TFL/post.sml
author paulson
Fri Oct 18 12:41:04 1996 +0200 (1996-10-18)
changeset 2112 3902e9af752f
child 2467 357adb429fda
permissions -rw-r--r--
Konrad Slind's TFL
     1 structure Tfl
     2  :sig
     3    structure Prim : TFL_sig
     4 
     5    val tgoalw : theory -> thm list -> thm -> thm list
     6    val tgoal: theory -> thm -> thm list
     7 
     8    val WF_TAC : thm list -> tactic
     9 
    10    val simplifier : thm -> thm
    11    val std_postprocessor : theory 
    12                            -> {induction:thm, rules:thm, TCs:term list list} 
    13                            -> {induction:thm, rules:thm, nested_tcs:thm list}
    14 
    15    val rfunction  : theory
    16                      -> (thm list -> thm -> thm)
    17                         -> term -> term  
    18                           -> {induction:thm, rules:thm, 
    19                               tcs:term list, theory:theory}
    20 
    21    val Rfunction : theory -> term -> term  
    22                    -> {induction:thm, rules:thm, 
    23                        theory:theory, tcs:term list}
    24 
    25    val function : theory -> term -> {theory:theory, eq_ind : thm}
    26    val lazyR_def : theory -> term -> {theory:theory, eqns : thm}
    27 
    28    val tflcongs : theory -> thm list
    29 
    30   end = 
    31 struct
    32  structure Prim = Prim
    33 
    34  fun tgoalw thy defs thm = 
    35     let val L = Prim.termination_goals thm
    36         open USyntax
    37         val g = cterm_of (sign_of thy) (mk_prop(list_mk_conj L))
    38     in goalw_cterm defs g
    39     end;
    40 
    41  val tgoal = Utils.C tgoalw [];
    42 
    43  fun WF_TAC thms = REPEAT(FIRST1(map rtac thms))
    44  val WFtac = WF_TAC[wf_measure, wf_inv_image, wf_lex_prod, 
    45                     wf_pred_nat, wf_pred_list, wf_trancl];
    46 
    47  val terminator = simp_tac(HOL_ss addsimps[pred_nat_def,pred_list_def,
    48                                            fst_conv,snd_conv,
    49                                            mem_Collect_eq,lessI]) 1
    50                   THEN TRY(fast_tac set_cs 1);
    51 
    52  val simpls = [less_eq RS eq_reflection,
    53                lex_prod_def, measure_def, inv_image_def, 
    54                fst_conv RS eq_reflection, snd_conv RS eq_reflection,
    55                mem_Collect_eq RS eq_reflection(*, length_Cons RS eq_reflection*)];
    56 
    57  val std_postprocessor = Prim.postprocess{WFtac = WFtac,
    58                                     terminator = terminator, 
    59                                     simplifier = Prim.Rules.simpl_conv simpls};
    60 
    61  val simplifier = rewrite_rule (simpls @ #simps(rep_ss HOL_ss) @ 
    62                                 [pred_nat_def,pred_list_def]);
    63  fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy));
    64 
    65 
    66 local structure S = Prim.USyntax
    67 in
    68 fun func_of_cond_eqn tm =
    69   #1(S.strip_comb(#lhs(S.dest_eq(#2(S.strip_forall(#2(S.strip_imp tm)))))))
    70 end;
    71 
    72 
    73 val concl = #2 o Prim.Rules.dest_thm;
    74 
    75 (*---------------------------------------------------------------------------
    76  * Defining a function with an associated termination relation. Lots of
    77  * postprocessing takes place.
    78  *---------------------------------------------------------------------------*)
    79 local 
    80 structure S = Prim.USyntax
    81 structure R = Prim.Rules
    82 structure U = Utils
    83 
    84 val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl
    85 
    86 fun id_thm th = 
    87    let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th))))
    88    in S.aconv lhs rhs
    89    end handle _ => false
    90 
    91 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
    92 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
    93 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
    94 fun mk_meta_eq r = case concl_of r of
    95      Const("==",_)$_$_ => r
    96   |   _$(Const("op =",_)$_$_) => r RS eq_reflection
    97   |   _ => r RS P_imp_P_eq_True
    98 fun rewrite L = rewrite_rule (map mk_meta_eq (Utils.filter(not o id_thm) L))
    99 
   100 fun join_assums th = 
   101   let val {sign,...} = rep_thm th
   102       val tych = cterm_of sign
   103       val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
   104       val cntxtl = (#1 o S.strip_imp) lhs  (* cntxtl should = cntxtr *)
   105       val cntxtr = (#1 o S.strip_imp) rhs  (* but union is solider *)
   106       val cntxt = U.union S.aconv cntxtl cntxtr
   107   in 
   108   R.GEN_ALL 
   109   (R.DISCH_ALL 
   110     (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
   111   end
   112   val gen_all = S.gen_all
   113 in
   114 fun rfunction theory reducer R eqs = 
   115  let val _ = output(std_out, "Making definition..  ")
   116      val _ = flush_out std_out
   117      val {rules,theory, full_pats_TCs,
   118           TCs,...} = Prim.gen_wfrec_definition theory {R=R,eqs=eqs} 
   119      val f = func_of_cond_eqn(concl(R.CONJUNCT1 rules handle _ => rules))
   120      val _ = output(std_out, "Definition made.\n")
   121      val _ = output(std_out, "Proving induction theorem..  ")
   122      val _ = flush_out std_out
   123      val ind = Prim.mk_induction theory f R full_pats_TCs
   124      val _ = output(std_out, "Proved induction theorem.\n")
   125      val pp = std_postprocessor theory
   126      val _ = output(std_out, "Postprocessing..  ")
   127      val _ = flush_out std_out
   128      val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs}
   129      val normal_tcs = Prim.termination_goals rules
   130  in
   131  case nested_tcs
   132  of [] => (output(std_out, "Postprocessing done.\n");
   133            {theory=theory, induction=induction, rules=rules,tcs=normal_tcs})
   134   | L  => let val _ = output(std_out, "Simplifying nested TCs..  ")
   135               val (solved,simplified,stubborn) =
   136                U.itlist (fn th => fn (So,Si,St) =>
   137                      if (id_thm th) then (So, Si, th::St) else
   138                      if (solved th) then (th::So, Si, St) 
   139                      else (So, th::Si, St)) nested_tcs ([],[],[])
   140               val simplified' = map join_assums simplified
   141               val induction' = reducer (solved@simplified') induction
   142               val rules' = reducer (solved@simplified') rules
   143               val _ = output(std_out, "Postprocessing done.\n")
   144           in
   145           {induction = induction',
   146                rules = rules',
   147                  tcs = normal_tcs @
   148                       map (gen_all o S.rhs o #2 o S.strip_forall o concl)
   149                            (simplified@stubborn),
   150               theory = theory}
   151           end
   152  end
   153  handle (e as Utils.ERR _) => Utils.Raise e
   154      |     e               => print_exn e
   155 
   156 
   157 fun Rfunction thry = 
   158      rfunction thry 
   159        (fn thl => rewrite (map standard thl @ #simps(rep_ss HOL_ss)));
   160 
   161 
   162 end;
   163 
   164 
   165 local structure R = Prim.Rules
   166 in
   167 fun function theory eqs = 
   168  let val _ = output(std_out, "Making definition..  ")
   169      val {rules,R,theory,full_pats_TCs,...} = Prim.lazyR_def theory eqs
   170      val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules))
   171      val _ = output(std_out, "Definition made.\n")
   172      val _ = output(std_out, "Proving induction theorem..  ")
   173      val induction = Prim.mk_induction theory f R full_pats_TCs
   174       val _ = output(std_out, "Induction theorem proved.\n")
   175  in {theory = theory, 
   176      eq_ind = standard (induction RS (rules RS conjI))}
   177  end
   178  handle (e as Utils.ERR _) => Utils.Raise e
   179       |     e              => print_exn e
   180 end;
   181 
   182 
   183 fun lazyR_def theory eqs = 
   184    let val {rules,theory, ...} = Prim.lazyR_def theory eqs
   185    in {eqns=rules, theory=theory}
   186    end
   187    handle (e as Utils.ERR _) => Utils.Raise e
   188         |     e              => print_exn e;
   189 
   190 
   191  val () = Prim.Context.write[Thms.LET_CONG, Thms.COND_CONG];
   192 
   193 end;