src/Pure/simplifier.ML
author wenzelm
Sun Jul 08 19:51:58 2007 +0200 (2007-07-08)
changeset 23655 d2d1138e0ddc
parent 23598 e03a43b8178c
child 24024 c46bd50df3f9
permissions -rw-r--r--
replaced exception TableFun/GraphFun.DUPS by TableFun/GraphFun.DUP;
     1 (*  Title:      Pure/simplifier.ML
     2     ID:         $Id$
     3     Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
     4 
     5 Generic simplifier, suitable for most logics (see also
     6 meta_simplifier.ML for the actual meta-level rewriting engine).
     7 *)
     8 
     9 signature BASIC_SIMPLIFIER =
    10 sig
    11   include BASIC_META_SIMPLIFIER
    12   val print_simpset: theory -> unit
    13   val change_simpset_of: theory -> (simpset -> simpset) -> unit
    14   val change_simpset: (simpset -> simpset) -> unit
    15   val simpset_of: theory -> simpset
    16   val simpset: unit -> simpset
    17   val SIMPSET: (simpset -> tactic) -> tactic
    18   val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
    19   val Addsimps: thm list -> unit
    20   val Delsimps: thm list -> unit
    21   val Addsimprocs: simproc list -> unit
    22   val Delsimprocs: simproc list -> unit
    23   val Addcongs: thm list -> unit
    24   val Delcongs: thm list -> unit
    25   val local_simpset_of: Proof.context -> simpset
    26   val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
    27   val safe_asm_full_simp_tac: simpset -> int -> tactic
    28   val               simp_tac: simpset -> int -> tactic
    29   val           asm_simp_tac: simpset -> int -> tactic
    30   val          full_simp_tac: simpset -> int -> tactic
    31   val        asm_lr_simp_tac: simpset -> int -> tactic
    32   val      asm_full_simp_tac: simpset -> int -> tactic
    33   val               Simp_tac:            int -> tactic
    34   val           Asm_simp_tac:            int -> tactic
    35   val          Full_simp_tac:            int -> tactic
    36   val        Asm_lr_simp_tac:            int -> tactic
    37   val      Asm_full_simp_tac:            int -> tactic
    38   val          simplify: simpset -> thm -> thm
    39   val      asm_simplify: simpset -> thm -> thm
    40   val     full_simplify: simpset -> thm -> thm
    41   val   asm_lr_simplify: simpset -> thm -> thm
    42   val asm_full_simplify: simpset -> thm -> thm
    43 end;
    44 
    45 signature SIMPLIFIER =
    46 sig
    47   include BASIC_SIMPLIFIER
    48   val clear_ss: simpset -> simpset
    49   val debug_bounds: bool ref
    50   val inherit_context: simpset -> simpset -> simpset
    51   val the_context: simpset -> Proof.context
    52   val context: Proof.context -> simpset -> simpset
    53   val theory_context: theory  -> simpset -> simpset
    54   val simproc_i: theory -> string -> term list
    55     -> (theory -> simpset -> term -> thm option) -> simproc
    56   val simproc: theory -> string -> string list
    57     -> (theory -> simpset -> term -> thm option) -> simproc
    58   val          rewrite: simpset -> conv
    59   val      asm_rewrite: simpset -> conv
    60   val     full_rewrite: simpset -> conv
    61   val   asm_lr_rewrite: simpset -> conv
    62   val asm_full_rewrite: simpset -> conv
    63   val get_simpset: theory -> simpset
    64   val print_local_simpset: Proof.context -> unit
    65   val get_local_simpset: Proof.context -> simpset
    66   val put_local_simpset: simpset -> Proof.context -> Proof.context
    67   val get_ss: Context.generic -> simpset
    68   val map_ss: (simpset -> simpset) -> Context.generic -> Context.generic
    69   val attrib: (simpset * thm list -> simpset) -> attribute
    70   val simp_add: attribute
    71   val simp_del: attribute
    72   val cong_add: attribute
    73   val cong_del: attribute
    74   val get_simproc: Proof.context -> xstring -> simproc
    75   val def_simproc: {name: string, lhss: string list,
    76     proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
    77     local_theory -> local_theory
    78   val def_simproc_i: {name: string, lhss: term list,
    79     proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
    80     local_theory -> local_theory
    81   val cong_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
    82   val simp_modifiers': (Args.T list -> (Method.modifier * Args.T list)) list
    83   val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
    84   val method_setup: (Args.T list -> (Method.modifier * Args.T list)) list
    85     -> theory -> theory
    86   val easy_setup: thm -> thm list -> theory -> theory
    87 end;
    88 
    89 structure Simplifier: SIMPLIFIER =
    90 struct
    91 
    92 open MetaSimplifier;
    93 
    94 
    95 (** simpset data **)
    96 
    97 (* global simpsets *)
    98 
    99 structure GlobalSimpset = TheoryDataFun
   100 (
   101   type T = simpset ref;
   102   val empty = ref empty_ss;
   103   fun copy (ref ss) = ref ss: T;
   104   fun extend (ref ss) = ref (MetaSimplifier.inherit_context empty_ss ss);
   105   fun merge _ (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
   106 );
   107 
   108 val _ = Context.add_setup GlobalSimpset.init;
   109 fun print_simpset thy = print_ss (! (GlobalSimpset.get thy));
   110 val get_simpset = ! o GlobalSimpset.get;
   111 
   112 val change_simpset_of = change o GlobalSimpset.get;
   113 fun change_simpset f = change_simpset_of (ML_Context.the_context ()) f;
   114 
   115 fun simpset_of thy = MetaSimplifier.context (ProofContext.init thy) (get_simpset thy);
   116 val simpset = simpset_of o ML_Context.the_context;
   117 
   118 
   119 fun SIMPSET tacf st = tacf (simpset_of (Thm.theory_of_thm st)) st;
   120 fun SIMPSET' tacf i st = tacf (simpset_of (Thm.theory_of_thm st)) i st;
   121 
   122 fun Addsimps args = change_simpset (fn ss => ss addsimps args);
   123 fun Delsimps args = change_simpset (fn ss => ss delsimps args);
   124 fun Addsimprocs args = change_simpset (fn ss => ss addsimprocs args);
   125 fun Delsimprocs args = change_simpset (fn ss => ss delsimprocs args);
   126 fun Addcongs args = change_simpset (fn ss => ss addcongs args);
   127 fun Delcongs args = change_simpset (fn ss => ss delcongs args);
   128 
   129 
   130 (* local simpsets *)
   131 
   132 structure LocalSimpset = ProofDataFun
   133 (
   134   type T = simpset;
   135   val init = get_simpset;
   136 );
   137 
   138 val print_local_simpset = print_ss o LocalSimpset.get;
   139 val get_local_simpset = LocalSimpset.get;
   140 val put_local_simpset = LocalSimpset.put;
   141 
   142 fun local_simpset_of ctxt = MetaSimplifier.context ctxt (get_local_simpset ctxt);
   143 
   144 val _ = ML_Context.value_antiq "simpset"
   145   (Scan.succeed ("simpset", "Simplifier.local_simpset_of (ML_Context.the_local_context ())"));
   146 
   147 
   148 (* generic simpsets *)
   149 
   150 fun get_ss (Context.Theory thy) = simpset_of thy
   151   | get_ss (Context.Proof ctxt) = local_simpset_of ctxt;
   152 
   153 fun map_ss f (Context.Theory thy) = (change_simpset_of thy f; Context.Theory thy)
   154   | map_ss f (Context.Proof ctxt) = Context.Proof (LocalSimpset.map f ctxt);
   155 
   156 
   157 (* attributes *)
   158 
   159 fun attrib f = Thm.declaration_attribute (fn th => map_ss (fn ss => f (ss, [th])));
   160 
   161 val simp_add = attrib (op addsimps);
   162 val simp_del = attrib (op delsimps);
   163 val cong_add = attrib (op addcongs);
   164 val cong_del = attrib (op delcongs);
   165 
   166 
   167 
   168 (** named simprocs **)
   169 
   170 fun err_dup_simproc name = error ("Duplicate simproc: " ^ quote name);
   171 
   172 
   173 (* data *)
   174 
   175 structure Simprocs = GenericDataFun
   176 (
   177   type T = simproc NameSpace.table;
   178   val empty = NameSpace.empty_table;
   179   val extend = I;
   180   fun merge _ simprocs = NameSpace.merge_tables eq_simproc simprocs
   181     handle Symtab.DUP dup => err_dup_simproc dup;
   182 );
   183 
   184 
   185 (* get simprocs *)
   186 
   187 fun get_simproc ctxt xname =
   188   let
   189     val (space, tab) = Simprocs.get (Context.Proof ctxt);
   190     val name = NameSpace.intern space xname;
   191   in
   192     (case Symtab.lookup tab name of
   193       SOME proc => proc
   194     | NONE => error ("Undefined simplification procedure: " ^ quote name))
   195   end;
   196 
   197 val _ = ML_Context.value_antiq "simproc" (Scan.lift Args.name >> (fn name =>
   198   ("simproc",
   199     "Simplifier.get_simproc (ML_Context.the_local_context ()) " ^ ML_Syntax.print_string name)));
   200 
   201 
   202 (* define simprocs *)
   203 
   204 local
   205 
   206 fun gen_simproc prep {name, lhss, proc, identifier} lthy =
   207   let
   208     val naming = LocalTheory.full_naming lthy;
   209     val simproc = make_simproc
   210       {name = LocalTheory.full_name lthy name,
   211        lhss =
   212         let
   213           val lhss' = prep lthy lhss;
   214           val ctxt' = lthy
   215             |> fold Variable.declare_term lhss'
   216             |> fold Variable.auto_fixes lhss';
   217         in Variable.export_terms ctxt' lthy lhss' end
   218         |> map (Thm.cterm_of (ProofContext.theory_of lthy)),
   219        proc = proc,
   220        identifier = identifier}
   221       |> morph_simproc (LocalTheory.target_morphism lthy);
   222   in
   223     lthy |> LocalTheory.declaration (fn phi => fn context =>
   224       let
   225         val name' = Morphism.name phi name;
   226         val simproc' = morph_simproc phi simproc;
   227       in
   228         context
   229         |> Simprocs.map (fn simprocs =>
   230             NameSpace.extend_table naming [(name', simproc')] simprocs
   231               handle Symtab.DUP dup => err_dup_simproc dup)
   232         |> map_ss (fn ss => ss addsimprocs [simproc'])
   233       end)
   234   end;
   235 
   236 in
   237 
   238 val def_simproc = gen_simproc ProofContext.read_terms;
   239 val def_simproc_i = gen_simproc ProofContext.cert_terms;
   240 
   241 end;
   242 
   243 
   244 
   245 (** simplification tactics and rules **)
   246 
   247 fun solve_all_tac solvers ss =
   248   let
   249     val (_, {subgoal_tac, ...}) = MetaSimplifier.rep_ss ss;
   250     val solve_tac = subgoal_tac (MetaSimplifier.set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
   251   in DEPTH_SOLVE (solve_tac 1) end;
   252 
   253 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
   254 fun generic_simp_tac safe mode ss =
   255   let
   256     val (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = MetaSimplifier.rep_ss ss;
   257     val loop_tac = FIRST' (map (fn (_, tac) => tac ss) (rev loop_tacs));
   258     val solve_tac = FIRST' (map (MetaSimplifier.solver ss)
   259       (rev (if safe then solvers else unsafe_solvers)));
   260 
   261     fun simp_loop_tac i =
   262       asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
   263       (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
   264   in simp_loop_tac end;
   265 
   266 local
   267 
   268 fun simp rew mode ss thm =
   269   let
   270     val (_, {solvers = (unsafe_solvers, _), ...}) = MetaSimplifier.rep_ss ss;
   271     val tacf = solve_all_tac (rev unsafe_solvers);
   272     fun prover s th = Option.map #1 (Seq.pull (tacf s th));
   273   in rew mode prover ss thm end;
   274 
   275 in
   276 
   277 val simp_thm = simp MetaSimplifier.rewrite_thm;
   278 val simp_cterm = simp MetaSimplifier.rewrite_cterm;
   279 
   280 end;
   281 
   282 
   283 (* tactics *)
   284 
   285 val simp_tac = generic_simp_tac false (false, false, false);
   286 val asm_simp_tac = generic_simp_tac false (false, true, false);
   287 val full_simp_tac = generic_simp_tac false (true, false, false);
   288 val asm_lr_simp_tac = generic_simp_tac false (true, true, false);
   289 val asm_full_simp_tac = generic_simp_tac false (true, true, true);
   290 val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
   291 
   292 (*the abstraction over the proof state delays the dereferencing*)
   293 fun          Simp_tac i st =          simp_tac (simpset ()) i st;
   294 fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;
   295 fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;
   296 fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;
   297 fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;
   298 
   299 
   300 (* conversions *)
   301 
   302 val          simplify = simp_thm (false, false, false);
   303 val      asm_simplify = simp_thm (false, true, false);
   304 val     full_simplify = simp_thm (true, false, false);
   305 val   asm_lr_simplify = simp_thm (true, true, false);
   306 val asm_full_simplify = simp_thm (true, true, true);
   307 
   308 val          rewrite = simp_cterm (false, false, false);
   309 val      asm_rewrite = simp_cterm (false, true, false);
   310 val     full_rewrite = simp_cterm (true, false, false);
   311 val   asm_lr_rewrite = simp_cterm (true, true, false);
   312 val asm_full_rewrite = simp_cterm (true, true, true);
   313 
   314 
   315 
   316 (** concrete syntax of attributes **)
   317 
   318 (* add / del *)
   319 
   320 val simpN = "simp";
   321 val congN = "cong";
   322 val addN = "add";
   323 val delN = "del";
   324 val onlyN = "only";
   325 val no_asmN = "no_asm";
   326 val no_asm_useN = "no_asm_use";
   327 val no_asm_simpN = "no_asm_simp";
   328 val asm_lrN = "asm_lr";
   329 
   330 
   331 (* conversions *)
   332 
   333 local
   334 
   335 fun conv_mode x =
   336   ((Args.parens (Args.$$$ no_asmN) >> K simplify ||
   337     Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||
   338     Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||
   339     Scan.succeed asm_full_simplify) |> Scan.lift) x;
   340 
   341 in
   342 
   343 val simplified =
   344   Attrib.syntax (conv_mode -- Attrib.thms >> (fn (f, ths) => Thm.rule_attribute (fn x =>
   345     f ((if null ths then I else MetaSimplifier.clear_ss) (get_ss x) addsimps ths))));
   346 
   347 end;
   348 
   349 
   350 (* setup attributes *)
   351 
   352 val _ = Context.add_setup
   353  (Attrib.add_attributes
   354    [(simpN, Attrib.add_del_args simp_add simp_del, "declaration of Simplifier rule"),
   355     (congN, Attrib.add_del_args cong_add cong_del, "declaration of Simplifier congruence rule"),
   356     ("simplified", simplified, "simplified rule")]);
   357 
   358 
   359 
   360 (** proof methods **)
   361 
   362 (* simplification *)
   363 
   364 val simp_options =
   365  (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
   366   Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
   367   Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
   368   Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
   369   Scan.succeed asm_full_simp_tac);
   370 
   371 fun simp_flags x = (Scan.repeat
   372   (Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat)
   373     >> setmp MetaSimplifier.simp_depth_limit)
   374   >> (curry (Library.foldl op o) I o rev)) x;
   375 
   376 val cong_modifiers =
   377  [Args.$$$ congN -- Args.colon >> K ((I, cong_add): Method.modifier),
   378   Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add),
   379   Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del)];
   380 
   381 val simp_modifiers =
   382  [Args.$$$ simpN -- Args.colon >> K (I, simp_add),
   383   Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add),
   384   Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del),
   385   Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
   386     >> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
   387    @ cong_modifiers;
   388 
   389 val simp_modifiers' =
   390  [Args.add -- Args.colon >> K (I, simp_add),
   391   Args.del -- Args.colon >> K (I, simp_del),
   392   Args.$$$ onlyN -- Args.colon
   393     >> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
   394    @ cong_modifiers;
   395 
   396 fun simp_args more_mods =
   397   Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags)
   398     (more_mods @ simp_modifiers');
   399 
   400 fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
   401   ALLGOALS (Method.insert_tac (prems @ facts)) THEN
   402     (FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));
   403 
   404 fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
   405   HEADGOAL (Method.insert_tac (prems @ facts) THEN'
   406       ((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt)));
   407 
   408 
   409 
   410 (** setup **)
   411 
   412 fun method_setup more_mods = Method.add_methods
   413  [(simpN, simp_args more_mods simp_method', "simplification"),
   414   ("simp_all", simp_args more_mods simp_method, "simplification (all goals)")];
   415 
   416 fun easy_setup reflect trivs = method_setup [] #> (fn thy =>
   417   let
   418     val trivialities = Drule.reflexive_thm :: trivs;
   419 
   420     fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac];
   421     val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
   422 
   423     (*no premature instantiation of variables during simplification*)
   424     fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac];
   425     val safe_solver = mk_solver "easy safe" safe_solver_tac;
   426 
   427     fun mk_eq thm =
   428       if can Logic.dest_equals (Thm.concl_of thm) then [thm]
   429       else [thm RS reflect] handle THM _ => [];
   430 
   431     fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);
   432   in
   433     GlobalSimpset.get thy :=
   434       empty_ss setsubgoaler asm_simp_tac
   435       setSSolver safe_solver
   436       setSolver unsafe_solver
   437       setmksimps mksimps;
   438     thy
   439   end);
   440 
   441 end;
   442 
   443 structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
   444 open BasicSimplifier;