (HOLogic.dest_Trueprop (concl_of rl)), rl);
   155 
   156 (*lcp: put a theorem into Isabelle form, using meta-level connectives*)
   157 val meta_outer =
   158   curry_rule o standard o
   159   rule_by_tactic (REPEAT (FIRSTGOAL (resolve_tac [allI, impI, conjI] ORELSE' etac conjE)));
   160 
   161 (*Strip off the outer !P*)
   162 val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
   163 
   164 fun simplify_defn strict thy cs ss congs wfs id pats def0 =
   165    let val def = freezeT def0 RS meta_eq_to_obj_eq
   166        val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats))
   167        val {lhs=f,rhs} = S.dest_eq (concl def)
   168        val (_,[R,_]) = S.strip_comb rhs
   169        val {induction, rules, tcs} =
   170              proof_stage strict cs ss wfs theory
   171                {f = f, R = R, rules = rules,
   172                 full_pats_TCs = full_pats_TCs,
   173                 TCs = TCs}
   174        val rules' = map (standard o Rulify.rulify_no_asm) (R.CONJUNCTS rules)
   175    in  {induct = meta_outer (Rulify.rulify_no_asm (induction RS spec')),
   176         rules = ListPair.zip(rules', rows),
   177         tcs = (termination_goals rules') @ tcs}
   178    end
   179   handle U.ERR {mesg,func,module} =>
   180                error (mesg ^
   181                       "\n    (In TFL function " ^ module ^ "." ^ func ^ ")");
   182 
   183 (*---------------------------------------------------------------------------
   184  * Defining a function with an associated termination relation.
   185  *---------------------------------------------------------------------------*)
   186 fun define_i strict thy cs ss congs wfs fid R eqs =
   187   let val {functional,pats} = Prim.mk_functional thy eqs
   188       val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional
   189   in (thy, simplify_defn strict thy cs ss congs wfs fid pats def) end;
   190 
   191 fun define strict thy cs ss congs wfs fid R seqs =
   192   define_i strict thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)
   193     handle U.ERR {mesg,...} => error mesg;
   194 
   195 
   196 (*---------------------------------------------------------------------------
   197  *
   198  *     Definitions with synthesized termination relation
   199  *
   200  *---------------------------------------------------------------------------*)
   201 
   202 fun func_of_cond_eqn tm =
   203   #1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm)))))));
   204 
   205 fun defer_i thy congs fid eqs =
   206  let val {rules,R,theory,full_pats_TCs,SV,...} =
   207              Prim.lazyR_def thy (Sign.base_name fid) congs eqs
   208      val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules));
   209      val dummy = message "Proving induction theorem ...";
   210      val induction = Prim.mk_induction theory
   211                         {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
   212  in (theory,
   213      (*return the conjoined induction rule and recursion equations,
   214        with assumptions remaining to discharge*)
   215      standard (induction RS (rules RS conjI)))
   216  end
   217 
   218 fun defer thy congs fid seqs =
   219   defer_i thy congs fid (map (read_term thy) seqs)
   220     handle U.ERR {mesg,...} => error mesg;
   221 end;
   222 
   223 end;