(* Title: Provers/clasimp.ML
Author: David von Oheimb, TU Muenchen
Combination of classical reasoner and simplifier (depends on
splitter.ML, classical.ML, blast.ML).
*)
signature CLASIMP_DATA =
sig
structure Splitter: SPLITTER
structure Classical: CLASSICAL
structure Blast: BLAST
val notE: thm
val iffD1: thm
val iffD2: thm
end;
signature CLASIMP =
sig
val addSss: Proof.context -> Proof.context
val addss: Proof.context -> Proof.context
val clarsimp_tac: Proof.context -> int -> tactic
val mk_auto_tac: Proof.context -> int -> int -> tactic
val auto_tac: Proof.context -> tactic
val force_tac: Proof.context -> int -> tactic
val fast_force_tac: Proof.context -> int -> tactic
val slow_simp_tac: Proof.context -> int -> tactic
val best_simp_tac: Proof.context -> int -> tactic
val iff_add: attribute
val iff_add': attribute
val iff_del: attribute
val iff_modifiers: Method.modifier parser list
val clasimp_modifiers: Method.modifier parser list
end;
functor Clasimp(Data: CLASIMP_DATA): CLASIMP =
struct
structure Splitter = Data.Splitter;
structure Classical = Data.Classical;
structure Blast = Data.Blast;
(* simp as classical wrapper *)
(* FIXME !? *)
fun clasimp f name tac ctxt = f (ctxt, (name, fn _ => CHANGED o tac ctxt));
(*Add a simpset to the claset!*)
(*Caution: only one simpset added can be added by each of addSss and addss*)
val addSss = clasimp Classical.addSafter "safe_asm_full_simp_tac" Simplifier.safe_asm_full_simp_tac;
val addss = clasimp Classical.addbefore "asm_full_simp_tac" Simplifier.asm_full_simp_tac;
(* iffs: addition of rules to simpsets and clasets simultaneously *)
local
(*Takes (possibly conditional) theorems of the form A<->B to
the Safe Intr rule B==>A and
the Safe Destruct rule A==>B.
Also ~A goes to the Safe Elim rule A ==> ?R
Failing other cases, A is added as a Safe Intr rule*)
fun add_iff safe unsafe =
Thm.declaration_attribute (fn th => fn context =>
let
val n = Thm.nprems_of th;
val (elim, intro) = if n = 0 then safe else unsafe;
val zero_rotate = zero_var_indexes o rotate_prems n;
val decls =
[(intro, zero_rotate (th RS Data.iffD2)),
(elim, Tactic.make_elim (zero_rotate (th RS Data.iffD1)))]
handle THM _ => [(elim, zero_rotate (th RS Data.notE))]
handle THM _ => [(intro, th)];
in fold (uncurry Thm.attribute_declaration) decls context end);
fun del_iff del = Thm.declaration_attribute (fn th => fn context =>
let
val zero_rotate = zero_var_indexes o rotate_prems (Thm.nprems_of th);
val rls =
[zero_rotate (th RS Data.iffD2), Tactic.make_elim (zero_rotate (th RS Data.iffD1))]
handle THM _ => [zero_rotate (th RS Data.notE)]
handle THM _ => [th];
in fold (Thm.attribute_declaration del) rls context end);
in
val iff_add =
Thm.declaration_attribute (fn th =>
Thm.attribute_declaration (add_iff
(Classical.safe_elim NONE, Classical.safe_intro NONE)
(Classical.unsafe_elim NONE, Classical.unsafe_intro NONE)) th
#> Thm.attribute_declaration Simplifier.simp_add th);
val iff_add' =
add_iff
(Context_Rules.elim_query NONE, Context_Rules.intro_query NONE)
(Context_Rules.elim_query NONE, Context_Rules.intro_query NONE);
val iff_del =
Thm.declaration_attribute (fn th =>
Thm.attribute_declaration (del_iff Classical.rule_del) th #>
Thm.attribute_declaration (del_iff Context_Rules.rule_del) th #>
Thm.attribute_declaration Simplifier.simp_del th);
end;
(* tactics *)
fun clarsimp_tac ctxt =
Simplifier.safe_asm_full_simp_tac ctxt THEN_ALL_NEW
Classical.clarify_tac (addSss ctxt);
(* auto_tac *)
(* a variant of depth_tac that avoids interference of the simplifier
with dup_step_tac when they are combined by auto_tac *)
local
fun slow_step_tac' ctxt =
Classical.appWrappers ctxt
(Classical.instp_step_tac ctxt APPEND' Classical.unsafe_step_tac ctxt);
in
fun nodup_depth_tac ctxt m i st =
SELECT_GOAL
(Classical.safe_steps_tac ctxt 1 THEN_ELSE
(DEPTH_SOLVE (nodup_depth_tac ctxt m 1),
Classical.inst0_step_tac ctxt 1 APPEND COND (K (m = 0)) no_tac
(slow_step_tac' ctxt 1 THEN DEPTH_SOLVE (nodup_depth_tac ctxt (m - 1) 1)))) i st;
end;
(*Designed to be idempotent, except if Blast.depth_tac instantiates variables
in some of the subgoals*)
fun mk_auto_tac ctxt m n =
let
val main_tac =
Blast.depth_tac ctxt m (* fast but can't use wrappers *)
ORELSE'
(CHANGED o nodup_depth_tac (addss ctxt) n); (* slower but more general *)
in
PARALLEL_ALLGOALS (Simplifier.asm_full_simp_tac ctxt) THEN
TRY (Classical.safe_tac ctxt) THEN
REPEAT_DETERM (FIRSTGOAL main_tac) THEN
TRY (Classical.safe_tac (addSss ctxt)) THEN
prune_params_tac ctxt
end;
fun auto_tac ctxt = mk_auto_tac ctxt 4 2;
(* force_tac *)
(* aimed to solve the given subgoal totally, using whatever tools possible *)
fun force_tac ctxt =
let val ctxt' = addss ctxt in
SELECT_GOAL
(Classical.clarify_tac ctxt' 1 THEN
IF_UNSOLVED (Simplifier.asm_full_simp_tac ctxt 1) THEN
ALLGOALS (Classical.first_best_tac ctxt'))
end;
(* basic combinations *)
val fast_force_tac = Classical.fast_tac o addss;
val slow_simp_tac = Classical.slow_tac o addss;
val best_simp_tac = Classical.best_tac o addss;
(** concrete syntax **)
(* attributes *)
val _ =
Theory.setup
(Attrib.setup @{binding iff}
(Scan.lift
(Args.del >> K iff_del ||
Scan.option Args.add -- Args.query >> K iff_add' ||
Scan.option Args.add >> K iff_add))
"declaration of Simplifier / Classical rules");
(* method modifiers *)
val iffN = "iff";
val iff_modifiers =
[Args.$$$ iffN -- Scan.option Args.add -- Args.colon >> K (Method.modifier iff_add \<^here>),
Args.$$$ iffN -- Scan.option Args.add -- Args.query_colon >> K (Method.modifier iff_add' \<^here>),
Args.$$$ iffN -- Args.del -- Args.colon >> K (Method.modifier iff_del \<^here>)];
val clasimp_modifiers =
Simplifier.simp_modifiers @ Splitter.split_modifiers @
Classical.cla_modifiers @ iff_modifiers;
(* methods *)
fun clasimp_method' tac =
Method.sections clasimp_modifiers >> K (SIMPLE_METHOD' o tac);
val auto_method =
Scan.lift (Scan.option (Parse.nat -- Parse.nat)) --|
Method.sections clasimp_modifiers >>
(fn NONE => SIMPLE_METHOD o CHANGED_PROP o auto_tac
| SOME (m, n) => (fn ctxt => SIMPLE_METHOD (CHANGED_PROP (mk_auto_tac ctxt m n))));
val _ =
Theory.setup
(Method.setup @{binding fastforce} (clasimp_method' fast_force_tac) "combined fast and simp" #>
Method.setup @{binding slowsimp} (clasimp_method' slow_simp_tac) "combined slow and simp" #>
Method.setup @{binding bestsimp} (clasimp_method' best_simp_tac) "combined best and simp" #>
Method.setup @{binding force} (clasimp_method' force_tac) "force" #>
Method.setup @{binding auto} auto_method "auto" #>
Method.setup @{binding clarsimp} (clasimp_method' (CHANGED_PROP oo clarsimp_tac))
"clarify simplified goal");
end;