Solvers are now named and stamped.
(* 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, map (Thm.strip_shyps o Drule.zero_var_indexes) o 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 asm_simpN = "asm_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)];
val simp_args = Method.only_sectioned_args simp_modifiers';
fun simp_meth thin cut tac ctxt = Method.METHOD (fn facts =>
FIRSTGOAL
((if thin then REPEAT_DETERM o etac Drule.thin_rl else K all_tac)
THEN' (if cut then Method.insert_tac facts else K all_tac)
THEN' tac (get_local_simpset ctxt)));
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 true true (CHANGED oo asm_full_simp_tac),
"full simplification (including facts, excluding assumptions)"),
(asm_simpN, simp_method false true (CHANGED oo asm_full_simp_tac),
"full simplification (including facts and assumptions)"),
("simp_tac", simp_method false false simp_tac, "simp_tac (improper!)"),
("asm_simp_tac", simp_method false false asm_simp_tac, "asm_simp_tac (improper!)"),
("full_simp_tac", simp_method false false full_simp_tac, "full_simp_tac (improper!)"),
("asm_full_simp_tac", simp_method false false asm_full_simp_tac, "asm_full_simp_tac (improper!)"),
("asm_lr_simp_tac", simp_method false false 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;