(* Title: Provers/clasimp.ML
Author: David von Oheimb, TU Muenchen
Combination of classical reasoner and simplifier (depends on
splitter.ML, classical.ML, blast.ML).
*)
infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2
addSss addss addss' addIffs delIffs;
signature CLASIMP_DATA =
sig
structure Splitter: SPLITTER
structure Classical: CLASSICAL
structure Blast: BLAST
sharing type Classical.claset = Blast.claset
val notE: thm
val iffD1: thm
val iffD2: thm
end
signature CLASIMP =
sig
include CLASIMP_DATA
type claset
type clasimpset
val get_css: Context.generic -> clasimpset
val map_css: (clasimpset -> clasimpset) -> Context.generic -> Context.generic
val clasimpset_of: Proof.context -> 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 addss': claset * simpset -> claset
val addIffs: clasimpset * thm list -> clasimpset
val delIffs: clasimpset * thm list -> clasimpset
val clarsimp_tac: clasimpset -> int -> tactic
val mk_auto_tac: clasimpset -> int -> int -> tactic
val auto_tac: clasimpset -> tactic
val force_tac: clasimpset -> int -> tactic
val fast_simp_tac: clasimpset -> int -> tactic
val slow_simp_tac: clasimpset -> int -> tactic
val best_simp_tac: clasimpset -> int -> tactic
val attrib: (clasimpset * thm list -> clasimpset) -> attribute
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
val clasimp_setup: theory -> theory
end;
functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
struct
open Data;
(* type clasimpset *)
type claset = Classical.claset;
type clasimpset = claset * simpset;
fun get_css context = (Classical.get_cs context, Simplifier.get_ss context);
fun map_css f context =
let val (cs', ss') = f (get_css context)
in context |> Classical.map_cs (K cs') |> Simplifier.map_ss (K ss') end;
fun clasimpset_of ctxt = (Classical.claset_of ctxt, Simplifier.simpset_of ctxt);
(* 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.addSafter (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));
fun cs addss' ss = Classical.addbefore (cs, ("asm_full_simp_tac",
CHANGED o Simplifier.asm_lr_simp_tac ss));
(* iffs: addition of rules to simpsets and clasets simultaneously *)
(*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*)
local
fun addIff decls1 decls2 simp ((cs, ss), th) =
let
val n = nprems_of th;
val (elim, intro) = if n = 0 then decls1 else decls2;
val zero_rotate = zero_var_indexes o rotate_prems n;
in
(elim (intro (cs, [zero_rotate (th RS iffD2)]),
[Tactic.make_elim (zero_rotate (th RS iffD1))])
handle THM _ => (elim (cs, [zero_rotate (th RS notE)])
handle THM _ => intro (cs, [th])),
simp (ss, [th]))
end;
fun delIff delcs delss ((cs, ss), th) =
let val zero_rotate = zero_var_indexes o rotate_prems (nprems_of th) in
(delcs (cs, [zero_rotate (th RS iffD2),
Tactic.make_elim (zero_rotate (th RS iffD1))])
handle THM _ => (delcs (cs, [zero_rotate (th RS notE)])
handle THM _ => delcs (cs, [th])),
delss (ss, [th]))
end;
fun modifier att (x, ths) =
fst (Library.foldl_map (Library.apply [att]) (x, rev ths));
val addXIs = modifier (Context_Rules.intro_query NONE);
val addXEs = modifier (Context_Rules.elim_query NONE);
val delXs = modifier Context_Rules.rule_del;
in
val op addIffs =
Library.foldl
(addIff (Classical.addSEs, Classical.addSIs)
(Classical.addEs, Classical.addIs)
Simplifier.addsimps);
val op delIffs = Library.foldl (delIff Classical.delrules Simplifier.delsimps);
fun addIffs_generic (x, ths) =
Library.foldl (addIff (addXEs, addXIs) (addXEs, addXIs) #1) ((x, ()), ths) |> #1;
fun delIffs_generic (x, ths) =
Library.foldl (delIff delXs #1) ((x, ()), ths) |> #1;
end;
(* tacticals *)
fun clarsimp_tac (cs, ss) =
safe_asm_full_simp_tac ss THEN_ALL_NEW
Classical.clarify_tac (cs addSss ss);
(* 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;
(* 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;
(* 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 *)
(* attributes *)
fun attrib f = Thm.declaration_attribute (fn th => map_css (fn css => f (css, [th])));
fun attrib' f (x, th) = (f (x, [th]), th);
val iff_add = attrib (op addIffs);
val iff_add' = attrib' addIffs_generic;
val iff_del = attrib (op delIffs) o attrib' delIffs_generic;
fun iff_att x = (Scan.lift
(Args.del >> K iff_del ||
Scan.option Args.add -- Args.query >> K iff_add' ||
Scan.option Args.add >> K iff_add)) x;
(* method modifiers *)
val iffN = "iff";
val iff_modifiers =
[Args.$$$ iffN -- Scan.option Args.add -- Args.colon >> K ((I, iff_add): Method.modifier),
Args.$$$ iffN -- Scan.option Args.add -- Args.query_colon >> K (I, iff_add'),
Args.$$$ iffN -- Args.del -- Args.colon >> K (I, iff_del)];
val clasimp_modifiers =
Simplifier.simp_modifiers @ Splitter.split_modifiers @
Classical.cla_modifiers @ iff_modifiers;
(* methods *)
fun clasimp_meth tac prems ctxt = METHOD (fn facts =>
ALLGOALS (Method.insert_tac (prems @ facts)) THEN tac (clasimpset_of ctxt));
fun clasimp_meth' tac prems ctxt = METHOD (fn facts =>
HEADGOAL (Method.insert_tac (prems @ facts) THEN' tac (clasimpset_of ctxt)));
fun clasimp_method' tac =
Args.bang_facts --| Method.sections clasimp_modifiers >> (clasimp_meth' tac);
val auto_method =
Args.bang_facts -- Scan.lift (Scan.option (OuterParse.nat -- OuterParse.nat)) --|
Method.sections clasimp_modifiers >>
(fn (prems, NONE) => clasimp_meth (CHANGED_PROP o auto_tac) prems
| (prems, SOME (m, n)) => clasimp_meth (CHANGED_PROP o (fn css => mk_auto_tac css m n)) prems);
(* theory setup *)
val clasimp_setup =
Attrib.setup @{binding iff} iff_att "declaration of Simplifier / Classical rules" #>
Method.setup @{binding fastsimp} (clasimp_method' fast_simp_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;