(* Title: Pure/simplifier.ML
Author: Tobias Nipkow and Markus Wenzel, TU Muenchen
Generic simplifier, suitable for most logics (see also
raw_simplifier.ML for the actual meta-level rewriting engine).
*)
signature BASIC_SIMPLIFIER =
sig
include BASIC_RAW_SIMPLIFIER
val simp_tac: Proof.context -> int -> tactic
val asm_simp_tac: Proof.context -> int -> tactic
val full_simp_tac: Proof.context -> int -> tactic
val asm_lr_simp_tac: Proof.context -> int -> tactic
val asm_full_simp_tac: Proof.context -> int -> tactic
val safe_simp_tac: Proof.context -> int -> tactic
val safe_asm_simp_tac: Proof.context -> int -> tactic
val safe_full_simp_tac: Proof.context -> int -> tactic
val safe_asm_lr_simp_tac: Proof.context -> int -> tactic
val safe_asm_full_simp_tac: Proof.context -> int -> tactic
val simplify: Proof.context -> thm -> thm
val asm_simplify: Proof.context -> thm -> thm
val full_simplify: Proof.context -> thm -> thm
val asm_lr_simplify: Proof.context -> thm -> thm
val asm_full_simplify: Proof.context -> thm -> thm
end;
signature SIMPLIFIER =
sig
include BASIC_SIMPLIFIER
val map_ss: (Proof.context -> Proof.context) -> Context.generic -> Context.generic
val pretty_simpset: Proof.context -> Pretty.T
val default_mk_sym: Proof.context -> thm -> thm option
val debug_bounds: bool Unsynchronized.ref
val prems_of: Proof.context -> thm list
val add_simp: thm -> Proof.context -> Proof.context
val del_simp: thm -> Proof.context -> Proof.context
val add_eqcong: thm -> Proof.context -> Proof.context
val del_eqcong: thm -> Proof.context -> Proof.context
val add_cong: thm -> Proof.context -> Proof.context
val del_cong: thm -> Proof.context -> Proof.context
val add_prems: thm list -> Proof.context -> Proof.context
val mksimps: Proof.context -> thm -> thm list
val set_mksimps: (Proof.context -> thm -> thm list) -> Proof.context -> Proof.context
val set_mkcong: (Proof.context -> thm -> thm) -> Proof.context -> Proof.context
val set_mksym: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context
val set_mkeqTrue: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context
val set_termless: (term * term -> bool) -> Proof.context -> Proof.context
val set_subgoaler: (Proof.context -> int -> tactic) -> Proof.context -> Proof.context
val simproc_global_i: theory -> string -> term list ->
(Proof.context -> term -> thm option) -> simproc
val simproc_global: theory -> string -> string list ->
(Proof.context -> term -> thm option) -> simproc
val rewrite: Proof.context -> conv
val asm_rewrite: Proof.context -> conv
val full_rewrite: Proof.context -> conv
val asm_lr_rewrite: Proof.context -> conv
val asm_full_rewrite: Proof.context -> conv
val attrib: (thm -> Proof.context -> Proof.context) -> attribute
val simp_add: attribute
val simp_del: attribute
val cong_add: attribute
val cong_del: attribute
val check_simproc: Proof.context -> xstring * Position.T -> string
val the_simproc: Proof.context -> string -> simproc
val def_simproc: {name: binding, lhss: term list,
proc: morphism -> Proof.context -> cterm -> thm option, identifier: thm list} ->
local_theory -> local_theory
val def_simproc_cmd: {name: binding, lhss: string list,
proc: morphism -> Proof.context -> cterm -> thm option, identifier: thm list} ->
local_theory -> local_theory
val cong_modifiers: Method.modifier parser list
val simp_modifiers': Method.modifier parser list
val simp_modifiers: Method.modifier parser list
val method_setup: Method.modifier parser list -> theory -> theory
val easy_setup: thm -> thm list -> theory -> theory
end;
structure Simplifier: SIMPLIFIER =
struct
open Raw_Simplifier;
(** pretty printing **)
fun pretty_simpset ctxt =
let
val pretty_term = Syntax.pretty_term ctxt;
val pretty_thm = Display.pretty_thm ctxt;
val pretty_thm_item = Display.pretty_thm_item ctxt;
fun pretty_proc (name, lhss) =
Pretty.big_list (name ^ ":") (map (Pretty.item o single o pretty_term o Thm.term_of) lhss);
fun pretty_cong_name (const, name) =
pretty_term ((if const then Const else Free) (name, dummyT));
fun pretty_cong (name, thm) =
Pretty.block [pretty_cong_name name, Pretty.str ":", Pretty.brk 1, pretty_thm thm];
val {simps, procs, congs, loopers, unsafe_solvers, safe_solvers, ...} =
dest_ss (simpset_of ctxt);
in
[Pretty.big_list "simplification rules:" (map (pretty_thm_item o #2) simps),
Pretty.big_list "simplification procedures:" (map pretty_proc (sort_wrt #1 procs)),
Pretty.big_list "congruences:" (map pretty_cong congs),
Pretty.strs ("loopers:" :: map quote loopers),
Pretty.strs ("unsafe solvers:" :: map quote unsafe_solvers),
Pretty.strs ("safe solvers:" :: map quote safe_solvers)]
|> Pretty.chunks
end;
(** declarations **)
(* attributes *)
fun attrib f = Thm.declaration_attribute (map_ss o f);
val simp_add = attrib add_simp;
val simp_del = attrib del_simp;
val cong_add = attrib add_cong;
val cong_del = attrib del_cong;
(** named simprocs **)
structure Simprocs = Generic_Data
(
type T = simproc Name_Space.table;
val empty : T = Name_Space.empty_table "simproc";
val extend = I;
fun merge data : T = Name_Space.merge_tables data;
);
(* get simprocs *)
val get_simprocs = Simprocs.get o Context.Proof;
fun check_simproc ctxt = Name_Space.check (Context.Proof ctxt) (get_simprocs ctxt) #> #1;
val the_simproc = Name_Space.get o get_simprocs;
val _ = Theory.setup
(ML_Antiquote.value (Binding.name "simproc")
(Args.context -- Scan.lift (Parse.position Args.name)
>> (fn (ctxt, name) =>
"Simplifier.the_simproc ML_context " ^ ML_Syntax.print_string (check_simproc ctxt name))));
(* define simprocs *)
local
fun gen_simproc prep {name = b, lhss, proc, identifier} lthy =
let
val simproc = make_simproc
{name = Local_Theory.full_name lthy b,
lhss =
let
val lhss' = prep lthy lhss;
val ctxt' = fold Variable.auto_fixes lhss' lthy;
in Variable.export_terms ctxt' lthy lhss' end
|> map (Thm.cterm_of (Proof_Context.theory_of lthy)),
proc = proc,
identifier = identifier};
in
lthy |> Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => fn context =>
let
val b' = Morphism.binding phi b;
val simproc' = transform_simproc phi simproc;
in
context
|> Simprocs.map (#2 o Name_Space.define context true (b', simproc'))
|> map_ss (fn ctxt => ctxt addsimprocs [simproc'])
end)
end;
in
val def_simproc = gen_simproc Syntax.check_terms;
val def_simproc_cmd = gen_simproc Syntax.read_terms;
end;
(** simplification tactics and rules **)
fun solve_all_tac solvers ctxt =
let
val {subgoal_tac, ...} = Raw_Simplifier.internal_ss (simpset_of ctxt);
val solve_tac = subgoal_tac (Raw_Simplifier.set_solvers solvers ctxt) 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 ctxt =
let
val {loop_tacs, solvers = (unsafe_solvers, solvers), ...} =
Raw_Simplifier.internal_ss (simpset_of ctxt);
val loop_tac = FIRST' (map (fn (_, tac) => tac ctxt) (rev loop_tacs));
val solve_tac = FIRST' (map (Raw_Simplifier.solver ctxt)
(rev (if safe then solvers else unsafe_solvers)));
fun simp_loop_tac i =
Raw_Simplifier.generic_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ctxt i THEN
(solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
in PREFER_GOAL (simp_loop_tac 1) end;
local
fun simp rew mode ctxt thm =
let
val {solvers = (unsafe_solvers, _), ...} = Raw_Simplifier.internal_ss (simpset_of ctxt);
val tacf = solve_all_tac (rev unsafe_solvers);
fun prover s th = Option.map #1 (Seq.pull (tacf s th));
in rew mode prover ctxt thm end;
in
val simp_thm = simp Raw_Simplifier.rewrite_thm;
val simp_cterm = simp Raw_Simplifier.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);
(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
val safe_simp_tac = generic_simp_tac true (false, false, false);
val safe_asm_simp_tac = generic_simp_tac true (false, true, false);
val safe_full_simp_tac = generic_simp_tac true (true, false, false);
val safe_asm_lr_simp_tac = generic_simp_tac true (true, true, false);
val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
(* 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 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 (Raw_Simplifier.map_ss (fn ctxt => f (ctxt, [transform_simproc phi simproc])))));
in
val simproc_att =
(Args.context -- Scan.lift add_del) :|-- (fn (ctxt, decl) =>
Scan.repeat1 (Scan.lift (Args.named_attribute (decl o the_simproc ctxt o check_simproc ctxt))))
>> (fn atts => Thm.declaration_attribute (fn th =>
fold (fn att => Thm.attribute_declaration (Morphism.form att) th) atts));
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.$$$ no_asm_useN) >> K full_simplify ||
Scan.succeed asm_full_simplify) |> Scan.lift) x;
in
val simplified = conv_mode -- Attrib.thms >>
(fn (f, ths) => Thm.rule_attribute (fn context =>
f ((if null ths then I else Raw_Simplifier.clear_simpset)
(Context.proof_of context) addsimps ths)));
end;
(* setup attributes *)
val _ = Theory.setup
(Attrib.setup (Binding.name simpN) (Attrib.add_del simp_add simp_del)
"declaration of Simplifier rewrite rule" #>
Attrib.setup (Binding.name congN) (Attrib.add_del cong_add cong_del)
"declaration of Simplifier congruence rule" #>
Attrib.setup (Binding.name "simproc") simproc_att
"declaration of simplification procedures" #>
Attrib.setup (Binding.name "simplified") simplified "simplified rule");
(** method syntax **)
val cong_modifiers =
[Args.$$$ 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.$$$ onlyN -- Args.colon >> K (Raw_Simplifier.clear_simpset, simp_add)]
@ cong_modifiers;
val simp_modifiers' =
[Args.add -- Args.colon >> K (I, simp_add),
Args.del -- Args.colon >> K (I, simp_del),
Args.$$$ onlyN -- Args.colon >> K (Raw_Simplifier.clear_simpset, simp_add)]
@ cong_modifiers;
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_method more_mods meth =
Scan.lift simp_options --|
Method.sections (more_mods @ simp_modifiers') >>
(fn tac => fn ctxt => METHOD (fn facts => meth ctxt tac facts));
(** setup **)
fun method_setup more_mods =
Method.setup (Binding.name simpN)
(simp_method more_mods (fn ctxt => fn tac => fn facts =>
HEADGOAL (Method.insert_tac facts THEN'
(CHANGED_PROP oo tac) ctxt)))
"simplification" #>
Method.setup (Binding.name "simp_all")
(simp_method more_mods (fn ctxt => fn tac => fn facts =>
ALLGOALS (Method.insert_tac facts) THEN
(CHANGED_PROP o PARALLEL_GOALS o ALLGOALS o tac) ctxt))
"simplification (all goals)";
fun easy_setup reflect trivs = method_setup [] #> Context.theory_map (map_ss (fn ctxt0 =>
let
val trivialities = Drule.reflexive_thm :: trivs;
fun unsafe_solver_tac ctxt =
FIRST' [resolve_tac (trivialities @ Raw_Simplifier.prems_of ctxt), assume_tac];
val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
(*no premature instantiation of variables during simplification*)
fun safe_solver_tac ctxt =
FIRST' [match_tac (trivialities @ Raw_Simplifier.prems_of ctxt), 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 (Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm);
in
empty_simpset ctxt0
setSSolver safe_solver
setSolver unsafe_solver
|> set_subgoaler asm_simp_tac
|> set_mksimps (K mksimps)
end));
end;
structure Basic_Simplifier: BASIC_SIMPLIFIER = Simplifier;
open Basic_Simplifier;