src/Pure/simplifier.ML
author wenzelm
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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 change_global_ss: (simpset * thm list -> simpset) -> theory attribute
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  val change_local_ss: (simpset * thm list -> simpset) -> Proof.context attribute
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  val simp_add_global: theory attribute
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  val simp_del_global: theory attribute
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  val simp_add_local: Proof.context attribute
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  val simp_del_local: Proof.context attribute
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  val cong_add_global: theory attribute
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  val cong_del_global: theory attribute
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  val cong_add_local: Proof.context attribute
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  val cong_del_local: Proof.context 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) list
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  val easy_setup: thm -> thm list -> (theory -> theory) list
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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 change_global_ss f (thy, th) = (change_simpset_of thy (fn ss => f (ss, [th])); (thy, th));
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fun change_local_ss f (ctxt, th) = (LocalSimpset.map (fn ss => f (ss, [th])) ctxt, th);
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val simp_add_global = change_global_ss (op addsimps);
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val simp_del_global = change_global_ss (op delsimps);
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val simp_add_local = change_local_ss (op addsimps);
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val simp_del_local = change_local_ss (op delsimps);
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val cong_add_global = change_global_ss (op addcongs);
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val cong_del_global = change_global_ss (op delcongs);
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val cong_add_local = change_local_ss (op addcongs);
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val cong_del_local = change_local_ss (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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val simp_attr =
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 (Attrib.add_del_args simp_add_global simp_del_global,
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  Attrib.add_del_args simp_add_local simp_del_local);
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val cong_attr =
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 (Attrib.add_del_args cong_add_global cong_del_global,
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  Attrib.add_del_args cong_add_local cong_del_local);
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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.$$$ no_asm_useN) >> K full_simplify ||
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    Scan.succeed asm_full_simplify) |> Scan.lift) x;
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fun simplified_att get args =
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  Attrib.syntax (conv_mode -- args >> (fn (f, ths) => Attrib.rule (fn x =>
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    f ((if null ths then I else MetaSimplifier.clear_ss) (get x) addsimps ths))));
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in
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val simplified_attr =
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 (simplified_att simpset_of Attrib.global_thmss,
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  simplified_att local_simpset_of Attrib.local_thmss);
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end;
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(* setup attributes *)
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val _ = Context.add_setup
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 [Attrib.add_attributes
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   [(simpN, simp_attr, "declaration of simplification rule"),
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    (congN, cong_attr, "declaration of Simplifier congruence rule"),
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    ("simplified", simplified_attr, "simplified rule")]];
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(** proof methods **)
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(* simplification *)
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val simp_options =
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 (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
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  Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
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  Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
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  Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
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  Scan.succeed asm_full_simp_tac);
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fun simp_flags x = (Scan.repeat
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  (Args.parens (Args.$$$ "depth_limit" -- Args.colon |-- Args.nat)
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    >> setmp MetaSimplifier.simp_depth_limit)
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  >> (curry (Library.foldl op o) I o rev)) x;
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val cong_modifiers =
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 [Args.$$$ congN -- Args.colon >> K ((I, cong_add_local): Method.modifier),
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  Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add_local),
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  Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del_local)];
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val simp_modifiers =
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 [Args.$$$ simpN -- Args.colon >> K (I, simp_add_local),
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  Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add_local),
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  Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del_local),
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  Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
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    >> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add_local)]
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   @ cong_modifiers;
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val simp_modifiers' =
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 [Args.add -- Args.colon >> K (I, simp_add_local),
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  Args.del -- Args.colon >> K (I, simp_del_local),
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  Args.$$$ onlyN -- Args.colon >> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add_local)]
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   @ cong_modifiers;
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fun simp_args more_mods =
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  Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options -- Scan.lift simp_flags)
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    (more_mods @ simp_modifiers');
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fun simp_method ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
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  ALLGOALS (Method.insert_tac (prems @ facts)) THEN
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    (FLAGS o CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));
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fun simp_method' ((prems, tac), FLAGS) ctxt = Method.METHOD (fn facts =>
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  HEADGOAL (Method.insert_tac (prems @ facts) THEN'
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      ((FLAGS o CHANGED_PROP) oo tac) (local_simpset_of ctxt)));
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(* setup methods *)
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fun setup_methods more_mods = Method.add_methods
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 [(simpN, simp_args more_mods simp_method', "simplification"),
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  ("simp_all", simp_args more_mods simp_method, "simplification (all goals)")];
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fun method_setup mods = [setup_methods mods];
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(** easy_setup **)
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fun easy_setup reflect trivs =
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  let
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    val trivialities = Drule.reflexive_thm :: trivs;
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    fun unsafe_solver_tac prems = FIRST' [resolve_tac (trivialities @ prems), assume_tac];
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    val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
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    (*no premature instantiation of variables during simplification*)
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    fun safe_solver_tac prems = FIRST' [match_tac (trivialities @ prems), eq_assume_tac];
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    val safe_solver = mk_solver "easy safe" safe_solver_tac;
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    fun mk_eq thm =
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      if Logic.is_equals (Thm.concl_of thm) then [thm]
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      else [thm RS reflect] handle THM _ => [];
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    fun mksimps thm = mk_eq (Drule.forall_elim_vars (#maxidx (Thm.rep_thm thm) + 1) thm);
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    fun init_ss thy =
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      (GlobalSimpset.get thy :=
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        empty_ss setsubgoaler asm_simp_tac
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        setSSolver safe_solver
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        setSolver unsafe_solver
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        setmksimps mksimps; thy);
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  in method_setup [] @ [init_ss] end;
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open MetaSimplifier;
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end;
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structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
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open BasicSimplifier;