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