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(* Title: Pure/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
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meta_simplifier.ML for the actual meta-level rewriting engine).
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*)
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signature BASIC_SIMPLIFIER =
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sig
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include BASIC_META_SIMPLIFIER
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val print_simpset: theory -> unit
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val change_simpset_of: theory -> (simpset -> simpset) -> unit
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val change_simpset: (simpset -> simpset) -> unit
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val simpset_of: theory -> simpset
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val simpset: unit -> 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 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 Addcongs: thm list -> unit
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val Delcongs: thm list -> unit
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val local_simpset_of: Proof.context -> simpset
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val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
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val safe_asm_full_simp_tac: simpset -> int -> tactic
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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_lr_simp_tac: simpset -> int -> tactic
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val 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_lr_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_lr_simplify: simpset -> thm -> thm
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val asm_full_simplify: simpset -> thm -> thm
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end;
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signature SIMPLIFIER =
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sig
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include BASIC_SIMPLIFIER
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val clear_ss: simpset -> simpset
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val debug_bounds: bool ref
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val inherit_context: simpset -> simpset -> simpset
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val the_context: simpset -> Proof.context
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val context: Proof.context -> simpset -> simpset
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val theory_context: theory -> simpset -> simpset
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val simproc_i: theory -> string -> term list
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-> (theory -> simpset -> term -> thm option) -> simproc
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val simproc: theory -> string -> string list
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-> (theory -> simpset -> term -> thm option) -> simproc
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val rewrite: simpset -> cterm -> thm
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val asm_rewrite: simpset -> cterm -> thm
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val full_rewrite: simpset -> cterm -> thm
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val asm_lr_rewrite: simpset -> cterm -> thm
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val asm_full_rewrite: simpset -> cterm -> thm
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val get_simpset: theory -> simpset
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val print_local_simpset: Proof.context -> unit
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val get_local_simpset: Proof.context -> simpset
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val put_local_simpset: simpset -> Proof.context -> Proof.context
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val attrib: (simpset * thm list -> simpset) -> attribute
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val simp_add: attribute
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val simp_del: attribute
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val cong_add: attribute
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val cong_del: attribute
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val cong_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
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val simp_modifiers': (Args.T list -> (Method.modifier * Args.T list)) list
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val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
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val method_setup: (Args.T list -> (Method.modifier * Args.T list)) list
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-> theory -> theory
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val easy_setup: thm -> thm list -> theory -> theory
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end;
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structure Simplifier: SIMPLIFIER =
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struct
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(** simpset data **)
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(* global simpsets *)
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structure GlobalSimpset = TheoryDataFun
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(struct
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val name = "Pure/simpset";
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type T = simpset ref;
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val empty = ref empty_ss;
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fun copy (ref ss) = ref ss: T; (*create new reference!*)
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fun extend (ref ss) = ref (MetaSimplifier.inherit_context empty_ss ss);
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fun merge _ (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
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fun print _ (ref ss) = print_ss ss;
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end);
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val _ = Context.add_setup GlobalSimpset.init;
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val print_simpset = GlobalSimpset.print;
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val get_simpset = ! o GlobalSimpset.get;
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val change_simpset_of = change o GlobalSimpset.get;
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fun change_simpset f = change_simpset_of (Context.the_context ()) f;
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fun simpset_of thy = MetaSimplifier.context (ProofContext.init thy) (get_simpset thy);
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val simpset = simpset_of o Context.the_context;
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fun SIMPSET tacf st = tacf (simpset_of (Thm.theory_of_thm st)) st;
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fun SIMPSET' tacf i st = tacf (simpset_of (Thm.theory_of_thm st)) i st;
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fun Addsimps args = change_simpset (fn ss => ss addsimps args);
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fun Delsimps args = change_simpset (fn ss => ss delsimps args);
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fun Addsimprocs args = change_simpset (fn ss => ss addsimprocs args);
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fun Delsimprocs args = change_simpset (fn ss => ss delsimprocs args);
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fun Addcongs args = change_simpset (fn ss => ss addcongs args);
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fun Delcongs args = change_simpset (fn ss => ss delcongs args);
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(* local simpsets *)
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structure LocalSimpset = ProofDataFun
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(struct
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val name = "Pure/simpset";
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type T = simpset;
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val init = get_simpset;
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fun print _ ss = print_ss ss;
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end);
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val _ = Context.add_setup LocalSimpset.init;
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val print_local_simpset = LocalSimpset.print;
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val get_local_simpset = LocalSimpset.get;
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val put_local_simpset = LocalSimpset.put;
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fun local_simpset_of ctxt = MetaSimplifier.context ctxt (get_local_simpset ctxt);
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(* attributes *)
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fun attrib f = Thm.declaration_attribute (fn th =>
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fn Context.Theory thy => (change_simpset_of thy (fn ss => f (ss, [th])); Context.Theory thy)
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| Context.Proof ctxt => Context.Proof (LocalSimpset.map (fn ss => f (ss, [th])) ctxt));
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val simp_add = attrib (op addsimps);
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val simp_del = attrib (op delsimps);
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val cong_add = attrib (op addcongs);
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val cong_del = attrib (op delcongs);
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(** simplification tactics and rules **)
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fun solve_all_tac solvers ss =
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let
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val (_, {subgoal_tac, ...}) = MetaSimplifier.rep_ss ss;
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val solve_tac = subgoal_tac (MetaSimplifier.set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
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in DEPTH_SOLVE (solve_tac 1) end;
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(*NOTE: may instantiate unknowns that appear also in other subgoals*)
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fun generic_simp_tac safe mode ss =
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let
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val (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = MetaSimplifier.rep_ss ss;
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val loop_tac = FIRST' (map (fn (_, tac) => tac ss) loop_tacs);
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val solve_tac = FIRST' (map (MetaSimplifier.solver ss)
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(if safe then solvers else unsafe_solvers));
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fun simp_loop_tac i =
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asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
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(solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
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in simp_loop_tac end;
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local
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fun simp rew mode ss thm =
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let
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val (_, {solvers = (unsafe_solvers, _), ...}) = MetaSimplifier.rep_ss ss;
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val tacf = solve_all_tac unsafe_solvers;
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fun prover s th = Option.map #1 (Seq.pull (tacf s th));
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in rew mode prover ss thm end;
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in
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val simp_thm = simp MetaSimplifier.rewrite_thm;
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val simp_cterm = simp MetaSimplifier.rewrite_cterm;
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end;
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(* tactics *)
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val simp_tac = generic_simp_tac false (false, false, false);
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val asm_simp_tac = generic_simp_tac false (false, true, false);
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val full_simp_tac = generic_simp_tac false (true, false, false);
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val asm_lr_simp_tac = generic_simp_tac false (true, true, false);
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val asm_full_simp_tac = generic_simp_tac false (true, true, true);
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val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
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(*the abstraction over the proof state delays the dereferencing*)
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fun Simp_tac i st = simp_tac (simpset ()) i st;
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fun Asm_simp_tac i st = asm_simp_tac (simpset ()) i st;
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fun Full_simp_tac i st = full_simp_tac (simpset ()) i st;
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fun Asm_lr_simp_tac i st = asm_lr_simp_tac (simpset ()) i st;
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fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;
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(* conversions *)
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val simplify = simp_thm (false, false, false);
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val asm_simplify = simp_thm (false, true, false);
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val full_simplify = simp_thm (true, false, false);
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val asm_lr_simplify = simp_thm (true, true, false);
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val asm_full_simplify = simp_thm (true, true, true);
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val rewrite = simp_cterm (false, false, false);
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val asm_rewrite = simp_cterm (false, true, false);
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val full_rewrite = simp_cterm (true, false, false);
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val asm_lr_rewrite = simp_cterm (true, true, false);
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val asm_full_rewrite = simp_cterm (true, true, true);
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(** concrete syntax of attributes **)
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(* add / del *)
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val simpN = "simp";
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val congN = "cong";
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val addN = "add";
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val delN = "del";
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val onlyN = "only";
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val no_asmN = "no_asm";
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val no_asm_useN = "no_asm_use";
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val no_asm_simpN = "no_asm_simp";
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val asm_lrN = "asm_lr";
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(* conversions *)
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local
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fun conv_mode x =
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((Args.parens (Args.$$$ no_asmN) >> K simplify ||
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Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||
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Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||
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Scan.succeed asm_full_simplify) |> Scan.lift) x;
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fun get_ss (Context.Theory thy) = simpset_of thy
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| get_ss (Context.Proof ctxt) = local_simpset_of ctxt;
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in
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val simplified =
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wenzelm@18988
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Attrib.syntax (conv_mode -- Attrib.thms >> (fn (f, ths) => Thm.rule_attribute (fn x =>
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wenzelm@18688
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f ((if null ths then I else MetaSimplifier.clear_ss) (get_ss x) addsimps ths))));
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end;
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(* setup attributes *)
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val _ = Context.add_setup
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wenzelm@18708
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(Attrib.add_attributes
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[(simpN, Attrib.add_del_args simp_add simp_del, "declaration of Simplifier rule"),
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wenzelm@18728
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(congN, Attrib.add_del_args cong_add cong_del, "declaration of Simplifier congruence rule"),
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wenzelm@18728
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266 |
("simplified", simplified, "simplified rule")]);
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wenzelm@16014
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267 |
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wenzelm@16014
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268 |
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wenzelm@16014
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269 |
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wenzelm@16014
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270 |
(** proof methods **)
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wenzelm@16014
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271 |
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wenzelm@16014
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272 |
(* simplification *)
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wenzelm@16014
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273 |
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wenzelm@16014
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274 |
val simp_options =
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wenzelm@16014
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275 |
(Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
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wenzelm@16014
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276 |
Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
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wenzelm@16014
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277 |
Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
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wenzelm@16014
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278 |
Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
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wenzelm@16014
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279 |
Scan.succeed asm_full_simp_tac);
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wenzelm@16014
|
280 |
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wenzelm@16685
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281 |
fun simp_flags x = (Scan.repeat
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wenzelm@16684
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282 |
(Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat)
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wenzelm@16684
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283 |
>> setmp MetaSimplifier.simp_depth_limit)
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wenzelm@16709
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284 |
>> (curry (Library.foldl op o) I o rev)) x;
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wenzelm@16684
|
285 |
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wenzelm@16014
|
286 |
val cong_modifiers =
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wenzelm@18728
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287 |
[Args.$$$ congN -- Args.colon >> K ((I, cong_add): Method.modifier),
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wenzelm@18728
|
288 |
Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add),
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wenzelm@18728
|
289 |
Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del)];
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wenzelm@16014
|
290 |
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wenzelm@16014
|
291 |
val simp_modifiers =
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wenzelm@18728
|
292 |
[Args.$$$ simpN -- Args.colon >> K (I, simp_add),
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wenzelm@18728
|
293 |
Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add),
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wenzelm@18728
|
294 |
Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del),
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wenzelm@17883
|
295 |
Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
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wenzelm@18728
|
296 |
>> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
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wenzelm@16014
|
297 |
@ cong_modifiers;
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wenzelm@16014
|
298 |
|
wenzelm@16014
|
299 |
val simp_modifiers' =
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wenzelm@18728
|
300 |
[Args.add -- Args.colon >> K (I, simp_add),
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wenzelm@18728
|
301 |
Args.del -- Args.colon >> K (I, simp_del),
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wenzelm@18688
|
302 |
Args.$$$ onlyN -- Args.colon
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wenzelm@18728
|
303 |
>> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
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wenzelm@16014
|
304 |
@ cong_modifiers;
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wenzelm@16014
|
305 |
|
wenzelm@16014
|
306 |
fun simp_args more_mods =
|
wenzelm@16684
|
307 |
Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags)
|
wenzelm@16684
|
308 |
(more_mods @ simp_modifiers');
|
wenzelm@16014
|
309 |
|
wenzelm@16684
|
310 |
fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
|
wenzelm@16684
|
311 |
ALLGOALS (Method.insert_tac (prems @ facts)) THEN
|
wenzelm@16684
|
312 |
(FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));
|
wenzelm@16014
|
313 |
|
wenzelm@16684
|
314 |
fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
|
wenzelm@16014
|
315 |
HEADGOAL (Method.insert_tac (prems @ facts) THEN'
|
wenzelm@16684
|
316 |
((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt)));
|
wenzelm@16014
|
317 |
|
wenzelm@16014
|
318 |
|
wenzelm@16014
|
319 |
|
wenzelm@18708
|
320 |
(** setup **)
|
wenzelm@18708
|
321 |
|
wenzelm@18708
|
322 |
fun method_setup more_mods = Method.add_methods
|
wenzelm@16014
|
323 |
[(simpN, simp_args more_mods simp_method', "simplification"),
|
wenzelm@16014
|
324 |
("simp_all", simp_args more_mods simp_method, "simplification (all goals)")];
|
wenzelm@16014
|
325 |
|
wenzelm@18708
|
326 |
fun easy_setup reflect trivs = method_setup [] #> (fn thy =>
|
wenzelm@16014
|
327 |
let
|
wenzelm@16014
|
328 |
val trivialities = Drule.reflexive_thm :: trivs;
|
wenzelm@16014
|
329 |
|
wenzelm@16014
|
330 |
fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac];
|
wenzelm@16014
|
331 |
val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
|
wenzelm@16014
|
332 |
|
wenzelm@16014
|
333 |
(*no premature instantiation of variables during simplification*)
|
wenzelm@16014
|
334 |
fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac];
|
wenzelm@16014
|
335 |
val safe_solver = mk_solver "easy safe" safe_solver_tac;
|
wenzelm@16014
|
336 |
|
wenzelm@16014
|
337 |
fun mk_eq thm =
|
wenzelm@20872
|
338 |
if can Logic.dest_equals (Thm.concl_of thm) then [thm]
|
wenzelm@16014
|
339 |
else [thm RS reflect] handle THM _ => [];
|
wenzelm@16014
|
340 |
|
wenzelm@16014
|
341 |
fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);
|
wenzelm@18708
|
342 |
in
|
wenzelm@18708
|
343 |
GlobalSimpset.get thy :=
|
wenzelm@18708
|
344 |
empty_ss setsubgoaler asm_simp_tac
|
wenzelm@18708
|
345 |
setSSolver safe_solver
|
wenzelm@18708
|
346 |
setSolver unsafe_solver
|
wenzelm@18708
|
347 |
setmksimps mksimps;
|
wenzelm@18708
|
348 |
thy
|
wenzelm@18708
|
349 |
end);
|
wenzelm@16014
|
350 |
|
wenzelm@17883
|
351 |
|
wenzelm@17883
|
352 |
open MetaSimplifier;
|
wenzelm@17883
|
353 |
|
wenzelm@16014
|
354 |
end;
|
wenzelm@16014
|
355 |
|
wenzelm@16014
|
356 |
structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
|
wenzelm@16014
|
357 |
open BasicSimplifier;
|