(* Title: Pure/simplifier.ML ID: $Id: simplifier.ML,v 2.9 2005/09/29 13:50:46 wenzelm Exp $ Author: Tobias Nipkow and Markus Wenzel, TU Muenchen Generic simplifier, suitable for most logics (see also meta_simplifier.ML for the actual meta-level rewriting engine). *) signature BASIC_SIMPLIFIER = sig include BASIC_META_SIMPLIFIER type context_solver val mk_context_solver: string -> (Proof.context -> thm list -> int -> tactic) -> context_solver type context_simproc val mk_context_simproc: string -> cterm list -> (Proof.context -> simpset -> term -> thm option) -> context_simproc val print_simpset: theory -> unit val simpset_ref_of_sg: theory -> simpset ref (*obsolete*) val simpset_ref_of: theory -> simpset ref val simpset_of_sg: theory -> simpset (*obsolete*) val simpset_of: theory -> simpset val SIMPSET: (simpset -> tactic) -> tactic val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic val simpset: unit -> simpset val simpset_ref: unit -> simpset ref val Addsimps: thm list -> unit val Delsimps: thm list -> unit val Addsimprocs: simproc list -> unit val Delsimprocs: simproc list -> unit val Addcongs: thm list -> unit val Delcongs: thm list -> unit val local_simpset_of: Proof.context -> simpset val safe_asm_full_simp_tac: simpset -> int -> tactic val simp_tac: simpset -> int -> tactic val asm_simp_tac: simpset -> int -> tactic val full_simp_tac: simpset -> int -> tactic val asm_lr_simp_tac: simpset -> int -> tactic val asm_full_simp_tac: simpset -> int -> tactic val Simp_tac: int -> tactic val Asm_simp_tac: int -> tactic val Full_simp_tac: int -> tactic val Asm_lr_simp_tac: int -> tactic val Asm_full_simp_tac: int -> tactic val simplify: simpset -> thm -> thm val asm_simplify: simpset -> thm -> thm val full_simplify: simpset -> thm -> thm val asm_lr_simplify: simpset -> thm -> thm val asm_full_simplify: simpset -> thm -> thm end; signature SIMPLIFIER = sig include BASIC_SIMPLIFIER val clear_ss: simpset -> simpset val debug_bounds: bool ref val inherit_bounds: simpset -> simpset -> simpset val simproc_i: theory -> string -> term list -> (theory -> simpset -> term -> thm option) -> simproc val simproc: theory -> string -> string list -> (theory -> simpset -> term -> thm option) -> simproc val context_simproc_i: theory -> string -> term list -> (Proof.context -> simpset -> term -> thm option) -> context_simproc val context_simproc: theory -> string -> string list -> (Proof.context -> simpset -> term -> thm option) -> context_simproc val rewrite: simpset -> cterm -> thm val asm_rewrite: simpset -> cterm -> thm val full_rewrite: simpset -> cterm -> thm val asm_lr_rewrite: simpset -> cterm -> thm val asm_full_rewrite: simpset -> cterm -> thm val add_context_simprocs: context_simproc list -> theory -> theory val del_context_simprocs: context_simproc list -> theory -> theory val set_context_subgoaler: (Proof.context -> simpset -> int -> tactic) -> theory -> theory val reset_context_subgoaler: theory -> theory val add_context_looper: string * (Proof.context -> int -> Tactical.tactic) -> theory -> theory val del_context_looper: string -> theory -> theory val add_context_unsafe_solver: context_solver -> theory -> theory val add_context_safe_solver: context_solver -> theory -> theory val print_local_simpset: Proof.context -> unit val get_local_simpset: Proof.context -> simpset val put_local_simpset: simpset -> Proof.context -> Proof.context val change_global_ss: (simpset * thm list -> simpset) -> theory attribute val change_local_ss: (simpset * thm list -> simpset) -> Proof.context attribute val simp_add_global: theory attribute val simp_del_global: theory attribute val simp_add_local: Proof.context attribute val simp_del_local: Proof.context attribute val cong_add_global: theory attribute val cong_del_global: theory attribute val cong_add_local: Proof.context attribute val cong_del_local: Proof.context attribute val change_simpset_of: (simpset * 'a -> simpset) -> 'a -> theory -> theory val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list val method_setup: (Args.T list -> (Method.modifier * Args.T list)) list -> (theory -> theory) list val easy_setup: thm -> thm list -> (theory -> theory) list end; structure Simplifier: SIMPLIFIER = struct open MetaSimplifier; (** context dependent simpset components **) (* datatype context_solver *) datatype context_solver = ContextSolver of (string * (Proof.context -> thm list -> int -> tactic)) * stamp; fun mk_context_solver name f = ContextSolver ((name, f), stamp ()); fun eq_context_solver (ContextSolver (_, id1), ContextSolver (_, id2)) = (id1 = id2); val merge_context_solvers = gen_merge_lists eq_context_solver; (* datatype context_simproc *) datatype context_simproc = ContextSimproc of (string * cterm list * (Proof.context -> simpset -> term -> thm option)) * stamp; fun mk_context_simproc name lhss f = ContextSimproc ((name, lhss, f), stamp ()); fun eq_context_simproc (ContextSimproc (_, id1), ContextSimproc (_, id2)) = (id1 = id2); val merge_context_simprocs = gen_merge_lists eq_context_simproc; fun context_simproc_i thy name = mk_context_simproc name o map (Thm.cterm_of thy o Logic.varify); fun context_simproc thy name = context_simproc_i thy name o map (Sign.read_term thy); (* datatype context_ss *) datatype context_ss = ContextSS of {simprocs: context_simproc list, subgoal_tac: (Proof.context -> simpset -> int -> tactic) option, loop_tacs: (string * (Proof.context -> int -> tactic)) list, unsafe_solvers: context_solver list, solvers: context_solver list}; fun context_ss ctxt ss ctxt_ss = let val ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} = ctxt_ss; fun prep_simproc (ContextSimproc ((name, lhss, f), _)) = mk_simproc name lhss (K (f ctxt)); fun add_loop (name, f) simpset = simpset addloop (name, f ctxt); fun add_solver add (ContextSolver ((name, f), _)) simpset = add (simpset, mk_solver name (f ctxt)); in ((case subgoal_tac of NONE => ss | SOME tac => ss setsubgoaler tac ctxt) addsimprocs map prep_simproc simprocs) |> fold_rev add_loop loop_tacs |> fold_rev (add_solver (op addSolver)) unsafe_solvers |> fold_rev (add_solver (op addSSolver)) solvers end; fun make_context_ss (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) = ContextSS {simprocs = simprocs, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, unsafe_solvers = unsafe_solvers, solvers = solvers}; val empty_context_ss = make_context_ss ([], NONE, [], [], []); fun merge_context_ss (ctxt_ss1, ctxt_ss2) = let val ContextSS {simprocs = simprocs1, subgoal_tac = subgoal_tac1, loop_tacs = loop_tacs1, unsafe_solvers = unsafe_solvers1, solvers = solvers1} = ctxt_ss1; val ContextSS {simprocs = simprocs2, subgoal_tac = subgoal_tac2, loop_tacs = loop_tacs2, unsafe_solvers = unsafe_solvers2, solvers = solvers2} = ctxt_ss2; val simprocs' = merge_context_simprocs simprocs1 simprocs2; val subgoal_tac' = (case subgoal_tac1 of NONE => subgoal_tac2 | some => some); val loop_tacs' = merge_alists loop_tacs1 loop_tacs2; val unsafe_solvers' = merge_context_solvers unsafe_solvers1 unsafe_solvers2; val solvers' = merge_context_solvers solvers1 solvers2; in make_context_ss (simprocs', subgoal_tac', loop_tacs', unsafe_solvers', solvers') end; (** global and local simpset data **) (* theory data kind 'Pure/simpset' *) structure GlobalSimpset = TheoryDataFun (struct val name = "Pure/simpset"; type T = simpset ref * context_ss; val empty = (ref empty_ss, empty_context_ss); fun copy (ref ss, ctxt_ss) = (ref ss, ctxt_ss): T; (*create new reference!*) val extend = copy; fun merge _ ((ref ss1, ctxt_ss1), (ref ss2, ctxt_ss2)) = (ref (merge_ss (ss1, ss2)), merge_context_ss (ctxt_ss1, ctxt_ss2)); fun print _ (ref ss, _) = print_ss ss; end); val _ = Context.add_setup [GlobalSimpset.init]; val print_simpset = GlobalSimpset.print; val simpset_ref_of = #1 o GlobalSimpset.get; val simpset_ref_of_sg = simpset_ref_of; val get_context_ss = #2 o GlobalSimpset.get o ProofContext.theory_of; fun map_context_ss f = GlobalSimpset.map (apsnd (fn ContextSS {simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers} => make_context_ss (f (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers)))); (* access global simpset *) val simpset_of = ! o simpset_ref_of; val simpset_of_sg = simpset_of; fun SIMPSET tacf state = tacf (simpset_of (Thm.theory_of_thm state)) state; fun SIMPSET' tacf i state = tacf (simpset_of (Thm.theory_of_thm state)) i state; val simpset = simpset_of o Context.the_context; val simpset_ref = simpset_ref_of o Context.the_context; (* change global simpset *) fun change_simpset_of f x thy = let val r = simpset_ref_of thy in r := f (! r, x); thy end; fun change_simpset f x = (change_simpset_of f x (Context.the_context ()); ()); val Addsimps = change_simpset (op addsimps); val Delsimps = change_simpset (op delsimps); val Addsimprocs = change_simpset (op addsimprocs); val Delsimprocs = change_simpset (op delsimprocs); val Addcongs = change_simpset (op addcongs); val Delcongs = change_simpset (op delcongs); (* change context dependent components *) fun add_context_simprocs procs = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (merge_context_simprocs procs simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers)); fun del_context_simprocs procs = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (gen_rems eq_context_simproc (simprocs, procs), subgoal_tac, loop_tacs, unsafe_solvers, solvers)); fun set_context_subgoaler tac = map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) => (simprocs, SOME tac, loop_tacs, unsafe_solvers, solvers)); val reset_context_subgoaler = map_context_ss (fn (simprocs, _, loop_tacs, unsafe_solvers, solvers) => (simprocs, NONE, loop_tacs, unsafe_solvers, solvers)); fun add_context_looper (name, tac) = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (simprocs, subgoal_tac, merge_alists [(name, tac)] loop_tacs, unsafe_solvers, solvers)); fun del_context_looper name = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (simprocs, subgoal_tac, filter_out (equal name o #1) loop_tacs, unsafe_solvers, solvers)); fun add_context_unsafe_solver solver = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (simprocs, subgoal_tac, loop_tacs, merge_context_solvers [solver] unsafe_solvers, solvers)); fun add_context_safe_solver solver = map_context_ss (fn (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, solvers) => (simprocs, subgoal_tac, loop_tacs, unsafe_solvers, merge_context_solvers [solver] solvers)); (* proof data kind 'Pure/simpset' *) structure LocalSimpset = ProofDataFun (struct val name = "Pure/simpset"; type T = simpset; val init = simpset_of; fun print ctxt ss = print_ss (context_ss ctxt ss (get_context_ss ctxt)); end); val _ = Context.add_setup [LocalSimpset.init]; val print_local_simpset = LocalSimpset.print; val get_local_simpset = LocalSimpset.get; val put_local_simpset = LocalSimpset.put; fun map_local_simpset f ctxt = put_local_simpset (f (get_local_simpset ctxt)) ctxt; fun local_simpset_of ctxt = context_ss ctxt (get_local_simpset ctxt) (get_context_ss ctxt); (* attributes *) fun change_global_ss f (thy, th) = let val r = simpset_ref_of thy in r := f (! r, [th]); (thy, th) end; fun change_local_ss f (ctxt, th) = let val ss = f (get_local_simpset ctxt, [th]) in (put_local_simpset ss ctxt, th) end; val simp_add_global = change_global_ss (op addsimps); val simp_del_global = change_global_ss (op delsimps); val simp_add_local = change_local_ss (op addsimps); val simp_del_local = change_local_ss (op delsimps); val cong_add_global = change_global_ss (op addcongs); val cong_del_global = change_global_ss (op delcongs); val cong_add_local = change_local_ss (op addcongs); val cong_del_local = change_local_ss (op delcongs); (* tactics *) val simp_tac = generic_simp_tac false (false, false, false); val asm_simp_tac = generic_simp_tac false (false, true, false); val full_simp_tac = generic_simp_tac false (true, false, false); val asm_lr_simp_tac = generic_simp_tac false (true, true, false); val asm_full_simp_tac = generic_simp_tac false (true, true, true); val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true); (*the abstraction over the proof state delays the dereferencing*) fun Simp_tac i st = simp_tac (simpset ()) i st; fun Asm_simp_tac i st = asm_simp_tac (simpset ()) i st; fun Full_simp_tac i st = full_simp_tac (simpset ()) i st; fun Asm_lr_simp_tac i st = asm_lr_simp_tac (simpset ()) i st; fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st; (* conversions *) val simplify = simp_thm (false, false, false); val asm_simplify = simp_thm (false, true, false); val full_simplify = simp_thm (true, false, false); val asm_lr_simplify = simp_thm (true, true, false); val asm_full_simplify = simp_thm (true, true, true); val rewrite = simp_cterm (false, false, false); val asm_rewrite = simp_cterm (false, true, false); val full_rewrite = simp_cterm (true, false, false); val asm_lr_rewrite = simp_cterm (true, true, false); val asm_full_rewrite = simp_cterm (true, true, true); (** concrete syntax of attributes **) (* add / del *) val simpN = "simp"; val congN = "cong"; val addN = "add"; val delN = "del"; val onlyN = "only"; val no_asmN = "no_asm"; val no_asm_useN = "no_asm_use"; val no_asm_simpN = "no_asm_simp"; val asm_lrN = "asm_lr"; val simp_attr = (Attrib.add_del_args simp_add_global simp_del_global, Attrib.add_del_args simp_add_local simp_del_local); val cong_attr = (Attrib.add_del_args cong_add_global cong_del_global, Attrib.add_del_args cong_add_local cong_del_local); (* conversions *) local fun conv_mode x = ((Args.parens (Args.$$$ no_asmN) >> K simplify || Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify || Args.parens (Args.$$$ no_asm_useN) >> K full_simplify || Scan.succeed asm_full_simplify) |> Scan.lift) x; fun simplified_att get args = Attrib.syntax (conv_mode -- args >> (fn (f, ths) => Drule.rule_attribute (fn x => f ((if null ths then I else clear_ss) (get x) addsimps ths)))); in val simplified_attr = (simplified_att simpset_of Attrib.global_thmss, simplified_att local_simpset_of Attrib.local_thmss); end; (* setup attributes *) val _ = Context.add_setup [Attrib.add_attributes [(simpN, simp_attr, "declaration of simplification rule"), (congN, cong_attr, "declaration of Simplifier congruence rule"), ("simplified", simplified_attr, "simplified rule")]]; (** proof methods **) (* simplification *) val simp_options = (Args.parens (Args.$$$ no_asmN) >> K simp_tac || Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac || Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac || Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac || Scan.succeed asm_full_simp_tac); fun simp_flags x = (Scan.repeat (Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat) >> setmp MetaSimplifier.simp_depth_limit) >> (curry (Library.foldl op o) I o rev)) x; val cong_modifiers = [Args.$$$ congN -- Args.colon >> K ((I, cong_add_local):Method.modifier), Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add_local), Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del_local)]; val simp_modifiers = [Args.$$$ simpN -- Args.colon >> K (I, simp_add_local), Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add_local), Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del_local), Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)] @ cong_modifiers; val simp_modifiers' = [Args.add -- Args.colon >> K (I, simp_add_local), Args.del -- Args.colon >> K (I, simp_del_local), Args.$$$ onlyN -- Args.colon >> K (map_local_simpset clear_ss, simp_add_local)] @ cong_modifiers; fun simp_args more_mods = Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags) (more_mods @ simp_modifiers'); fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts => ALLGOALS (Method.insert_tac (prems @ facts)) THEN (FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt)); fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts => HEADGOAL (Method.insert_tac (prems @ facts) THEN' ((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt))); (* setup methods *) fun setup_methods more_mods = Method.add_methods [(simpN, simp_args more_mods simp_method', "simplification"), ("simp_all", simp_args more_mods simp_method, "simplification (all goals)")]; fun method_setup mods = [setup_methods mods]; (** easy_setup **) fun easy_setup reflect trivs = let val trivialities = Drule.reflexive_thm :: trivs; fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac]; val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac; (*no premature instantiation of variables during simplification*) fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac]; val safe_solver = mk_solver "easy safe" safe_solver_tac; fun mk_eq thm = if Logic.is_equals (Thm.concl_of thm) then [thm] else [thm RS reflect] handle THM _ => []; fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm); fun init_ss thy = (simpset_ref_of thy := empty_ss setsubgoaler asm_simp_tac setSSolver safe_solver setSolver unsafe_solver setmksimps mksimps; thy); in method_setup [] @ [init_ss] end; end; structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier; open BasicSimplifier;