src/Provers/simplifier.ML

\isakeyword: fixed italic correction;

(*  Title:      Provers/simplifier.ML
    ID:         $Id$
    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen

Generic simplifier, suitable for most logics.  See Pure/thm.ML for the
actual meta-level rewriting engine.
*)

infix 4
  setsubgoaler setloop addloop delloop setSSolver addSSolver setSolver
  addSolver addsimps delsimps addeqcongs deleqcongs
  setmksimps setmkeqTrue setmksym settermless addsimprocs delsimprocs;

signature BASIC_SIMPLIFIER =
sig
  type simproc
  val mk_simproc: string -> cterm list
    -> (Sign.sg -> thm list -> term -> thm option) -> simproc
  type solver
  val mk_solver: string -> (thm list -> int -> tactic) -> solver
  type simpset
  val empty_ss: simpset
  val rep_ss: simpset ->
   {mss: meta_simpset,
    subgoal_tac:        simpset -> int -> tactic,
    loop_tacs:          (string * (int -> tactic))list,
    unsafe_solvers: solver list,
           solvers: solver list};
  val print_ss: simpset -> unit
  val print_simpset: theory -> unit
  val setsubgoaler: simpset *  (simpset -> int -> tactic) -> simpset
  val setloop:      simpset *             (int -> tactic) -> simpset
  val addloop:      simpset *  (string * (int -> tactic)) -> simpset
  val delloop:      simpset *   string                    -> simpset
  val setSSolver:   simpset * solver -> simpset
  val addSSolver:   simpset * solver -> simpset
  val setSolver:    simpset * solver -> simpset
  val addSolver:    simpset * solver -> simpset
  val setmksimps:   simpset * (thm -> thm list) -> simpset
  val setmkeqTrue:  simpset * (thm -> thm option) -> simpset
  val setmksym:     simpset * (thm -> thm option) -> simpset
  val settermless:  simpset * (term * term -> bool) -> simpset
  val addsimps:     simpset * thm list -> simpset
  val delsimps:     simpset * thm list -> simpset
  val addeqcongs:   simpset * thm list -> simpset
  val deleqcongs:   simpset * thm list -> simpset
  val addsimprocs:  simpset * simproc list -> simpset
  val delsimprocs:  simpset * simproc list -> simpset
  val merge_ss:     simpset * simpset -> simpset
  val prems_of_ss:  simpset -> thm list
  val simpset_ref_of_sg: Sign.sg -> simpset ref
  val simpset_ref_of: theory -> simpset ref
  val simpset_of_sg: Sign.sg -> simpset
  val simpset_of: theory -> simpset
  val SIMPSET: (simpset -> tactic) -> tactic
  val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
  val simpset: unit -> simpset
  val simpset_ref: unit -> simpset ref
  val Addsimps: thm list -> unit
  val Delsimps: thm list -> unit
  val Addsimprocs: simproc list -> unit
  val Delsimprocs: simproc list -> unit
  val               simp_tac: simpset -> int -> tactic
  val           asm_simp_tac: simpset -> int -> tactic
  val          full_simp_tac: simpset -> int -> tactic
  val        asm_lr_simp_tac: simpset -> int -> tactic
  val      asm_full_simp_tac: simpset -> int -> tactic
  val safe_asm_full_simp_tac: simpset -> int -> tactic
  val               Simp_tac:            int -> tactic
  val           Asm_simp_tac:            int -> tactic
  val          Full_simp_tac:            int -> tactic
  val        Asm_lr_simp_tac:            int -> tactic
  val      Asm_full_simp_tac:            int -> tactic
  val          simplify: simpset -> thm -> thm
  val      asm_simplify: simpset -> thm -> thm
  val     full_simplify: simpset -> thm -> thm
  val asm_full_simplify: simpset -> thm -> thm
end;

signature SIMPLIFIER =
sig
  include BASIC_SIMPLIFIER
  val          rewrite: simpset -> cterm -> thm
  val      asm_rewrite: simpset -> cterm -> thm
  val     full_rewrite: simpset -> cterm -> thm
  val asm_full_rewrite: simpset -> cterm -> thm
  val print_local_simpset: Proof.context -> unit
  val get_local_simpset: Proof.context -> simpset
  val put_local_simpset: simpset -> Proof.context -> Proof.context
  val simp_add_global: theory attribute
  val simp_del_global: theory attribute
  val simp_add_local: Proof.context attribute
  val simp_del_local: Proof.context attribute
  val change_simpset_of: (simpset * 'a -> simpset) -> 'a -> theory -> theory
  val simp_modifiers: (Args.T list -> (Method.modifier * Args.T list)) list
  val setup: (theory -> theory) list
end;

structure Simplifier: SIMPLIFIER =
struct


(** simplification procedures **)

(* datatype simproc *)

datatype simproc =
  Simproc of string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp;

fun mk_simproc name lhss proc =
  Simproc (name, map (Thm.cterm_fun Logic.varify) lhss, proc, stamp ());

fun rep_simproc (Simproc args) = args;

(** solvers **)

datatype solver = Solver of string * (thm list -> int -> tactic) * stamp;

fun mk_solver name solver = Solver(name, solver, stamp());

fun eq_solver (Solver(_,_,s1),Solver(_,_,s2)) = s1=s2;

val merge_solvers = generic_merge eq_solver I I;

fun app_sols [] _ _ = no_tac
  | app_sols (Solver(_,solver,_)::sols) thms i =
       solver thms i ORELSE app_sols sols thms i;

(** simplification sets **)

(* type simpset *)

datatype simpset =
  Simpset of {
    mss: meta_simpset,
    subgoal_tac:        simpset -> int -> tactic,
    loop_tacs:          (string * (int -> tactic))list,
    unsafe_solvers: solver list,
           solvers: solver list};

fun make_ss (mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers) =
  Simpset {mss = mss, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs,
    unsafe_solvers = unsafe_solvers, solvers = solvers};

val empty_ss =
  let val mss = Thm.set_mk_sym (Thm.empty_mss, Some o symmetric_fun)
  in make_ss (mss, K (K no_tac), [], [], []) end;

fun rep_ss (Simpset args) = args;
fun prems_of_ss (Simpset {mss, ...}) = Thm.prems_of_mss mss;


(* print simpsets *)

fun print_ss ss =
  let
    val Simpset {mss, ...} = ss;
    val {simps, procs, congs} = Thm.dest_mss mss;

    val pretty_thms = map Display.pretty_thm;
    fun pretty_proc (name, lhss) =
      Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
  in
    Pretty.writeln (Pretty.big_list "simplification rules:" (pretty_thms simps));
    Pretty.writeln (Pretty.big_list "simplification procedures:" (map pretty_proc procs));
    Pretty.writeln (Pretty.big_list "congruences:" (pretty_thms congs))
  end;


(* extend simpsets *)

fun (Simpset {mss, subgoal_tac = _, loop_tacs, unsafe_solvers, solvers})
    setsubgoaler subgoal_tac =
  make_ss (mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs = _, unsafe_solvers, solvers})
    setloop tac =
  make_ss (mss, subgoal_tac, [("",tac)], unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addloop tac = make_ss (mss, subgoal_tac, 
        (case assoc_string (loop_tacs,(fst tac)) of None => () | Some x => 
         warning ("overwriting looper "^fst tac); overwrite(loop_tacs,tac)),
           unsafe_solvers, solvers);

fun (ss as Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
 delloop name =
  let val (del, rest) = partition (fn (n, _) => n = name) loop_tacs in
    if null del then (warning ("No such looper in simpset: " ^ name); ss)
    else make_ss (mss, subgoal_tac, rest, unsafe_solvers, solvers)
  end;

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, ...})
    setSSolver solver =
  make_ss (mss, subgoal_tac, loop_tacs, unsafe_solvers, [solver]);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addSSolver sol =
  make_ss (mss, subgoal_tac, loop_tacs, unsafe_solvers,
           merge_solvers solvers [sol]);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers = _, solvers})
    setSolver unsafe_solver =
  make_ss (mss, subgoal_tac, loop_tacs, [unsafe_solver], solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addSolver sol =
  make_ss (mss, subgoal_tac, loop_tacs, 
    merge_solvers unsafe_solvers [sol], solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    setmksimps mk_simps =
  make_ss (Thm.set_mk_rews (mss, mk_simps), subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    setmkeqTrue mk_eq_True =
  make_ss (Thm.set_mk_eq_True (mss, mk_eq_True),
    subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    setmksym mksym =
  make_ss (Thm.set_mk_sym (mss, mksym),
    subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs,  unsafe_solvers, solvers})
    settermless termless =
  make_ss (Thm.set_termless (mss, termless), subgoal_tac, loop_tacs,
    unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addsimps rews =
  make_ss (Thm.add_simps (mss, rews), subgoal_tac, loop_tacs, 
	   unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    delsimps rews =
  make_ss (Thm.del_simps (mss, rews), subgoal_tac, loop_tacs, 
	   unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addeqcongs newcongs =
  make_ss (Thm.add_congs (mss, newcongs), subgoal_tac, loop_tacs, 
	   unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    deleqcongs oldcongs =
  make_ss (Thm.del_congs (mss, oldcongs), subgoal_tac, loop_tacs, 
	   unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    addsimprocs simprocs =
  make_ss
    (Thm.add_simprocs (mss, map rep_simproc simprocs),
      subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers})
    delsimprocs simprocs =
  make_ss
    (Thm.del_simprocs (mss, map rep_simproc simprocs),
      subgoal_tac, loop_tacs, unsafe_solvers, solvers);

fun clear_ss (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers}) =
  make_ss (Thm.clear_mss mss, subgoal_tac, loop_tacs, unsafe_solvers, solvers);


(* merge simpsets *)
(*NOTE: ignores subgoal_tac of 2nd simpset *)

fun merge_ss
   (Simpset {mss = mss1, loop_tacs = loop_tacs1, subgoal_tac,
             unsafe_solvers = unsafe_solvers1, solvers = solvers1},
    Simpset {mss = mss2, loop_tacs = loop_tacs2,
             unsafe_solvers = unsafe_solvers2, solvers = solvers2, ...}) =
  make_ss (Thm.merge_mss (mss1, mss2), subgoal_tac,
    merge_alists loop_tacs1 loop_tacs2,
    merge_solvers unsafe_solvers1 unsafe_solvers2,
    merge_solvers solvers1 solvers2);


(** global and local simpset data **)

(* theory data kind 'Provers/simpset' *)

structure GlobalSimpsetArgs =
struct
  val name = "Provers/simpset";
  type T = simpset ref;

  val empty = ref empty_ss;
  fun copy (ref ss) = (ref ss): T;            (*create new reference!*)
  val prep_ext = copy;
  fun merge (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
  fun print _ (ref ss) = print_ss ss;
end;

structure GlobalSimpset = TheoryDataFun(GlobalSimpsetArgs);
val print_simpset = GlobalSimpset.print;
val simpset_ref_of_sg = GlobalSimpset.get_sg;
val simpset_ref_of = GlobalSimpset.get;


(* access global simpset *)

val simpset_of_sg = ! o simpset_ref_of_sg;
val simpset_of = simpset_of_sg o Theory.sign_of;

fun SIMPSET tacf state = tacf (simpset_of_sg (Thm.sign_of_thm state)) state;
fun SIMPSET' tacf i state = tacf (simpset_of_sg (Thm.sign_of_thm state)) i state;

val simpset = simpset_of o Context.the_context;
val simpset_ref = simpset_ref_of_sg o Theory.sign_of o Context.the_context;


(* change global simpset *)

fun change_simpset_of f x thy =
  let val r = simpset_ref_of thy
  in r := f (! r, x); thy end;

fun change_simpset f x = (change_simpset_of f x (Context.the_context ()); ());

val Addsimps = change_simpset (op addsimps);
val Delsimps = change_simpset (op delsimps);
val Addsimprocs = change_simpset (op addsimprocs);
val Delsimprocs = change_simpset (op delsimprocs);


(* proof data kind 'Provers/simpset' *)

structure LocalSimpsetArgs =
struct
  val name = "Provers/simpset";
  type T = simpset;
  val init = simpset_of;
  fun print _ ss = print_ss ss;
end;

structure LocalSimpset = ProofDataFun(LocalSimpsetArgs);
val print_local_simpset = LocalSimpset.print;
val get_local_simpset = LocalSimpset.get;
val put_local_simpset = LocalSimpset.put;
fun map_local_simpset f ctxt = put_local_simpset (f (get_local_simpset ctxt)) ctxt;


(* attributes *)

fun change_global_ss f (thy, th) =
  let val r = simpset_ref_of thy
  in r := f (! r, [th]); (thy, th) end;

fun change_local_ss f (ctxt, th) =
  let val ss = f (get_local_simpset ctxt, [th])
  in (put_local_simpset ss ctxt, th) end;

val simp_add_global = change_global_ss (op addsimps);
val simp_del_global = change_global_ss (op delsimps);
val simp_add_local = change_local_ss (op addsimps);
val simp_del_local = change_local_ss (op delsimps);



(** simplification tactics **)

fun solve_all_tac (subgoal_tac, loop_tacs, unsafe_solvers) mss =
  let
    val ss =
      make_ss (mss, subgoal_tac, loop_tacs,unsafe_solvers,unsafe_solvers);
    val solve1_tac = (subgoal_tac ss THEN_ALL_NEW (K no_tac)) 1
  in DEPTH_SOLVE solve1_tac end;

fun loop_tac loop_tacs = FIRST'(map snd loop_tacs);

(*unsafe: may instantiate unknowns that appear also in other subgoals*)
fun basic_gen_simp_tac mode solvers =
  fn (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, ...}) =>
    let
      fun simp_loop_tac i =
        asm_rewrite_goal_tac mode
          (solve_all_tac (subgoal_tac,loop_tacs,unsafe_solvers))
          mss i
        THEN (solvers (prems_of_mss mss) i ORELSE
              TRY ((loop_tac loop_tacs THEN_ALL_NEW simp_loop_tac) i))
    in simp_loop_tac end;

fun gen_simp_tac mode 
      (ss as Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, ...}) =
  basic_gen_simp_tac mode (app_sols unsafe_solvers) ss;

val          simp_tac = gen_simp_tac (false, false, false);
val      asm_simp_tac = gen_simp_tac (false, true, false);
val     full_simp_tac = gen_simp_tac (true,  false, false);
val   asm_lr_simp_tac = gen_simp_tac (true,  true, false);
val asm_full_simp_tac = gen_simp_tac (true,  true, true);

(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
fun safe_asm_full_simp_tac (ss as Simpset {mss, subgoal_tac, loop_tacs, 
	unsafe_solvers, solvers}) = 
  basic_gen_simp_tac (true, true, true) (app_sols solvers) ss;

(*the abstraction over the proof state delays the dereferencing*)
fun          Simp_tac i st =          simp_tac (simpset ()) i st;
fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;
fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;
fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;
fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;



(** simplification rules and conversions **)

fun simp rew mode 
     (Simpset {mss, subgoal_tac, loop_tacs, unsafe_solvers, ...}) thm =
  let
    val tacf = solve_all_tac (subgoal_tac, loop_tacs, unsafe_solvers);
    fun prover m th = apsome fst (Seq.pull (tacf m th));
  in rew mode prover mss thm end;

val simp_thm = simp Drule.rewrite_thm;
val simp_cterm = simp Drule.rewrite_cterm;

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_full_simplify = simp_thm (true, true, false);

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_full_rewrite = simp_cterm (true, true, false);



(** concrete syntax of attributes **)

(* add / del *)

val simpN = "simp";
val addN = "add";
val delN = "del";
val onlyN = "only";
val otherN = "other";

fun simp_att change =
  (Args.$$$ addN >> K (op addsimps) ||
    Args.$$$ delN >> K (op delsimps) ||
    Scan.succeed (op addsimps))
  >> change
  |> Scan.lift
  |> Attrib.syntax;

val simp_attr = (simp_att change_global_ss, simp_att change_local_ss);


(* conversions *)

fun conv_attr f =
  (Attrib.no_args (Drule.rule_attribute (f o simpset_of)),
    Attrib.no_args (Drule.rule_attribute (f o get_local_simpset)));


(* setup_attrs *)

val setup_attrs = Attrib.add_attributes
 [(simpN,               simp_attr, "simplification rule"),
  ("simplify",          conv_attr simplify, "simplify rule"),
  ("asm_simplify",      conv_attr asm_simplify, "simplify rule, using assumptions"),
  ("full_simplify",     conv_attr full_simplify, "fully simplify rule"),
  ("asm_full_simplify", conv_attr asm_full_simplify, "fully simplify rule, using assumptions")];



(** proof methods **)

(* simplification *)

val simp_modifiers =
 [Args.$$$ simpN -- Args.$$$ addN >> K (I, simp_add_local),
  Args.$$$ simpN -- Args.$$$ delN >> K (I, simp_del_local),
  Args.$$$ simpN -- Args.$$$ onlyN >> K (map_local_simpset clear_ss, simp_add_local),
  Args.$$$ otherN >> K (I, I)];

val simp_modifiers' =
 [Args.$$$ addN >> K (I, simp_add_local),
  Args.$$$ delN >> K (I, simp_del_local),
  Args.$$$ onlyN >> K (map_local_simpset clear_ss, simp_add_local),
  Args.$$$ otherN >> K (I, I)];

fun simp_method tac =
  (fn prems => fn ctxt => Method.METHOD (fn facts =>
    FIRSTGOAL (Method.insert_tac (prems @ facts) THEN' tac (get_local_simpset ctxt))))
  |> Method.bang_sectioned_args simp_modifiers';
  

(* setup_methods *)

val setup_methods = Method.add_methods
 [(simpN,               simp_method (CHANGED oo asm_full_simp_tac), "full simplification"),
  ("simp_tac",          simp_method simp_tac, "simp_tac (improper!)"),
  ("asm_simp_tac",      simp_method asm_simp_tac, "asm_simp_tac (improper!)"),
  ("full_simp_tac",     simp_method full_simp_tac, "full_simp_tac (improper!)"),
  ("asm_full_simp_tac", simp_method asm_full_simp_tac, "asm_full_simp_tac (improper!)"),
  ("asm_lr_simp_tac",   simp_method asm_lr_simp_tac, "asm_lr_simp_tac (improper!)")];



(** theory setup **)

val setup = [GlobalSimpset.init, LocalSimpset.init, setup_attrs, setup_methods];


end;


structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
open BasicSimplifier;