src/HOL/simpdata.ML
author wenzelm
Sun Nov 12 21:14:49 2006 +0100 (2006-11-12)
changeset 21313 26fc3a45547c
parent 21163 6860f161111c
child 21551 d276e7d25017
permissions -rw-r--r--
mk_atomize: careful matching against rules admits overloading;
     1 (*  Title:      HOL/simpdata.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1991  University of Cambridge
     5 
     6 Instantiation of the generic simplifier for HOL.
     7 *)
     8 
     9 (** tools setup **)
    10 
    11 structure Quantifier1 = Quantifier1Fun
    12 (struct
    13   (*abstract syntax*)
    14   fun dest_eq ((c as Const("op =",_)) $ s $ t) = SOME (c, s, t)
    15     | dest_eq _ = NONE;
    16   fun dest_conj ((c as Const("op &",_)) $ s $ t) = SOME (c, s, t)
    17     | dest_conj _ = NONE;
    18   fun dest_imp ((c as Const("op -->",_)) $ s $ t) = SOME (c, s, t)
    19     | dest_imp _ = NONE;
    20   val conj = HOLogic.conj
    21   val imp  = HOLogic.imp
    22   (*rules*)
    23   val iff_reflection = HOL.eq_reflection
    24   val iffI = HOL.iffI
    25   val iff_trans = HOL.trans
    26   val conjI= HOL.conjI
    27   val conjE= HOL.conjE
    28   val impI = HOL.impI
    29   val mp   = HOL.mp
    30   val uncurry = thm "uncurry"
    31   val exI  = HOL.exI
    32   val exE  = HOL.exE
    33   val iff_allI = thm "iff_allI"
    34   val iff_exI = thm "iff_exI"
    35   val all_comm = thm "all_comm"
    36   val ex_comm = thm "ex_comm"
    37 end);
    38 
    39 structure HOL =
    40 struct
    41 
    42 open HOL;
    43 
    44 val Eq_FalseI = thm "Eq_FalseI";
    45 val Eq_TrueI = thm "Eq_TrueI";
    46 val simp_implies_def = thm "simp_implies_def";
    47 val simp_impliesI = thm "simp_impliesI";
    48 
    49 fun mk_meta_eq r = r RS eq_reflection;
    50 fun safe_mk_meta_eq r = mk_meta_eq r handle Thm.THM _ => r;
    51 
    52 fun mk_eq thm = case concl_of thm
    53   (*expects Trueprop if not == *)
    54   of Const ("==",_) $ _ $ _ => thm
    55    | _ $ (Const ("op =", _) $ _ $ _) => mk_meta_eq thm
    56    | _ $ (Const ("Not", _) $ _) => thm RS Eq_FalseI
    57    | _ => thm RS Eq_TrueI;
    58 
    59 fun mk_eq_True r =
    60   SOME (r RS meta_eq_to_obj_eq RS Eq_TrueI) handle Thm.THM _ => NONE;
    61 
    62 (* Produce theorems of the form
    63   (P1 =simp=> ... =simp=> Pn => x == y) ==> (P1 =simp=> ... =simp=> Pn => x = y)
    64 *)
    65 fun lift_meta_eq_to_obj_eq i st =
    66   let
    67     fun count_imp (Const ("HOL.simp_implies", _) $ P $ Q) = 1 + count_imp Q
    68       | count_imp _ = 0;
    69     val j = count_imp (Logic.strip_assums_concl (List.nth (prems_of st, i - 1)))
    70   in if j = 0 then meta_eq_to_obj_eq
    71     else
    72       let
    73         val Ps = map (fn k => Free ("P" ^ string_of_int k, propT)) (1 upto j);
    74         fun mk_simp_implies Q = foldr (fn (R, S) =>
    75           Const ("HOL.simp_implies", propT --> propT --> propT) $ R $ S) Q Ps
    76         val aT = TFree ("'a", HOLogic.typeS);
    77         val x = Free ("x", aT);
    78         val y = Free ("y", aT)
    79       in Goal.prove_global (Thm.theory_of_thm st) []
    80         [mk_simp_implies (Logic.mk_equals (x, y))]
    81         (mk_simp_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (x, y))))
    82         (fn prems => EVERY
    83          [rewrite_goals_tac [simp_implies_def],
    84           REPEAT (ares_tac (meta_eq_to_obj_eq :: map (rewrite_rule [simp_implies_def]) prems) 1)])
    85       end
    86   end;
    87 
    88 (*Congruence rules for = (instead of ==)*)
    89 fun mk_meta_cong rl = zero_var_indexes
    90   (let val rl' = Seq.hd (TRYALL (fn i => fn st =>
    91      rtac (lift_meta_eq_to_obj_eq i st) i st) rl)
    92    in mk_meta_eq rl' handle THM _ =>
    93      if can Logic.dest_equals (concl_of rl') then rl'
    94      else error "Conclusion of congruence rules must be =-equality"
    95    end);
    96 
    97 fun mk_atomize pairs =
    98   let
    99     fun atoms thm =
   100       let
   101         fun res th = map (fn rl => th RS rl);   (*exception THM*)
   102         fun res_fixed rls =
   103           if Thm.maxidx_of (Thm.adjust_maxidx_thm ~1 thm) = ~1 then res thm rls
   104           else Variable.trade (K (fn [thm'] => res thm' rls)) (Variable.thm_context thm) [thm];
   105       in
   106         case concl_of thm
   107           of Const ("Trueprop", _) $ p => (case head_of p
   108             of Const (a, _) => (case AList.lookup (op =) pairs a
   109               of SOME rls => (maps atoms (res_fixed rls) handle THM _ => [thm])
   110               | NONE => [thm])
   111             | _ => [thm])
   112           | _ => [thm]
   113       end;
   114   in atoms end;
   115 
   116 fun mksimps pairs =
   117   map_filter (try mk_eq) o mk_atomize pairs o gen_all;
   118 
   119 fun unsafe_solver_tac prems =
   120   (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
   121   FIRST'[resolve_tac(reflexive_thm :: TrueI :: refl :: prems), atac, etac FalseE];
   122 val unsafe_solver = mk_solver "HOL unsafe" unsafe_solver_tac;
   123 
   124 (*No premature instantiation of variables during simplification*)
   125 fun safe_solver_tac prems =
   126   (fn i => REPEAT_DETERM (match_tac [simp_impliesI] i)) THEN'
   127   FIRST'[match_tac(reflexive_thm :: TrueI :: refl :: prems),
   128          eq_assume_tac, ematch_tac [FalseE]];
   129 val safe_solver = mk_solver "HOL safe" safe_solver_tac;
   130 
   131 end;
   132 
   133 structure SplitterData =
   134 struct
   135   structure Simplifier = Simplifier
   136   val mk_eq           = HOL.mk_eq
   137   val meta_eq_to_iff  = HOL.meta_eq_to_obj_eq
   138   val iffD            = HOL.iffD2
   139   val disjE           = HOL.disjE
   140   val conjE           = HOL.conjE
   141   val exE             = HOL.exE
   142   val contrapos       = HOL.contrapos_nn
   143   val contrapos2      = HOL.contrapos_pp
   144   val notnotD         = HOL.notnotD
   145 end;
   146 
   147 structure Splitter = SplitterFun(SplitterData);
   148 
   149 
   150 (* integration of simplifier with classical reasoner *)
   151 
   152 structure Clasimp = ClasimpFun
   153  (structure Simplifier = Simplifier and Splitter = Splitter
   154   and Classical  = Classical and Blast = Blast
   155   val iffD1 = HOL.iffD1 val iffD2 = HOL.iffD2 val notE = HOL.notE);
   156 
   157 structure HOL =
   158 struct
   159 
   160 open HOL;
   161 
   162 val mksimps_pairs =
   163   [("op -->", [mp]), ("op &", [thm "conjunct1", thm "conjunct2"]),
   164    ("All", [spec]), ("True", []), ("False", []),
   165    ("HOL.If", [thm "if_bool_eq_conj" RS iffD1])];
   166 
   167 val simpset_basic =
   168   Simplifier.theory_context (the_context ()) empty_ss
   169     setsubgoaler asm_simp_tac
   170     setSSolver safe_solver
   171     setSolver unsafe_solver
   172     setmksimps (mksimps mksimps_pairs)
   173     setmkeqTrue mk_eq_True
   174     setmkcong mk_meta_cong;
   175 
   176 fun simplify rews = Simplifier.full_simplify (simpset_basic addsimps rews);
   177 
   178 fun unfold_tac ths =
   179   let val ss0 = Simplifier.clear_ss simpset_basic addsimps ths
   180   in fn ss => ALLGOALS (full_simp_tac (Simplifier.inherit_context ss ss0)) end;
   181 
   182 
   183 
   184 (** simprocs **)
   185 
   186 (* simproc for proving "(y = x) == False" from premise "~(x = y)" *)
   187 
   188 val use_neq_simproc = ref true;
   189 
   190 local
   191   val thy = the_context ();
   192   val neq_to_EQ_False = thm "not_sym" RS HOL.Eq_FalseI;
   193   fun neq_prover sg ss (eq $ lhs $ rhs) =
   194     let
   195       fun test thm = (case #prop (rep_thm thm) of
   196                     _ $ (Not $ (eq' $ l' $ r')) =>
   197                       Not = HOLogic.Not andalso eq' = eq andalso
   198                       r' aconv lhs andalso l' aconv rhs
   199                   | _ => false)
   200     in if !use_neq_simproc then case find_first test (prems_of_ss ss)
   201      of NONE => NONE
   202       | SOME thm => SOME (thm RS neq_to_EQ_False)
   203      else NONE
   204     end
   205 in
   206 
   207 val neq_simproc = Simplifier.simproc thy "neq_simproc" ["x = y"] neq_prover;
   208 
   209 end;
   210 
   211 
   212 (* simproc for Let *)
   213 
   214 val use_let_simproc = ref true;
   215 
   216 local
   217   val thy = the_context ();
   218   val Let_folded = thm "Let_folded";
   219   val Let_unfold = thm "Let_unfold";
   220   val (f_Let_unfold, x_Let_unfold) =
   221       let val [(_$(f$x)$_)] = prems_of Let_unfold
   222       in (cterm_of thy f, cterm_of thy x) end
   223   val (f_Let_folded, x_Let_folded) =
   224       let val [(_$(f$x)$_)] = prems_of Let_folded
   225       in (cterm_of thy f, cterm_of thy x) end;
   226   val g_Let_folded =
   227       let val [(_$_$(g$_))] = prems_of Let_folded in cterm_of thy g end;
   228 in
   229 
   230 val let_simproc =
   231   Simplifier.simproc thy "let_simp" ["Let x f"]
   232    (fn sg => fn ss => fn t =>
   233      let val ctxt = Simplifier.the_context ss;
   234          val ([t'], ctxt') = Variable.import_terms false [t] ctxt;
   235      in Option.map (hd o Variable.export ctxt' ctxt o single)
   236       (case t' of (Const ("Let",_)$x$f) => (* x and f are already in normal form *)
   237          if not (!use_let_simproc) then NONE
   238          else if is_Free x orelse is_Bound x orelse is_Const x
   239          then SOME (thm "Let_def")
   240          else
   241           let
   242              val n = case f of (Abs (x,_,_)) => x | _ => "x";
   243              val cx = cterm_of sg x;
   244              val {T=xT,...} = rep_cterm cx;
   245              val cf = cterm_of sg f;
   246              val fx_g = Simplifier.rewrite ss (Thm.capply cf cx);
   247              val (_$_$g) = prop_of fx_g;
   248              val g' = abstract_over (x,g);
   249            in (if (g aconv g')
   250                then
   251                   let
   252                     val rl = cterm_instantiate [(f_Let_unfold,cf),(x_Let_unfold,cx)] Let_unfold;
   253                   in SOME (rl OF [fx_g]) end
   254                else if Term.betapply (f,x) aconv g then NONE (*avoid identity conversion*)
   255                else let
   256                      val abs_g'= Abs (n,xT,g');
   257                      val g'x = abs_g'$x;
   258                      val g_g'x = symmetric (beta_conversion false (cterm_of sg g'x));
   259                      val rl = cterm_instantiate
   260                                [(f_Let_folded,cterm_of sg f),(x_Let_folded,cx),
   261                                 (g_Let_folded,cterm_of sg abs_g')]
   262                                Let_folded;
   263                    in SOME (rl OF [transitive fx_g g_g'x])
   264                    end)
   265            end
   266         | _ => NONE)
   267      end)
   268 
   269 end;
   270 
   271 
   272 (* generic refutation procedure *)
   273 
   274 (* parameters:
   275 
   276    test: term -> bool
   277    tests if a term is at all relevant to the refutation proof;
   278    if not, then it can be discarded. Can improve performance,
   279    esp. if disjunctions can be discarded (no case distinction needed!).
   280 
   281    prep_tac: int -> tactic
   282    A preparation tactic to be applied to the goal once all relevant premises
   283    have been moved to the conclusion.
   284 
   285    ref_tac: int -> tactic
   286    the actual refutation tactic. Should be able to deal with goals
   287    [| A1; ...; An |] ==> False
   288    where the Ai are atomic, i.e. no top-level &, | or EX
   289 *)
   290 
   291 local
   292   val nnf_simpset =
   293     empty_ss setmkeqTrue mk_eq_True
   294     setmksimps (mksimps mksimps_pairs)
   295     addsimps [thm "imp_conv_disj", thm "iff_conv_conj_imp", thm "de_Morgan_disj", thm "de_Morgan_conj",
   296       thm "not_all", thm "not_ex", thm "not_not"];
   297   fun prem_nnf_tac i st =
   298     full_simp_tac (Simplifier.theory_context (Thm.theory_of_thm st) nnf_simpset) i st;
   299 in
   300 fun refute_tac test prep_tac ref_tac =
   301   let val refute_prems_tac =
   302         REPEAT_DETERM
   303               (eresolve_tac [conjE, exE] 1 ORELSE
   304                filter_prems_tac test 1 ORELSE
   305                etac disjE 1) THEN
   306         ((etac notE 1 THEN eq_assume_tac 1) ORELSE
   307          ref_tac 1);
   308   in EVERY'[TRY o filter_prems_tac test,
   309             REPEAT_DETERM o etac rev_mp, prep_tac, rtac ccontr, prem_nnf_tac,
   310             SELECT_GOAL (DEPTH_SOLVE refute_prems_tac)]
   311   end;
   312 end;
   313 
   314 val defALL_regroup =
   315   Simplifier.simproc (the_context ())
   316     "defined ALL" ["ALL x. P x"] Quantifier1.rearrange_all;
   317 
   318 val defEX_regroup =
   319   Simplifier.simproc (the_context ())
   320     "defined EX" ["EX x. P x"] Quantifier1.rearrange_ex;
   321 
   322 
   323 val simpset_simprocs = simpset_basic
   324   addsimprocs [defALL_regroup, defEX_regroup, neq_simproc, let_simproc]
   325 
   326 end;