1 (* Title: Pure/simplifier.ML
2 Author: Tobias Nipkow and Markus Wenzel, TU Muenchen
4 Generic simplifier, suitable for most logics (see also
5 raw_simplifier.ML for the actual meta-level rewriting engine).
8 signature BASIC_SIMPLIFIER =
10 include BASIC_RAW_SIMPLIFIER
11 val map_simpset: (simpset -> simpset) -> Proof.context -> Proof.context
12 val simpset_of: Proof.context -> simpset
13 val global_simpset_of: theory -> simpset
14 val Addsimprocs: simproc list -> unit
15 val Delsimprocs: simproc list -> unit
16 val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
17 val safe_asm_full_simp_tac: simpset -> int -> tactic
18 val simp_tac: simpset -> int -> tactic
19 val asm_simp_tac: simpset -> int -> tactic
20 val full_simp_tac: simpset -> int -> tactic
21 val asm_lr_simp_tac: simpset -> int -> tactic
22 val asm_full_simp_tac: simpset -> int -> tactic
23 val simplify: simpset -> thm -> thm
24 val asm_simplify: simpset -> thm -> thm
25 val full_simplify: simpset -> thm -> thm
26 val asm_lr_simplify: simpset -> thm -> thm
27 val asm_full_simplify: simpset -> thm -> thm
30 signature SIMPLIFIER =
32 include BASIC_SIMPLIFIER
33 val map_simpset_global: (simpset -> simpset) -> theory -> theory
34 val pretty_ss: Proof.context -> simpset -> Pretty.T
35 val clear_ss: simpset -> simpset
36 val default_mk_sym: simpset -> thm -> thm option
37 val debug_bounds: bool Unsynchronized.ref
38 val prems_of: simpset -> thm list
39 val add_simp: thm -> simpset -> simpset
40 val del_simp: thm -> simpset -> simpset
41 val add_eqcong: thm -> simpset -> simpset
42 val del_eqcong: thm -> simpset -> simpset
43 val add_cong: thm -> simpset -> simpset
44 val del_cong: thm -> simpset -> simpset
45 val add_prems: thm list -> simpset -> simpset
46 val mksimps: simpset -> thm -> thm list
47 val set_mksimps: (simpset -> thm -> thm list) -> simpset -> simpset
48 val set_mkcong: (simpset -> thm -> thm) -> simpset -> simpset
49 val set_mksym: (simpset -> thm -> thm option) -> simpset -> simpset
50 val set_mkeqTrue: (simpset -> thm -> thm option) -> simpset -> simpset
51 val set_termless: (term * term -> bool) -> simpset -> simpset
52 val set_subgoaler: (simpset -> int -> tactic) -> simpset -> simpset
53 val inherit_context: simpset -> simpset -> simpset
54 val the_context: simpset -> Proof.context
55 val context: Proof.context -> simpset -> simpset
56 val global_context: theory -> simpset -> simpset
57 val with_context: Proof.context -> (simpset -> simpset) -> simpset -> simpset
58 val simproc_global_i: theory -> string -> term list ->
59 (theory -> simpset -> term -> thm option) -> simproc
60 val simproc_global: theory -> string -> string list ->
61 (theory -> simpset -> term -> thm option) -> simproc
62 val rewrite: simpset -> conv
63 val asm_rewrite: simpset -> conv
64 val full_rewrite: simpset -> conv
65 val asm_lr_rewrite: simpset -> conv
66 val asm_full_rewrite: simpset -> conv
67 val get_ss: Context.generic -> simpset
68 val map_ss: (simpset -> simpset) -> Context.generic -> Context.generic
69 val attrib: (thm -> simpset -> simpset) -> attribute
70 val simp_add: attribute
71 val simp_del: attribute
72 val cong_add: attribute
73 val cong_del: attribute
74 val check_simproc: Proof.context -> xstring * Position.T -> string
75 val the_simproc: Proof.context -> string -> simproc
76 val def_simproc: {name: binding, lhss: term list,
77 proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
78 local_theory -> local_theory
79 val def_simproc_cmd: {name: binding, lhss: string list,
80 proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
81 local_theory -> local_theory
82 val cong_modifiers: Method.modifier parser list
83 val simp_modifiers': Method.modifier parser list
84 val simp_modifiers: Method.modifier parser list
85 val method_setup: Method.modifier parser list -> theory -> theory
86 val easy_setup: thm -> thm list -> theory -> theory
89 structure Simplifier: SIMPLIFIER =
97 structure Data = Generic_Data
99 type T = simpset * simproc Name_Space.table;
100 val empty : T = (empty_ss, Name_Space.empty_table "simproc");
101 fun extend (ss, tab) = (Raw_Simplifier.inherit_context empty_ss ss, tab);
102 fun merge ((ss1, tab1), (ss2, tab2)) =
103 (merge_ss (ss1, ss2), Name_Space.merge_tables (tab1, tab2));
106 val get_ss = fst o Data.get;
108 fun map_ss f context =
109 Data.map (apfst ((Raw_Simplifier.with_context (Context.proof_of context) f))) context;
111 val get_simprocs = snd o Data.get o Context.Proof;
115 (** pretty printing **)
117 fun pretty_ss ctxt ss =
119 val pretty_cterm = Syntax.pretty_term ctxt o Thm.term_of;
120 val pretty_thm = Display.pretty_thm ctxt;
121 fun pretty_proc (name, lhss) = Pretty.big_list (name ^ ":") (map pretty_cterm lhss);
122 fun pretty_cong (name, thm) =
123 Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, pretty_thm thm];
125 val {simps, procs, congs, loopers, unsafe_solvers, safe_solvers, ...} = dest_ss ss;
127 [Pretty.big_list "simplification rules:" (map (pretty_thm o #2) simps),
128 Pretty.big_list "simplification procedures:" (map pretty_proc (sort_wrt #1 procs)),
129 Pretty.big_list "congruences:" (map pretty_cong congs),
130 Pretty.strs ("loopers:" :: map quote loopers),
131 Pretty.strs ("unsafe solvers:" :: map quote unsafe_solvers),
132 Pretty.strs ("safe solvers:" :: map quote safe_solvers)]
142 fun attrib f = Thm.declaration_attribute (map_ss o f);
144 val simp_add = attrib add_simp;
145 val simp_del = attrib del_simp;
146 val cong_add = attrib add_cong;
147 val cong_del = attrib del_cong;
152 fun map_simpset f = Context.proof_map (map_ss f);
153 fun simpset_of ctxt = Raw_Simplifier.context ctxt (get_ss (Context.Proof ctxt));
155 val _ = Context.>> (Context.map_theory
156 (ML_Antiquote.value (Binding.name "simpset")
157 (Scan.succeed "Simplifier.simpset_of (ML_Context.the_local_context ())")));
162 fun map_simpset_global f = Context.theory_map (map_ss f);
163 fun global_simpset_of thy =
164 Raw_Simplifier.context (Proof_Context.init_global thy) (get_ss (Context.Theory thy));
166 fun Addsimprocs args = Context.>> (map_ss (fn ss => ss addsimprocs args));
167 fun Delsimprocs args = Context.>> (map_ss (fn ss => ss delsimprocs args));
171 (** named simprocs **)
175 fun check_simproc ctxt = Name_Space.check (Context.Proof ctxt) (get_simprocs ctxt) #> #1;
176 val the_simproc = Name_Space.get o get_simprocs;
179 Context.>> (Context.map_theory
180 (ML_Antiquote.value (Binding.name "simproc")
181 (Args.context -- Scan.lift (Parse.position Args.name)
182 >> (fn (ctxt, name) =>
183 "Simplifier.the_simproc (ML_Context.the_local_context ()) " ^
184 ML_Syntax.print_string (check_simproc ctxt name)))));
187 (* define simprocs *)
191 fun gen_simproc prep {name = b, lhss, proc, identifier} lthy =
193 val simproc = make_simproc
194 {name = Local_Theory.full_name lthy b,
197 val lhss' = prep lthy lhss;
198 val ctxt' = fold Variable.auto_fixes lhss' lthy;
199 in Variable.export_terms ctxt' lthy lhss' end
200 |> map (Thm.cterm_of (Proof_Context.theory_of lthy)),
202 identifier = identifier};
204 lthy |> Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => fn context =>
206 val b' = Morphism.binding phi b;
207 val simproc' = transform_simproc phi simproc;
210 |> Data.map (fn (ss, tab) =>
211 (ss addsimprocs [simproc'], #2 (Name_Space.define context true (b', simproc') tab)))
217 val def_simproc = gen_simproc Syntax.check_terms;
218 val def_simproc_cmd = gen_simproc Syntax.read_terms;
224 (** simplification tactics and rules **)
226 fun solve_all_tac solvers ss =
228 val (_, {subgoal_tac, ...}) = Raw_Simplifier.internal_ss ss;
229 val solve_tac = subgoal_tac (Raw_Simplifier.set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
230 in DEPTH_SOLVE (solve_tac 1) end;
232 (*NOTE: may instantiate unknowns that appear also in other subgoals*)
233 fun generic_simp_tac safe mode ss =
235 val (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = Raw_Simplifier.internal_ss ss;
236 val loop_tac = FIRST' (map (fn (_, tac) => tac ss) (rev loop_tacs));
237 val solve_tac = FIRST' (map (Raw_Simplifier.solver ss)
238 (rev (if safe then solvers else unsafe_solvers)));
240 fun simp_loop_tac i =
241 Raw_Simplifier.generic_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
242 (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
243 in SELECT_GOAL (simp_loop_tac 1) end;
247 fun simp rew mode ss thm =
249 val (_, {solvers = (unsafe_solvers, _), ...}) = Raw_Simplifier.internal_ss ss;
250 val tacf = solve_all_tac (rev unsafe_solvers);
251 fun prover s th = Option.map #1 (Seq.pull (tacf s th));
252 in rew mode prover ss thm end;
256 val simp_thm = simp Raw_Simplifier.rewrite_thm;
257 val simp_cterm = simp Raw_Simplifier.rewrite_cterm;
264 val simp_tac = generic_simp_tac false (false, false, false);
265 val asm_simp_tac = generic_simp_tac false (false, true, false);
266 val full_simp_tac = generic_simp_tac false (true, false, false);
267 val asm_lr_simp_tac = generic_simp_tac false (true, true, false);
268 val asm_full_simp_tac = generic_simp_tac false (true, true, true);
269 val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
274 val simplify = simp_thm (false, false, false);
275 val asm_simplify = simp_thm (false, true, false);
276 val full_simplify = simp_thm (true, false, false);
277 val asm_lr_simplify = simp_thm (true, true, false);
278 val asm_full_simplify = simp_thm (true, true, true);
280 val rewrite = simp_cterm (false, false, false);
281 val asm_rewrite = simp_cterm (false, true, false);
282 val full_rewrite = simp_cterm (true, false, false);
283 val asm_lr_rewrite = simp_cterm (true, true, false);
284 val asm_full_rewrite = simp_cterm (true, true, true);
288 (** concrete syntax of attributes **)
295 val no_asmN = "no_asm";
296 val no_asm_useN = "no_asm_use";
297 val no_asm_simpN = "no_asm_simp";
298 val asm_lrN = "asm_lr";
306 (Args.del -- Args.colon >> K (op delsimprocs) ||
307 Scan.option (Args.add -- Args.colon) >> K (op addsimprocs))
308 >> (fn f => fn simproc => fn phi => Thm.declaration_attribute
309 (K (map_ss (fn ss => f (ss, [transform_simproc phi simproc])))));
314 (Args.context -- Scan.lift add_del) :|-- (fn (ctxt, decl) =>
315 Scan.repeat1 (Scan.lift (Args.named_attribute (decl o the_simproc ctxt o check_simproc ctxt))))
316 >> (fn atts => Thm.declaration_attribute (fn th =>
317 fold (fn att => Thm.attribute_declaration (Morphism.form att) th) atts));
327 ((Args.parens (Args.$$$ no_asmN) >> K simplify ||
328 Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||
329 Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||
330 Scan.succeed asm_full_simplify) |> Scan.lift) x;
334 val simplified = conv_mode -- Attrib.thms >>
335 (fn (f, ths) => Thm.rule_attribute (fn context =>
336 f ((if null ths then I else Raw_Simplifier.clear_ss)
337 (simpset_of (Context.proof_of context)) addsimps ths)));
342 (* setup attributes *)
344 val _ = Context.>> (Context.map_theory
345 (Attrib.setup (Binding.name simpN) (Attrib.add_del simp_add simp_del)
346 "declaration of Simplifier rewrite rule" #>
347 Attrib.setup (Binding.name congN) (Attrib.add_del cong_add cong_del)
348 "declaration of Simplifier congruence rule" #>
349 Attrib.setup (Binding.name "simproc") simproc_att
350 "declaration of simplification procedures" #>
351 Attrib.setup (Binding.name "simplified") simplified "simplified rule"));
355 (** method syntax **)
358 [Args.$$$ congN -- Args.colon >> K ((I, cong_add): Method.modifier),
359 Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add),
360 Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del)];
363 [Args.$$$ simpN -- Args.colon >> K (I, simp_add),
364 Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add),
365 Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del),
366 Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
367 >> K (Context.proof_map (map_ss Raw_Simplifier.clear_ss), simp_add)]
370 val simp_modifiers' =
371 [Args.add -- Args.colon >> K (I, simp_add),
372 Args.del -- Args.colon >> K (I, simp_del),
373 Args.$$$ onlyN -- Args.colon
374 >> K (Context.proof_map (map_ss Raw_Simplifier.clear_ss), simp_add)]
378 (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
379 Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
380 Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
381 Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
382 Scan.succeed asm_full_simp_tac);
384 fun simp_method more_mods meth =
385 Scan.lift simp_options --|
386 Method.sections (more_mods @ simp_modifiers') >>
387 (fn tac => fn ctxt => METHOD (fn facts => meth ctxt tac facts));
393 fun method_setup more_mods =
394 Method.setup (Binding.name simpN)
395 (simp_method more_mods (fn ctxt => fn tac => fn facts =>
396 HEADGOAL (Method.insert_tac facts THEN'
397 (CHANGED_PROP oo tac) (simpset_of ctxt))))
399 Method.setup (Binding.name "simp_all")
400 (simp_method more_mods (fn ctxt => fn tac => fn facts =>
401 ALLGOALS (Method.insert_tac facts) THEN
402 (CHANGED_PROP o PARALLEL_GOALS o ALLGOALS o tac) (simpset_of ctxt)))
403 "simplification (all goals)";
405 fun easy_setup reflect trivs = method_setup [] #> Context.theory_map (map_ss (fn _ =>
407 val trivialities = Drule.reflexive_thm :: trivs;
409 fun unsafe_solver_tac ss =
410 FIRST' [resolve_tac (trivialities @ Raw_Simplifier.prems_of ss), assume_tac];
411 val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
413 (*no premature instantiation of variables during simplification*)
414 fun safe_solver_tac ss =
415 FIRST' [match_tac (trivialities @ Raw_Simplifier.prems_of ss), eq_assume_tac];
416 val safe_solver = mk_solver "easy safe" safe_solver_tac;
419 if can Logic.dest_equals (Thm.concl_of thm) then [thm]
420 else [thm RS reflect] handle THM _ => [];
422 fun mksimps thm = mk_eq (Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm);
425 setSSolver safe_solver
426 setSolver unsafe_solver
427 |> set_subgoaler asm_simp_tac
428 |> set_mksimps (K mksimps)
433 structure Basic_Simplifier: BASIC_SIMPLIFIER = Simplifier;
434 open Basic_Simplifier;