(* Title: Pure/simplifier.ML
ID: $Id$
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
val print_simpset: theory -> unit
val change_simpset_of: theory -> (simpset -> simpset) -> unit
val change_simpset: (simpset -> simpset) -> unit
val simpset_of: theory -> simpset
val simpset: unit -> simpset
val SIMPSET: (simpset -> tactic) -> tactic
val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
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 generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
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_context: simpset -> simpset -> simpset
val the_context: simpset -> Proof.context
val context: Proof.context -> simpset -> simpset
val theory_context: theory -> 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 rewrite: simpset -> conv
val asm_rewrite: simpset -> conv
val full_rewrite: simpset -> conv
val asm_lr_rewrite: simpset -> conv
val asm_full_rewrite: simpset -> conv
val get_simpset: theory -> simpset
val print_local_simpset: Proof.context -> unit
val get_local_simpset: Proof.context -> simpset
val put_local_simpset: simpset -> Proof.context -> Proof.context
val get_ss: Context.generic -> simpset
val map_ss: (simpset -> simpset) -> Context.generic -> Context.generic
val attrib: (simpset * thm list -> simpset) -> attribute
val simp_add: attribute
val simp_del: attribute
val cong_add: attribute
val cong_del: attribute
val get_simproc: Context.generic -> xstring -> simproc
val def_simproc: {name: string, lhss: string list,
proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
local_theory -> local_theory
val def_simproc_i: {name: string, lhss: term list,
proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
local_theory -> local_theory
val cong_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
val simp_modifiers': (Args.T list -> (Method.modifier * Args.T list)) list
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
val easy_setup: thm -> thm list -> theory -> theory
end;
structure Simplifier: SIMPLIFIER =
struct
open MetaSimplifier;
(** simpset data **)
(* global simpsets *)
structure GlobalSimpset = TheoryDataFun
(
type T = simpset ref;
val empty = ref empty_ss;
fun copy (ref ss) = ref ss: T;
fun extend (ref ss) = ref (MetaSimplifier.inherit_context empty_ss ss);
fun merge _ (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
);
val _ = Context.>> GlobalSimpset.init;
fun print_simpset thy = print_ss (! (GlobalSimpset.get thy));
val get_simpset = ! o GlobalSimpset.get;
fun change_simpset_of thy f = CRITICAL (fn () => change (GlobalSimpset.get thy) f);
fun change_simpset f = CRITICAL (fn () => change_simpset_of (ML_Context.the_global_context ()) f);
fun simpset_of thy = MetaSimplifier.context (ProofContext.init thy) (get_simpset thy);
val simpset = simpset_of o ML_Context.the_global_context;
fun SIMPSET tacf st = tacf (simpset_of (Thm.theory_of_thm st)) st;
fun SIMPSET' tacf i st = tacf (simpset_of (Thm.theory_of_thm st)) i st;
fun Addsimps args = change_simpset (fn ss => ss addsimps args);
fun Delsimps args = change_simpset (fn ss => ss delsimps args);
fun Addsimprocs args = change_simpset (fn ss => ss addsimprocs args);
fun Delsimprocs args = change_simpset (fn ss => ss delsimprocs args);
fun Addcongs args = change_simpset (fn ss => ss addcongs args);
fun Delcongs args = change_simpset (fn ss => ss delcongs args);
(* local simpsets *)
structure LocalSimpset = ProofDataFun
(
type T = simpset;
val init = get_simpset;
);
val print_local_simpset = print_ss o LocalSimpset.get;
val get_local_simpset = LocalSimpset.get;
val put_local_simpset = LocalSimpset.put;
fun local_simpset_of ctxt = MetaSimplifier.context ctxt (get_local_simpset ctxt);
val _ = ML_Context.value_antiq "simpset"
(Scan.succeed ("simpset", "Simplifier.local_simpset_of (ML_Context.the_local_context ())"));
(* generic simpsets *)
fun get_ss (Context.Theory thy) = simpset_of thy
| get_ss (Context.Proof ctxt) = local_simpset_of ctxt;
fun map_ss f (Context.Theory thy) = (change_simpset_of thy f; Context.Theory thy)
| map_ss f (Context.Proof ctxt) = Context.Proof (LocalSimpset.map f ctxt);
(* attributes *)
fun attrib f = Thm.declaration_attribute (fn th => map_ss (fn ss => f (ss, [th])));
val simp_add = attrib (op addsimps);
val simp_del = attrib (op delsimps);
val cong_add = attrib (op addcongs);
val cong_del = attrib (op delcongs);
(** named simprocs **)
fun err_dup_simproc name = error ("Duplicate simproc: " ^ quote name);
(* data *)
structure Simprocs = GenericDataFun
(
type T = simproc NameSpace.table;
val empty = NameSpace.empty_table;
val extend = I;
fun merge _ simprocs = NameSpace.merge_tables eq_simproc simprocs
handle Symtab.DUP dup => err_dup_simproc dup;
);
(* get simprocs *)
fun get_simproc context xname =
let
val (space, tab) = Simprocs.get context;
val name = NameSpace.intern space xname;
in
(case Symtab.lookup tab name of
SOME proc => proc
| NONE => error ("Undefined simplification procedure: " ^ quote name))
end;
val _ = ML_Context.value_antiq "simproc" (Scan.lift Args.name >> (fn name =>
("simproc",
"Simplifier.get_simproc (ML_Context.the_generic_context ()) " ^ ML_Syntax.print_string name)));
(* define simprocs *)
local
fun gen_simproc prep {name, lhss, proc, identifier} lthy =
let
val naming = LocalTheory.full_naming lthy;
val simproc = make_simproc
{name = LocalTheory.full_name lthy name,
lhss =
let
val lhss' = prep lthy lhss;
val ctxt' = lthy
|> fold Variable.declare_term lhss'
|> fold Variable.auto_fixes lhss';
in Variable.export_terms ctxt' lthy lhss' end
|> map (Thm.cterm_of (ProofContext.theory_of lthy)),
proc = proc,
identifier = identifier}
|> morph_simproc (LocalTheory.target_morphism lthy);
in
lthy |> LocalTheory.declaration (fn phi =>
let
val name' = Morphism.name phi name;
val simproc' = morph_simproc phi simproc;
in
Simprocs.map (fn simprocs =>
NameSpace.extend_table naming [(name', simproc')] simprocs
handle Symtab.DUP dup => err_dup_simproc dup)
#> map_ss (fn ss => ss addsimprocs [simproc'])
end)
end;
in
val def_simproc = gen_simproc Syntax.read_terms;
val def_simproc_i = gen_simproc Syntax.check_terms;
end;
(** simplification tactics and rules **)
fun solve_all_tac solvers ss =
let
val (_, {subgoal_tac, ...}) = MetaSimplifier.rep_ss ss;
val solve_tac = subgoal_tac (MetaSimplifier.set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
in DEPTH_SOLVE (solve_tac 1) end;
(*NOTE: may instantiate unknowns that appear also in other subgoals*)
fun generic_simp_tac safe mode ss =
let
val (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = MetaSimplifier.rep_ss ss;
val loop_tac = FIRST' (map (fn (_, tac) => tac ss) (rev loop_tacs));
val solve_tac = FIRST' (map (MetaSimplifier.solver ss)
(rev (if safe then solvers else unsafe_solvers)));
fun simp_loop_tac i =
asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
(solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
in simp_loop_tac end;
local
fun simp rew mode ss thm =
let
val (_, {solvers = (unsafe_solvers, _), ...}) = MetaSimplifier.rep_ss ss;
val tacf = solve_all_tac (rev unsafe_solvers);
fun prover s th = Option.map #1 (Seq.pull (tacf s th));
in rew mode prover ss thm end;
in
val simp_thm = simp MetaSimplifier.rewrite_thm;
val simp_cterm = simp MetaSimplifier.rewrite_cterm;
end;
(* 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";
(* simprocs *)
local
val add_del =
(Args.del -- Args.colon >> K (op delsimprocs) ||
Scan.option (Args.add -- Args.colon) >> K (op addsimprocs))
>> (fn f => fn simproc => fn phi => Thm.declaration_attribute
(K (map_ss (fn ss => f (ss, [morph_simproc phi simproc])))));
in
val simproc_att = Attrib.syntax
(Scan.peek (fn context =>
add_del :|-- (fn decl =>
Scan.repeat1 (Args.named_attribute (decl o get_simproc context))
>> (Library.apply o map Morphism.form))));
end;
(* 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.$$$ no_asm_useN) >> K full_simplify ||
Scan.succeed asm_full_simplify) |> Scan.lift) x;
in
val simplified =
Attrib.syntax (conv_mode -- Attrib.thms >> (fn (f, ths) => Thm.rule_attribute (fn x =>
f ((if null ths then I else MetaSimplifier.clear_ss) (get_ss x) addsimps ths))));
end;
(* setup attributes *)
val _ = Context.>>
(Attrib.add_attributes
[(simpN, Attrib.add_del_args simp_add simp_del, "declaration of Simplifier rewrite rule"),
(congN, Attrib.add_del_args cong_add cong_del, "declaration of Simplifier congruence rule"),
("simproc", simproc_att, "declaration of simplification procedures"),
("simplified", simplified, "simplified rule")]);
(** proof methods **)
(* simplification *)
val simp_options =
(Args.parens (Args.$$$ 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.$$$ asm_lrN) >> K asm_lr_simp_tac ||
Scan.succeed asm_full_simp_tac);
val cong_modifiers =
[Args.$$$ congN -- Args.colon >> K ((I, cong_add): Method.modifier),
Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add),
Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del)];
val simp_modifiers =
[Args.$$$ simpN -- Args.colon >> K (I, simp_add),
Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add),
Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del),
Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
>> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
@ cong_modifiers;
val simp_modifiers' =
[Args.add -- Args.colon >> K (I, simp_add),
Args.del -- Args.colon >> K (I, simp_del),
Args.$$$ onlyN -- Args.colon
>> K (LocalSimpset.map MetaSimplifier.clear_ss, simp_add)]
@ cong_modifiers;
fun simp_args more_mods =
Method.sectioned_args (Args.bang_facts -- Scan.lift simp_options)
(more_mods @ simp_modifiers');
fun simp_method (prems, tac) ctxt = Method.METHOD (fn facts =>
ALLGOALS (Method.insert_tac (prems @ facts)) THEN
(CHANGED_PROP o ALLGOALS o tac) (local_simpset_of ctxt));
fun simp_method' (prems, tac) ctxt = Method.METHOD (fn facts =>
HEADGOAL (Method.insert_tac (prems @ facts) THEN'
((CHANGED_PROP) oo tac) (local_simpset_of ctxt)));
(** setup **)
fun method_setup 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 easy_setup reflect trivs = method_setup [] #> (fn thy =>
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 can Logic.dest_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);
val _ = CRITICAL (fn () =>
GlobalSimpset.get thy :=
empty_ss setsubgoaler asm_simp_tac
setSSolver safe_solver
setSolver unsafe_solver
setmksimps mksimps);
in thy end);
end;
structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
open BasicSimplifier;