src/Provers/clasimp.ML
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(*  Title:      Provers/clasimp.ML
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    Author:     David von Oheimb, TU Muenchen
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Combination of classical reasoner and simplifier (depends on
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splitter.ML, classical.ML, blast.ML).
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*)
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infix 4 addSIs2 addSEs2 addSDs2 addIs2 addEs2 addDs2 addsimps2 delsimps2
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  addSss addss addss' addIffs delIffs;
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signature CLASIMP_DATA =
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sig
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  structure Splitter: SPLITTER
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  structure Classical: CLASSICAL
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  structure Blast: BLAST
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  sharing type Classical.claset = Blast.claset
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  val notE: thm
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  val iffD1: thm
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  val iffD2: thm
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end
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signature CLASIMP =
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sig
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  include CLASIMP_DATA
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  type claset
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  type clasimpset
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  val get_css: Context.generic -> clasimpset
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  val map_css: (clasimpset -> clasimpset) -> Context.generic -> Context.generic
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  val clasimpset_of: Proof.context -> clasimpset
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  val addSIs2: clasimpset * thm list -> clasimpset
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  val addSEs2: clasimpset * thm list -> clasimpset
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  val addSDs2: clasimpset * thm list -> clasimpset
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  val addIs2: clasimpset * thm list -> clasimpset
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  val addEs2: clasimpset * thm list -> clasimpset
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  val addDs2: clasimpset * thm list -> clasimpset
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  val addsimps2: clasimpset * thm list -> clasimpset
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  val delsimps2: clasimpset * thm list -> clasimpset
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  val addSss: claset * simpset -> claset
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  val addss: claset * simpset -> claset
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  val addss': claset * simpset -> claset
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  val addIffs: clasimpset * thm list -> clasimpset
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  val delIffs: clasimpset * thm list -> clasimpset
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  val clarsimp_tac: clasimpset -> int -> tactic
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  val mk_auto_tac: clasimpset -> int -> int -> tactic
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  val auto_tac: clasimpset -> tactic
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  val force_tac: clasimpset  -> int -> tactic
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  val fast_simp_tac: clasimpset -> int -> tactic
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  val slow_simp_tac: clasimpset -> int -> tactic
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  val best_simp_tac: clasimpset -> int -> tactic
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  val attrib: (clasimpset * thm list -> clasimpset) -> attribute
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  val iff_add: attribute
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  val iff_add': attribute
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  val iff_del: attribute
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  val iff_modifiers: Method.modifier parser list
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  val clasimp_modifiers: Method.modifier parser list
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  val clasimp_setup: theory -> theory
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end;
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functor ClasimpFun(Data: CLASIMP_DATA): CLASIMP =
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struct
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open Data;
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(* type clasimpset *)
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type claset = Classical.claset;
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type clasimpset = claset * simpset;
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fun get_css context = (Classical.get_cs context, Simplifier.get_ss context);
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fun map_css f context =
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  let
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    val (cs, ss) = get_css context;
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    val (cs', ss') = f (cs, Simplifier.context (Context.proof_of context) ss);
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  in
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    context
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    |> Classical.map_cs (K cs')
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    |> Simplifier.map_ss (K (Simplifier.inherit_context ss ss'))
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  end;
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fun clasimpset_of ctxt = (Classical.claset_of ctxt, Simplifier.simpset_of ctxt);
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(* clasimpset operations *)
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(*this interface for updating a clasimpset is rudimentary and just for
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  convenience for the most common cases*)
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fun pair_upd1 f ((a, b), x) = (f (a, x), b);
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fun pair_upd2 f ((a, b), x) = (a, f (b, x));
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fun op addSIs2   arg = pair_upd1 Classical.addSIs arg;
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fun op addSEs2   arg = pair_upd1 Classical.addSEs arg;
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fun op addSDs2   arg = pair_upd1 Classical.addSDs arg;
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fun op addIs2    arg = pair_upd1 Classical.addIs arg;
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fun op addEs2    arg = pair_upd1 Classical.addEs arg;
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fun op addDs2    arg = pair_upd1 Classical.addDs arg;
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fun op addsimps2 arg = pair_upd2 Simplifier.addsimps arg;
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fun op delsimps2 arg = pair_upd2 Simplifier.delsimps arg;
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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val safe_asm_full_simp_tac = Simplifier.generic_simp_tac true (true,true,true);
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(*Add a simpset to a classical set!*)
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(*Caution: only one simpset added can be added by each of addSss and addss*)
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fun cs addSss ss = Classical.addSafter (cs, ("safe_asm_full_simp_tac",
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                            CHANGED o safe_asm_full_simp_tac ss));
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fun cs addss  ss = Classical.addbefore  (cs, ("asm_full_simp_tac",
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                            CHANGED o Simplifier.asm_full_simp_tac ss));
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fun cs addss' ss = Classical.addbefore  (cs, ("asm_full_simp_tac",
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                            CHANGED o Simplifier.asm_lr_simp_tac ss));
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(* iffs: addition of rules to simpsets and clasets simultaneously *)
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(*Takes (possibly conditional) theorems of the form A<->B to
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        the Safe Intr     rule B==>A and
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        the Safe Destruct rule A==>B.
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  Also ~A goes to the Safe Elim rule A ==> ?R
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  Failing other cases, A is added as a Safe Intr rule*)
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local
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fun addIff decls1 decls2 simp ((cs, ss), th) =
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  let
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    val n = nprems_of th;
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    val (elim, intro) = if n = 0 then decls1 else decls2;
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    val zero_rotate = zero_var_indexes o rotate_prems n;
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  in
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    (elim (intro (cs, [zero_rotate (th RS iffD2)]),
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           [Tactic.make_elim (zero_rotate (th RS iffD1))])
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      handle THM _ => (elim (cs, [zero_rotate (th RS notE)])
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        handle THM _ => intro (cs, [th])),
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     simp (ss, [th]))
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  end;
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fun delIff delcs delss ((cs, ss), th) =
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  let val zero_rotate = zero_var_indexes o rotate_prems (nprems_of th) in
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    (delcs (cs, [zero_rotate (th RS iffD2),
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        Tactic.make_elim (zero_rotate (th RS iffD1))])
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      handle THM _ => (delcs (cs, [zero_rotate (th RS notE)])
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        handle THM _ => delcs (cs, [th])),
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     delss (ss, [th]))
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  end;
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fun modifier att (x, ths) =
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  fst (Library.foldl_map (Library.apply [att]) (x, rev ths));
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val addXIs = modifier (Context_Rules.intro_query NONE);
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val addXEs = modifier (Context_Rules.elim_query NONE);
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val delXs = modifier Context_Rules.rule_del;
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in
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val op addIffs =
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  Library.foldl
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      (addIff (Classical.addSEs, Classical.addSIs)
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              (Classical.addEs, Classical.addIs)
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              Simplifier.addsimps);
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val op delIffs = Library.foldl (delIff Classical.delrules Simplifier.delsimps);
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fun addIffs_generic (x, ths) =
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  Library.foldl (addIff (addXEs, addXIs) (addXEs, addXIs) #1) ((x, ()), ths) |> #1;
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fun delIffs_generic (x, ths) =
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  Library.foldl (delIff delXs #1) ((x, ()), ths) |> #1;
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end;
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(* tacticals *)
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fun clarsimp_tac (cs, ss) =
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  safe_asm_full_simp_tac ss THEN_ALL_NEW
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  Classical.clarify_tac (cs addSss ss);
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(* auto_tac *)
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fun blast_depth_tac cs m i thm =
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    Blast.depth_tac cs m i thm
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      handle Blast.TRANS s => (warning ("Blast_tac: " ^ s); Seq.empty);
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(* a variant of depth_tac that avoids interference of the simplifier
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   with dup_step_tac when they are combined by auto_tac *)
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local
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fun slow_step_tac' cs = Classical.appWrappers cs
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        (Classical.instp_step_tac cs APPEND' Classical.haz_step_tac cs);
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in fun nodup_depth_tac cs m i state = SELECT_GOAL
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   (Classical.safe_steps_tac cs 1 THEN_ELSE
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        (DEPTH_SOLVE (nodup_depth_tac cs m 1),
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         Classical.inst0_step_tac cs 1 APPEND COND (K (m=0)) no_tac
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             (slow_step_tac' cs 1 THEN DEPTH_SOLVE (nodup_depth_tac cs (m-1) 1))
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        )) i state;
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end;
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(*Designed to be idempotent, except if blast_depth_tac instantiates variables
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  in some of the subgoals*)
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fun mk_auto_tac (cs, ss) m n =
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    let val cs' = cs addss ss
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        val maintac =
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          blast_depth_tac cs m               (* fast but can't use wrappers *)
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          ORELSE'
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          (CHANGED o nodup_depth_tac cs' n); (* slower but more general *)
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    in  EVERY [ALLGOALS (Simplifier.asm_full_simp_tac ss),
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               TRY (Classical.safe_tac cs),
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               REPEAT (FIRSTGOAL maintac),
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               TRY (Classical.safe_tac (cs addSss ss)),
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               prune_params_tac]
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    end;
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fun auto_tac css = mk_auto_tac css 4 2;
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(* force_tac *)
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(* aimed to solve the given subgoal totally, using whatever tools possible *)
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fun force_tac (cs,ss) = let val cs' = cs addss ss in SELECT_GOAL (EVERY [
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        Classical.clarify_tac cs' 1,
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        IF_UNSOLVED (Simplifier.asm_full_simp_tac ss 1),
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        ALLGOALS (Classical.first_best_tac cs')]) end;
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(* basic combinations *)
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fun ADDSS tac (cs, ss) = let val cs' = cs addss ss in tac cs' end;
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val fast_simp_tac = ADDSS Classical.fast_tac;
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val slow_simp_tac = ADDSS Classical.slow_tac;
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val best_simp_tac = ADDSS Classical.best_tac;
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(* access clasimpset *)
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(* attributes *)
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fun attrib f = Thm.declaration_attribute (fn th => map_css (fn css => f (css, [th])));
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fun attrib' f (x, th) = (f (x, [th]), th);
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val iff_add = attrib (op addIffs);
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val iff_add' = attrib' addIffs_generic;
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val iff_del = attrib (op delIffs) o attrib' delIffs_generic;
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fun iff_att x = (Scan.lift
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 (Args.del >> K iff_del ||
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  Scan.option Args.add -- Args.query >> K iff_add' ||
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  Scan.option Args.add >> K iff_add)) x;
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(* method modifiers *)
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val iffN = "iff";
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val iff_modifiers =
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 [Args.$$$ iffN -- Scan.option Args.add -- Args.colon >> K ((I, iff_add): Method.modifier),
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  Args.$$$ iffN -- Scan.option Args.add -- Args.query_colon >> K (I, iff_add'),
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  Args.$$$ iffN -- Args.del -- Args.colon >> K (I, iff_del)];
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val clasimp_modifiers =
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  Simplifier.simp_modifiers @ Splitter.split_modifiers @
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  Classical.cla_modifiers @ iff_modifiers;
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(* methods *)
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fun clasimp_meth tac ctxt = METHOD (fn facts =>
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  ALLGOALS (Method.insert_tac facts) THEN tac (clasimpset_of ctxt));
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fun clasimp_meth' tac ctxt = METHOD (fn facts =>
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  HEADGOAL (Method.insert_tac facts THEN' tac (clasimpset_of ctxt)));
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fun clasimp_method' tac =
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  Method.sections clasimp_modifiers >> K (clasimp_meth' tac);
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val auto_method =
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  Scan.lift (Scan.option (OuterParse.nat -- OuterParse.nat)) --|
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    Method.sections clasimp_modifiers >>
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  (fn NONE => clasimp_meth (CHANGED_PROP o auto_tac)
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    | SOME (m, n) => clasimp_meth (CHANGED_PROP o (fn css => mk_auto_tac css m n)));
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(* theory setup *)
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val clasimp_setup =
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  Attrib.setup @{binding iff} iff_att "declaration of Simplifier / Classical rules" #>
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  Method.setup @{binding fastsimp} (clasimp_method' fast_simp_tac) "combined fast and simp" #>
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  Method.setup @{binding slowsimp} (clasimp_method' slow_simp_tac) "combined slow and simp" #>
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  Method.setup @{binding bestsimp} (clasimp_method' best_simp_tac) "combined best and simp" #>
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  Method.setup @{binding force} (clasimp_method' force_tac) "force" #>
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  Method.setup @{binding auto} auto_method "auto" #>
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  Method.setup @{binding clarsimp} (clasimp_method' (CHANGED_PROP oo clarsimp_tac))
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    "clarify simplified goal";
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end;