author | nipkow |
Fri, 06 Mar 1998 15:20:29 +0100 | |
changeset 4682 | ff081854fc86 |
parent 4677 | c4b07b8579fd |
child 4713 | bea2ab2e360b |
permissions | -rw-r--r-- |
1243 | 1 |
(* Title: Provers/simplifier.ML |
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ID: $Id$ |
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Author: Tobias Nipkow and Markus Wenzel, TU Muenchen |
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Generic simplifier, suitable for most logics. See also Pure/thm.ML |
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for the actual meta level rewriting engine. |
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*) |
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infix 4 |
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setsubgoaler setloop addloop delloop setSSolver addSSolver setSolver |
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addSolver addsimps delsimps addeqcongs deleqcongs |
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setmksimps setmkeqTrue setmksym settermless addsimprocs delsimprocs; |
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signature SIMPLIFIER = |
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sig |
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type simproc |
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val mk_simproc: string -> cterm list |
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-> (Sign.sg -> thm list -> term -> thm option) -> simproc |
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type simpset |
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val empty_ss: simpset |
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val rep_ss: simpset -> |
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{mss: meta_simpset, |
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subgoal_tac: simpset -> int -> tactic, |
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loop_tacs: (string * (int -> tactic))list, |
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finish_tac: thm list -> int -> tactic, |
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unsafe_finish_tac: thm list -> int -> tactic}; |
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val print_ss: simpset -> unit |
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val print_simpset: theory -> unit |
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val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset |
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val setloop: simpset * (int -> tactic) -> simpset |
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val addloop: simpset * (string * (int -> tactic)) -> simpset |
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val delloop: simpset * string -> simpset |
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val setSSolver: simpset * (thm list -> int -> tactic) -> simpset |
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val addSSolver: simpset * (thm list -> int -> tactic) -> simpset |
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val setSolver: simpset * (thm list -> int -> tactic) -> simpset |
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val addSolver: simpset * (thm list -> int -> tactic) -> simpset |
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val setmksimps: simpset * (thm -> thm list) -> simpset |
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val setmkeqTrue: simpset * (thm -> thm option) -> simpset |
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val setmksym: simpset * (thm -> thm option) -> simpset |
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val settermless: simpset * (term * term -> bool) -> simpset |
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val addsimps: simpset * thm list -> simpset |
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val delsimps: simpset * thm list -> simpset |
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val addeqcongs: simpset * thm list -> simpset |
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val deleqcongs: simpset * thm list -> simpset |
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val addsimprocs: simpset * simproc list -> simpset |
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val delsimprocs: simpset * simproc list -> simpset |
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val merge_ss: simpset * simpset -> simpset |
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val prems_of_ss: simpset -> thm list |
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val simpset_thy_data: string * (object * (object -> object) * |
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(object * object -> object) * (Sign.sg -> object -> unit)) |
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val simpset_ref_of_sg: Sign.sg -> simpset ref |
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val simpset_ref_of: theory -> simpset ref |
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val simpset_of_sg: Sign.sg -> simpset |
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val simpset_of: theory -> simpset |
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val SIMPSET: (simpset -> tactic) -> tactic |
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val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic |
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val simpset: unit -> simpset |
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val simpset_ref: unit -> simpset ref |
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val Addsimps: thm list -> unit |
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val Delsimps: thm list -> unit |
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val Addsimprocs: simproc list -> unit |
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val Delsimprocs: simproc list -> unit |
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val simp_tac: simpset -> int -> tactic |
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val asm_simp_tac: simpset -> int -> tactic |
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val full_simp_tac: simpset -> int -> tactic |
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val asm_full_simp_tac: simpset -> int -> tactic |
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val safe_asm_full_simp_tac: simpset -> int -> tactic |
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val Simp_tac: int -> tactic |
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val Asm_simp_tac: int -> tactic |
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val Full_simp_tac: int -> tactic |
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val Asm_full_simp_tac: int -> tactic |
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val simplify: simpset -> thm -> thm |
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val asm_simplify: simpset -> thm -> thm |
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val full_simplify: simpset -> thm -> thm |
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val asm_full_simplify: simpset -> thm -> thm |
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end; |
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structure Simplifier: SIMPLIFIER = |
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struct |
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(** simplification procedures **) |
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(* datatype simproc *) |
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datatype simproc = |
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Simproc of string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp; |
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fun mk_simproc name lhss proc = |
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Simproc (name, map (Thm.cterm_fun Logic.varify) lhss, proc, stamp ()); |
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fun rep_simproc (Simproc args) = args; |
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(** simplification sets **) |
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(* type simpset *) |
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datatype simpset = |
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Simpset of { |
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mss: meta_simpset, |
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subgoal_tac: simpset -> int -> tactic, |
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loop_tacs: (string * (int -> tactic))list, |
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finish_tac: thm list -> int -> tactic, |
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unsafe_finish_tac: thm list -> int -> tactic}; |
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fun make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac) = |
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Simpset {mss = mss, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, |
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finish_tac = finish_tac, unsafe_finish_tac = unsafe_finish_tac}; |
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val empty_ss = |
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let val mss = Thm.set_mk_sym(Thm.empty_mss, Some o symmetric_fun) |
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in make_ss (mss, K (K no_tac), [], K (K no_tac), K (K no_tac)) end; |
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fun rep_ss (Simpset args) = args; |
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fun prems_of_ss (Simpset {mss, ...}) = Thm.prems_of_mss mss; |
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(* print simpsets *) |
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fun print_ss ss = |
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let |
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val Simpset {mss, ...} = ss; |
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val {simps, procs, congs} = Thm.dest_mss mss; |
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val pretty_thms = map Display.pretty_thm; |
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fun pretty_proc (name, lhss) = |
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Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss); |
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in |
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Pretty.writeln (Pretty.big_list "simplification rules:" (pretty_thms simps)); |
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Pretty.writeln (Pretty.big_list "simplification procedures:" (map pretty_proc procs)); |
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Pretty.writeln (Pretty.big_list "congruences:" (pretty_thms congs)) |
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end; |
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(* extend simpsets *) |
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fun (Simpset {mss, subgoal_tac = _, loop_tacs, finish_tac, unsafe_finish_tac}) |
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setsubgoaler subgoal_tac = |
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make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs = _, finish_tac, unsafe_finish_tac}) |
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setloop tac = |
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make_ss (mss, subgoal_tac, [("",tac)], finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addloop atac = |
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make_ss (mss, subgoal_tac, overwrite(loop_tacs,atac), |
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finish_tac, unsafe_finish_tac); |
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fun (ss as Simpset {mss,subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac}) |
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delloop name = |
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let val (del,rest) = partition (fn (n,_) => n=name) loop_tacs |
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in if null del then (warning ("No such looper in simpset: " ^ name); ss) |
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else make_ss (mss, subgoal_tac, rest, finish_tac, unsafe_finish_tac) |
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end; |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac = _, unsafe_finish_tac}) |
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setSSolver finish_tac = |
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make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addSSolver tac = |
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make_ss (mss, subgoal_tac, loop_tacs, fn hyps => finish_tac hyps ORELSE' tac hyps, |
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unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac = _}) |
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setSolver unsafe_finish_tac = |
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make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addSolver tac = |
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make_ss (mss, subgoal_tac, loop_tacs, finish_tac, |
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fn hyps => unsafe_finish_tac hyps ORELSE' tac hyps); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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setmksimps mk_simps = |
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make_ss (Thm.set_mk_rews (mss, map (Thm.strip_shyps o Drule.zero_var_indexes) o mk_simps), |
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subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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setmkeqTrue mk_eq_True = |
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make_ss (Thm.set_mk_eq_True (mss, mk_eq_True), |
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subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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setmksym mksym = |
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make_ss (Thm.set_mk_sym (mss, mksym), |
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subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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settermless termless = |
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make_ss (Thm.set_termless (mss, termless), subgoal_tac, loop_tacs, |
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finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addsimps rews = |
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make_ss (Thm.add_simps (mss, rews), subgoal_tac, loop_tacs, |
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finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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delsimps rews = |
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make_ss (Thm.del_simps (mss, rews), subgoal_tac, loop_tacs, |
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finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addeqcongs newcongs = |
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make_ss (Thm.add_congs (mss, newcongs), subgoal_tac, loop_tacs, |
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finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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deleqcongs oldcongs = |
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make_ss (Thm.del_congs (mss, oldcongs), subgoal_tac, loop_tacs, |
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finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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addsimprocs simprocs = |
223 |
make_ss |
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(Thm.add_simprocs (mss, map rep_simproc simprocs), |
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subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) |
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delsimprocs simprocs = |
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make_ss |
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(Thm.del_simprocs (mss, map rep_simproc simprocs), |
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subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
2503 | 232 |
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233 |
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3551 | 234 |
(* merge simpsets *) (*NOTE: ignores tactics of 2nd simpset*) |
2503 | 235 |
|
3551 | 236 |
fun merge_ss |
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(Simpset {mss = mss1, loop_tacs = loop_tacs1, |
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subgoal_tac, finish_tac, unsafe_finish_tac}, |
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Simpset {mss = mss2, loop_tacs = loop_tacs2, ...}) = |
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make_ss (Thm.merge_mss (mss1, mss2), subgoal_tac, |
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foldl overwrite (loop_tacs1,loop_tacs2), |
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finish_tac, unsafe_finish_tac); |
2503 | 243 |
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244 |
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3557 | 245 |
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(** simpset theory data **) |
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(* data kind simpset *) |
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val simpsetK = "simpset"; |
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exception SimpsetData of simpset ref; |
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local |
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val empty = SimpsetData (ref empty_ss); |
0 | 255 |
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(*create new reference*) |
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fun prep_ext (SimpsetData (ref ss)) = SimpsetData (ref ss); |
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fun merge (SimpsetData (ref ss1), SimpsetData (ref ss2)) = |
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SimpsetData (ref (merge_ss (ss1, ss2))); |
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4259 | 262 |
fun print (_: Sign.sg) (SimpsetData (ref ss)) = print_ss ss; |
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in |
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val simpset_thy_data = (simpsetK, (empty, prep_ext, merge, print)); |
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end; |
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(* access simpset *) |
0 | 269 |
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4366 | 270 |
fun print_simpset thy = Display.print_data thy simpsetK; |
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fun simpset_ref_of_sg sg = |
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(case Sign.get_data sg simpsetK of |
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SimpsetData r => r |
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| _ => sys_error "simpset_ref_of_sg") |
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val simpset_ref_of = simpset_ref_of_sg o sign_of; |
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val simpset_of_sg = ! o simpset_ref_of_sg; |
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val simpset_of = simpset_of_sg o sign_of; |
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fun SIMPSET tacf state = tacf (simpset_of_sg (sign_of_thm state)) state; |
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fun SIMPSET' tacf i state = tacf (simpset_of_sg (sign_of_thm state)) i state; |
0 | 283 |
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val simpset = simpset_of o Context.get_context; |
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val simpset_ref = simpset_ref_of_sg o sign_of o Context.get_context; |
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286 |
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287 |
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(* change simpset *) |
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289 |
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fun change_simpset f x = simpset_ref () := (f (simpset (), x)); |
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291 |
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val Addsimps = change_simpset (op addsimps); |
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293 |
val Delsimps = change_simpset (op delsimps); |
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val Addsimprocs = change_simpset (op addsimprocs); |
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val Delsimprocs = change_simpset (op delsimprocs); |
2509 | 296 |
|
0 | 297 |
|
3557 | 298 |
|
2503 | 299 |
(** simplification tactics **) |
0 | 300 |
|
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301 |
fun solve_all_tac (subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac) mss = |
3557 | 302 |
let |
303 |
val ss = |
|
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304 |
make_ss (mss, subgoal_tac, loop_tacs, unsafe_finish_tac, unsafe_finish_tac); |
4612 | 305 |
val solve1_tac = (subgoal_tac ss THEN_ALL_NEW (K no_tac)) 1 |
3557 | 306 |
in DEPTH_SOLVE solve1_tac end; |
307 |
||
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308 |
fun loop_tac loop_tacs = FIRST'(map snd loop_tacs); |
3557 | 309 |
|
2629 | 310 |
(*not totally safe: may instantiate unknowns that appear also in other subgoals*) |
311 |
fun basic_gen_simp_tac mode = |
|
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312 |
fn (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) => |
3551 | 313 |
let |
4612 | 314 |
fun simp_loop_tac i = |
315 |
asm_rewrite_goal_tac mode |
|
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316 |
(solve_all_tac (subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac)) |
4612 | 317 |
mss i |
318 |
THEN (finish_tac (prems_of_mss mss) i ORELSE |
|
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319 |
TRY ((loop_tac loop_tacs THEN_ALL_NEW simp_loop_tac) i)) |
4612 | 320 |
in simp_loop_tac end; |
0 | 321 |
|
3551 | 322 |
fun gen_simp_tac mode (ss as Simpset {unsafe_finish_tac, ...}) = |
323 |
basic_gen_simp_tac mode (ss setSSolver unsafe_finish_tac); |
|
324 |
||
2629 | 325 |
|
2503 | 326 |
val simp_tac = gen_simp_tac (false, false); |
327 |
val asm_simp_tac = gen_simp_tac (false, true); |
|
328 |
val full_simp_tac = gen_simp_tac (true, false); |
|
329 |
val asm_full_simp_tac = gen_simp_tac (true, true); |
|
0 | 330 |
|
2629 | 331 |
(*not totally safe: may instantiate unknowns that appear also in other subgoals*) |
332 |
val safe_asm_full_simp_tac = basic_gen_simp_tac (true, true); |
|
333 |
||
3728 | 334 |
(** The abstraction over the proof state delays the dereferencing **) |
335 |
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336 |
fun Simp_tac i st = simp_tac (simpset ()) i st; |
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337 |
fun Asm_simp_tac i st = asm_simp_tac (simpset ()) i st; |
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338 |
fun Full_simp_tac i st = full_simp_tac (simpset ()) i st; |
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339 |
fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st; |
406 | 340 |
|
3557 | 341 |
|
342 |
||
343 |
(** simplification meta rules **) |
|
344 |
||
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|
345 |
fun simp mode (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) thm = |
3557 | 346 |
let |
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|
347 |
val tacf = solve_all_tac (subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac); |
4271
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348 |
fun prover m th = apsome fst (Seq.pull (tacf m th)); |
3557 | 349 |
in |
350 |
Drule.rewrite_thm mode prover mss thm |
|
351 |
end; |
|
352 |
||
353 |
val simplify = simp (false, false); |
|
354 |
val asm_simplify = simp (false, true); |
|
355 |
val full_simplify = simp (true, false); |
|
356 |
val asm_full_simplify = simp (true, true); |
|
357 |
||
358 |
||
1243 | 359 |
end; |