(* Title: Provers/clasimp.ML
ID: $Id$
Author: David von Oheimb, TU Muenchen
Combination of classical reasoner and simplifier (depends on
simplifier.ML, splitter.ML classical.ML, blast.ML).
*)
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2
addSss addss addIffs delIffs;
signature CLASIMP_DATA =
sig
structure Simplifier: SIMPLIFIER
structure Splitter: SPLITTER
structure Classical: CLASSICAL
structure Blast: BLAST
sharing type Classical.claset = Blast.claset
val dest_Trueprop: term -> term
val not_const: term
val iff_const: term
val notE: thm
val iffD1: thm
val iffD2: thm
val cla_make_elim: thm -> thm
end
signature CLASIMP =
sig
include CLASIMP_DATA
type claset
type simpset
type clasimpset
val addSIs2: clasimpset * thm list -> clasimpset
val addSEs2: clasimpset * thm list -> clasimpset
val addSDs2: clasimpset * thm list -> clasimpset
val addIs2: clasimpset * thm list -> clasimpset
val addEs2: clasimpset * thm list -> clasimpset
val addDs2: clasimpset * thm list -> clasimpset
val addsimps2: clasimpset * thm list -> clasimpset
val delsimps2: clasimpset * thm list -> clasimpset
val addSss: claset * simpset -> claset
val addss: claset * simpset -> claset
val addIffs: clasimpset * thm list -> clasimpset
val delIffs: clasimpset * thm list -> clasimpset
val AddIffs: thm list -> unit
val DelIffs: thm list -> unit
val CLASIMPSET: (clasimpset -> tactic) -> tactic
val CLASIMPSET': (clasimpset -> 'a -> tactic) -> 'a -> tactic
val clarsimp_tac: clasimpset -> int -> tactic
val Clarsimp_tac: int -> tactic
val mk_auto_tac: clasimpset -> int -> int -> tactic
val auto_tac: clasimpset -> tactic
val Auto_tac: tactic
val auto: unit -> unit
val force_tac: clasimpset -> int -> tactic
val Force_tac: int -> tactic
val force: int -> unit
val fast_simp_tac: clasimpset -> int -> tactic
val slow_simp_tac: clasimpset -> int -> tactic
val best_simp_tac: clasimpset -> int -> tactic
val change_global_css: (clasimpset * thm list -> clasimpset) -> theory attribute
val change_local_css: (clasimpset * thm list -> clasimpset) -> Proof.context attribute
val get_local_clasimpset: Proof.context -> clasimpset
val iff_add_global: theory attribute
val iff_del_global: theory attribute
val iff_add_local: Proof.context attribute
val iff_del_local: Proof.context attribute
val iff_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
val clasimp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
val setup: (theory -> theory) list
end;
functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
struct
open Data;
type claset = Classical.claset;
type simpset = Simplifier.simpset;
type clasimpset = claset * simpset;
(* clasimpset operations *)
(*this interface for updating a clasimpset is rudimentary and just for
convenience for the most common cases*)
fun pair_upd1 f ((a,b),x) = (f(a,x), b);
fun pair_upd2 f ((a,b),x) = (a, f(b,x));
fun op addSIs2 arg = pair_upd1 Classical.addSIs arg;
fun op addSEs2 arg = pair_upd1 Classical.addSEs arg;
fun op addSDs2 arg = pair_upd1 Classical.addSDs arg;
fun op addIs2 arg = pair_upd1 Classical.addIs arg;
fun op addEs2 arg = pair_upd1 Classical.addEs arg;
fun op addDs2 arg = pair_upd1 Classical.addDs arg;
fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;
fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;
(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
val safe_asm_full_simp_tac = Simplifier.generic_simp_tac true (true,true,true);
(*Add a simpset to a classical set!*)
(*Caution: only one simpset added can be added by each of addSss and addss*)
fun cs addSss ss = Classical.addSaltern (cs, ("safe_asm_full_simp_tac",
CHANGED o safe_asm_full_simp_tac ss));
fun cs addss ss = Classical.addbefore (cs, ("asm_full_simp_tac",
CHANGED o Simplifier.asm_full_simp_tac ss));
(* iffs: addition of rules to simpsets and clasets simultaneously *)
(*Takes UNCONDITIONAL 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*)
local
fun addIff ((cla, simp), th) =
(case dest_Trueprop (#prop (rep_thm th)) of
con $ _ $ _ =>
if con = Data.iff_const then
Classical.addSDs (Classical.addSIs (cla, [zero_var_indexes (th RS Data.iffD2)]),
[zero_var_indexes (th RS Data.iffD1)])
else Classical.addSIs (cla, [th])
| con $ A =>
if con = Data.not_const then Classical.addSEs (cla, [zero_var_indexes (th RS Data.notE)])
else Classical.addSIs (cla, [th])
| _ => Classical.addSIs (cla, [th]), Simplifier.addsimps (simp, [th]))
handle TERM _ => error ("iff add: theorem must be unconditional\n" ^ Display.string_of_thm th);
fun delIff ((cla, simp), th) =
(case dest_Trueprop (#prop (rep_thm th)) of
con $ _ $ _ =>
if con = Data.iff_const then
Classical.delrules (cla, [zero_var_indexes (th RS Data.iffD2),
Data.cla_make_elim (zero_var_indexes (th RS Data.iffD1))])
else Classical.delrules (cla, [th])
| con $ A =>
if con = Data.not_const then Classical.delrules (cla, [zero_var_indexes (th RS Data.notE)])
else Classical.delrules (cla, [th])
| _ => Classical.delrules (cla, [th]), Simplifier.delsimps (simp, [th]))
handle TERM _ =>
(warning ("iff del: ignoring conditional theorem\n" ^ string_of_thm th); (cla, simp));
fun store_clasimp (cla, simp) =
(Classical.claset_ref () := cla; Simplifier.simpset_ref () := simp);
in
val op addIffs = foldl addIff;
val op delIffs = foldl delIff;
fun AddIffs thms = store_clasimp ((Classical.claset (), Simplifier.simpset ()) addIffs thms);
fun DelIffs thms = store_clasimp ((Classical.claset (), Simplifier.simpset ()) delIffs thms);
end;
(* tacticals *)
fun CLASIMPSET tacf state =
Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss))) state;
fun CLASIMPSET' tacf i state =
Classical.CLASET (fn cs => Simplifier.SIMPSET (fn ss => tacf (cs, ss) i)) state;
fun clarsimp_tac (cs, ss) = safe_asm_full_simp_tac ss THEN_ALL_NEW
Classical.clarify_tac (cs addSss ss);
fun Clarsimp_tac i = clarsimp_tac (Classical.claset(), Simplifier.simpset()) i;
(* auto_tac *)
fun blast_depth_tac cs m i thm =
Blast.depth_tac cs m i thm
handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);
(* 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' cs = Classical.appWrappers cs
(Classical.instp_step_tac cs APPEND' Classical.haz_step_tac cs);
in fun nodup_depth_tac cs m i state = SELECT_GOAL
(Classical.safe_steps_tac cs 1 THEN_ELSE
(DEPTH_SOLVE (nodup_depth_tac cs m 1),
Classical.inst0_step_tac cs 1 APPEND COND (K (m=0)) no_tac
(slow_step_tac' cs 1 THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) 1))
)) i state;
end;
(*Designed to be idempotent, except if blast_depth_tac instantiates variables
in some of the subgoals*)
fun mk_auto_tac (cs, ss) m n =
let val cs' = cs addss ss
val maintac =
blast_depth_tac cs m (* fast but can't use wrappers *)
ORELSE'
(CHANGED o nodup_depth_tac cs' n); (* slower but more general *)
in EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),
TRY (Classical.safe_tac cs),
REPEAT (FIRSTGOAL maintac),
TRY (Classical.safe_tac (cs addSss ss)),
prune_params_tac]
end;
fun auto_tac css = mk_auto_tac css 4 2;
fun Auto_tac st = auto_tac (Classical.claset(), Simplifier.simpset()) st;
fun auto () = by Auto_tac;
(* force_tac *)
(* aimed to solve the given subgoal totally, using whatever tools possible *)
fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [
Classical.clarify_tac cs' 1,
IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),
ALLGOALS (Classical.first_best_tac cs')]) end;
fun Force_tac i = force_tac (Classical.claset(), Simplifier.simpset()) i;
fun force i = by (Force_tac i);
(* basic combinations *)
fun ADDSS tac (cs, ss) = let val cs' = cs addss ss in tac cs' end;
val fast_simp_tac = ADDSS Classical.fast_tac;
val slow_simp_tac = ADDSS Classical.slow_tac;
val best_simp_tac = ADDSS Classical.best_tac;
(* access clasimpset *)
fun change_global_css f (thy, th) =
let
val cs_ref = Classical.claset_ref_of thy;
val ss_ref = Simplifier.simpset_ref_of thy;
val (cs', ss') = f ((! cs_ref, ! ss_ref), [th]);
in cs_ref := cs'; ss_ref := ss'; (thy, th) end;
fun change_local_css f (ctxt, th) =
let
val cs = Classical.get_local_claset ctxt;
val ss = Simplifier.get_local_simpset ctxt;
val (cs', ss') = f ((cs, ss), [th]);
val ctxt' =
ctxt
|> Classical.put_local_claset cs'
|> Simplifier.put_local_simpset ss';
in (ctxt', th) end;
fun get_local_clasimpset ctxt =
(Classical.get_local_claset ctxt, Simplifier.get_local_simpset ctxt);
(* attributes *)
val iff_add_global = change_global_css (op addIffs);
val iff_del_global = change_global_css (op delIffs);
val iff_add_local = change_local_css (op addIffs);
val iff_del_local = change_local_css (op delIffs);
val iff_attr =
(Attrib.add_del_args iff_add_global iff_del_global,
Attrib.add_del_args iff_add_local iff_del_local);
(* method modifiers *)
val iffN = "iff";
val iff_modifiers =
[Args.$$$ iffN -- Args.colon >> K ((I, iff_add_local): Method.modifier),
Args.$$$ iffN -- Args.$$$ Args.addN -- Args.colon >> K (I, iff_add_local),
Args.$$$ iffN -- Args.$$$ Args.delN -- Args.colon >> K (I, iff_del_local)];
val clasimp_modifiers =
Simplifier.simp_modifiers @ Splitter.split_modifiers @
Classical.cla_modifiers @ iff_modifiers;
(* methods *)
fun clasimp_meth tac prems ctxt = Method.METHOD (fn facts =>
ALLGOALS (Method.insert_tac (prems @ facts)) THEN tac (get_local_clasimpset ctxt));
fun clasimp_meth' tac prems ctxt = Method.METHOD (fn facts =>
HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (get_local_clasimpset ctxt)));
val clasimp_method = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth;
val clasimp_method' = Method.bang_sectioned_args clasimp_modifiers o clasimp_meth';
fun auto_args m =
Method.bang_sectioned_args' clasimp_modifiers (Scan.lift (Scan.option (Args.nat -- Args.nat))) m;
fun auto_meth None = clasimp_meth (CHANGED o auto_tac)
| auto_meth (Some (m, n)) = clasimp_meth (CHANGED o (fn css => mk_auto_tac css m n));
(* theory setup *)
val setup =
[Attrib.add_attributes
[("iff", iff_attr, "declaration of Simplifier / Classical rules")],
Method.add_methods
[("fastsimp", clasimp_method' fast_simp_tac, "combined fast and simp"),
("slowsimp", clasimp_method' slow_simp_tac, "combined slow and simp"),
("bestsimp", clasimp_method' best_simp_tac, "combined best and simp"),
("force", clasimp_method' force_tac, "force"),
("auto", auto_args auto_meth, "auto"),
("clarsimp", clasimp_method' (CHANGED oo clarsimp_tac), "clarify simplified goal")]];
end;