(* ID: $Id$
Author: Claire Quigley
Copyright 2004 University of Cambridge
*)
structure ReduceAxiomsN =
(* Author: Jia Meng, Cambridge University Computer Laboratory
Remove irrelevant axioms used for a proof of a goal, with with iteration control
Initial version. Needs elaboration. *)
struct
fun add_term_consts_rm ncs (Const(c, _)) cs = if (c mem ncs) then cs else (c ins_string cs)
| add_term_consts_rm ncs (t $ u) cs =
add_term_consts_rm ncs t (add_term_consts_rm ncs u cs)
| add_term_consts_rm ncs (Abs(_,_,t)) cs = add_term_consts_rm ncs t cs
| add_term_consts_rm ncs _ cs = cs;
fun term_consts_rm ncs t = add_term_consts_rm ncs t [];
fun thm_consts_rm ncs thm = term_consts_rm ncs (prop_of thm);
fun consts_of_thm (n,thm) = thm_consts_rm ["Trueprop","==>","all","Ex","op &", "op |", "Not", "All", "op -->", "op =", "==", "True", "False"] thm;
fun consts_of_term term = term_consts_rm ["Trueprop","==>","all","Ex","op &", "op |", "Not", "All", "op -->", "op =", "==", "True", "False"] term;
fun make_pairs [] _ = []
| make_pairs (x::xs) y = (x,y)::(make_pairs xs y);
fun const_thm_list_aux [] cthms = cthms
| const_thm_list_aux (thm::thms) cthms =
let val consts = consts_of_thm thm
val cthms' = make_pairs consts thm
in const_thm_list_aux thms (cthms' @ cthms) end;
fun const_thm_list thms = const_thm_list_aux thms [];
fun make_thm_table thms = Symtab.make_multi (const_thm_list thms);
fun consts_in_goal goal = consts_of_term goal;
fun axioms_having_consts_aux [] tab thms = thms
| axioms_having_consts_aux (c::cs) tab thms =
let val thms2 = Option.getOpt (Symtab.lookup tab c, [])
in axioms_having_consts_aux cs tab (thms2 union thms) end;
fun axioms_having_consts cs tab = axioms_having_consts_aux cs tab [];
fun relevant_axioms goal thmTab n =
let fun relevant_axioms_aux1 cs k =
let val thms1 = axioms_having_consts cs thmTab
val cs1 = foldl (op union_string) [] (map consts_of_thm thms1)
in
if (cs1 subset cs) orelse n <= k then (k,thms1)
else relevant_axioms_aux1 (cs1 union cs) (k+1)
end
in relevant_axioms_aux1 (consts_in_goal goal) 1 end;
fun relevant_filter n goal thms =
if n<=0 then thms
else #2 (relevant_axioms goal (make_thm_table thms) n);
(* find the thms from thy that contain relevant constants, n is the iteration number *)
fun find_axioms_n thy goal n =
let val clasetR = ResAxioms.claset_rules_of_thy thy
val simpsetR = ResAxioms.simpset_rules_of_thy thy
val table = make_thm_table (clasetR @ simpsetR)
in relevant_axioms goal table n end;
fun find_axioms_n_c thy goal n =
let val current_thms = PureThy.thms_of thy
val table = make_thm_table current_thms
in relevant_axioms goal table n end;
end;
signature RES_CLASIMP =
sig
val blacklist : string list ref (*Theorems forbidden in the output*)
val theory_blacklist : string list ref (*entire blacklisted theories*)
val relevant : int ref
val use_simpset: bool ref
val get_clasimp_lemmas :
Proof.context -> term ->
(ResClause.clause * thm) Array.array * ResClause.clause list
end;
structure ResClasimp : RES_CLASIMP =
struct
val use_simpset = ref false; (*Performance is much better without simprules*)
(*In general, these produce clauses that are prolific (match too many equality or
membership literals) and relate to seldom-used facts. Some duplicate other rules.
FIXME: this blacklist needs to be maintained using theory data and added to using
an attribute.*)
val blacklist = ref
["Datatype.not_None_eq_iff2",
"Datatype.not_Some_eq_D",
"Datatype.not_Some_eq",
"Datatype.option.size_1",
"Datatype.option.size_2",
"Datatype.prod.size",
"Datatype.sum.size_1",
"Datatype.sum.size_2",
"Datatype.unit.size",
"Divides.dvd_0_left_iff",
"Finite_Set.card_0_eq",
"Finite_Set.card_infinite",
"Finite_Set.Max_ge",
"Finite_Set.Max_in",
"Finite_Set.Max_le_iff",
"Finite_Set.Max_less_iff",
"Finite_Set.max.f_below_strict_below.below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.max.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.Min_ge_iff",
"Finite_Set.Min_gr_iff",
"Finite_Set.Min_in",
"Finite_Set.Min_le",
"Finite_Set.min_max.below_inf_sup_Inf_Sup.inf_Sup_absorb",
"Finite_Set.min_max.below_inf_sup_Inf_Sup.sup_Inf_absorb",
"Finite_Set.min.f_below_strict_below.below_f_conv", (*duplicates in Orderings.*)
"Finite_Set.min.f_below_strict_below.strict_below_f_conv", (*duplicates in Orderings.*)
"Infinite_Set.atmost_one_unique",
"IntArith.zabs_less_one_iff",
"IntDef.Integ.Abs_Integ_inject",
"IntDef.Integ.Abs_Integ_inverse",
"IntDiv.zdvd_0_left",
"IntDiv.zero_less_zpower_abs_iff",
"List.append_eq_append_conv",
"List.Cons_in_lex",
"List.in_listsD",
"List.in_listsI",
"List.lists.Cons",
"List.listsE",
"List.take_eq_Nil",
"Nat.less_one",
"Nat.less_one", (*not directional? obscure*)
"Nat.not_gr0",
"Nat.one_eq_mult_iff", (*duplicate by symmetry*)
"NatArith.of_nat_0_eq_iff",
"NatArith.of_nat_eq_0_iff",
"NatArith.of_nat_le_0_iff",
"NatSimprocs.divide_le_0_iff_number_of", (*seldom used; often prolific*)
"NatSimprocs.divide_le_0_iff_number_of", (*too many clauses*)
"NatSimprocs.divide_less_0_iff_number_of",
"NatSimprocs.divide_less_0_iff_number_of", (*too many clauses*)
"NatSimprocs.equation_minus_iff_1", (*not directional*)
"NatSimprocs.equation_minus_iff_number_of", (*not directional*)
"NatSimprocs.le_minus_iff_1", (*not directional*)
"NatSimprocs.le_minus_iff_number_of", (*not directional*)
"NatSimprocs.less_minus_iff_1", (*not directional*)
"NatSimprocs.less_minus_iff_number_of", (*not directional*)
"NatSimprocs.minus_equation_iff_number_of", (*not directional*)
"NatSimprocs.minus_le_iff_1", (*not directional*)
"NatSimprocs.minus_le_iff_number_of", (*not directional*)
"NatSimprocs.minus_less_iff_1", (*not directional*)
"NatSimprocs.mult_le_cancel_left_number_of", (*excessive case analysis*)
"NatSimprocs.mult_le_cancel_right_number_of", (*excessive case analysis*)
"NatSimprocs.mult_less_cancel_left_number_of", (*excessive case analysis*)
"NatSimprocs.mult_less_cancel_right_number_of", (*excessive case analysis*)
"NatSimprocs.zero_le_divide_iff_number_of",
"NatSimprocs.zero_le_divide_iff_number_of", (*excessive case analysis*)
"NatSimprocs.zero_less_divide_iff_number_of",
"NatSimprocs.zero_less_divide_iff_number_of", (*excessive case analysis*)
"OrderedGroup.abs_0_eq",
"OrderedGroup.abs_0_eq", (*duplicate by symmetry*)
"OrderedGroup.diff_eq_0_iff_eq", (*prolific?*)
"OrderedGroup.join_0_eq_0",
"OrderedGroup.meet_0_eq_0",
"OrderedGroup.pprt_eq_0", (*obscure*)
"OrderedGroup.pprt_eq_id", (*obscure*)
"OrderedGroup.pprt_mono", (*obscure*)
"Parity.even_nat_power", (*obscure, somewhat prolilfic*)
"Parity.power_eq_0_iff_number_of",
"Parity.power_eq_0_iff_number_of",
"Parity.power_le_zero_eq_number_of",
"Parity.power_le_zero_eq_number_of", (*obscure and prolific*)
"Parity.power_less_zero_eq_number_of",
"Parity.zero_le_power_eq_number_of", (*obscure and prolific*)
"Parity.zero_less_power_eq_number_of", (*obscure and prolific*)
"Power.zero_less_power_abs_iff",
"Relation.diagI",
"Relation.ImageI",
"Ring_and_Field.divide_cancel_left", (*fields are seldom used & often prolific*)
"Ring_and_Field.divide_cancel_right",
"Ring_and_Field.divide_divide_eq_left",
"Ring_and_Field.divide_divide_eq_right",
"Ring_and_Field.divide_eq_0_iff",
"Ring_and_Field.divide_eq_1_iff",
"Ring_and_Field.divide_eq_eq_1",
"Ring_and_Field.divide_le_0_1_iff",
"Ring_and_Field.divide_le_eq_1_neg",
"Ring_and_Field.divide_le_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.divide_le_eq_1_pos",
"Ring_and_Field.divide_le_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.divide_less_0_1_iff",
"Ring_and_Field.divide_less_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.divide_less_eq_1_pos",
"Ring_and_Field.divide_less_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.eq_divide_eq_1",
"Ring_and_Field.eq_divide_eq_1", (*duplicate by symmetry*)
"Ring_and_Field.field_mult_cancel_left",
"Ring_and_Field.field_mult_cancel_right",
"Ring_and_Field.inverse_le_iff_le_neg",
"Ring_and_Field.inverse_le_iff_le",
"Ring_and_Field.inverse_less_iff_less_neg",
"Ring_and_Field.inverse_less_iff_less",
"Ring_and_Field.le_divide_eq_1_neg",
"Ring_and_Field.le_divide_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.le_divide_eq_1_pos",
"Ring_and_Field.le_divide_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.less_divide_eq_1_neg",
"Ring_and_Field.less_divide_eq_1_neg", (*obscure and prolific*)
"Ring_and_Field.less_divide_eq_1_pos",
"Ring_and_Field.less_divide_eq_1_pos", (*obscure and prolific*)
"Ring_and_Field.one_eq_divide_iff", (*duplicate by symmetry*)
"Set.Diff_eq_empty_iff", (*redundant with paramodulation*)
"Set.Diff_insert0",
"Set.disjoint_insert_1",
"Set.disjoint_insert_2",
"Set.empty_Union_conv", (*redundant with paramodulation*)
"Set.insert_disjoint_1",
"Set.insert_disjoint_2",
"Set.Int_UNIV", (*redundant with paramodulation*)
"Set.Inter_iff", (*We already have InterI, InterE*)
"Set.Inter_UNIV_conv_1",
"Set.Inter_UNIV_conv_2",
"Set.psubsetE", (*too prolific and obscure*)
"Set.psubsetI",
"Set.singleton_insert_inj_eq'",
"Set.singleton_insert_inj_eq",
"Set.singletonD", (*these two duplicate some "insert" lemmas*)
"Set.singletonI",
"Set.Un_empty", (*redundant with paramodulation*)
"Set.Union_empty_conv", (*redundant with paramodulation*)
"Set.Union_iff", (*We already have UnionI, UnionE*)
"SetInterval.atLeastAtMost_iff", (*obscure and prolific*)
"SetInterval.atLeastLessThan_iff", (*obscure and prolific*)
"SetInterval.greaterThanAtMost_iff", (*obscure and prolific*)
"SetInterval.greaterThanLessThan_iff", (*obscure and prolific*)
"SetInterval.ivl_subset", (*excessive case analysis*)
"Sum_Type.InlI",
"Sum_Type.InrI"];
(*These might be prolific but are probably OK, and min and max are basic.
"Orderings.max_less_iff_conj",
"Orderings.min_less_iff_conj",
"Orderings.min_max.below_inf.below_inf_conv",
"Orderings.min_max.below_sup.above_sup_conv",
Very prolific and somewhat obscure:
"Set.InterD",
"Set.UnionI",
*)
val theory_blacklist = ref
["Datatype_Universe.", (*unnecessary in virtually all proofs*)
"Equiv_Relations."]
val relevant = ref 0; (*Relevance filtering is off by default*)
(*The "name" of a theorem is its statement, if nothing else is available.*)
val plain_string_of_thm =
setmp show_question_marks false
(setmp print_mode []
(Pretty.setmp_margin 999 string_of_thm));
(*Returns the first substring enclosed in quotation marks, typically omitting
the [.] of meta-level assumptions.*)
val firstquoted = hd o (String.tokens (fn c => c = #"\""))
fun fake_thm_name th =
Context.theory_name (theory_of_thm th) ^ "." ^ firstquoted (plain_string_of_thm th);
fun put_name_pair ("",th) = (fake_thm_name th, th)
| put_name_pair (a,th) = (a,th);
(* outputs a list of (thm,clause) pairs *)
fun multi x 0 xlist = xlist
|multi x n xlist = multi x (n-1) (x::xlist);
fun clause_numbering ((clause, theorem), num_of_cls) =
let val numbers = 0 upto (num_of_cls - 1)
in
multi (clause, theorem) num_of_cls []
end;
(*Hashing to detect duplicate and variant clauses, e.g. from the [iff] attribute*)
exception HASH_CLAUSE and HASH_STRING;
(*Catches (for deletion) theorems automatically generated from other theorems*)
fun insert_suffixed_names ht x =
(Polyhash.insert ht (x^"_iff1", ());
Polyhash.insert ht (x^"_iff2", ());
Polyhash.insert ht (x^"_dest", ()));
fun banned_theory s = exists (fn thy => String.isPrefix thy s) (!theory_blacklist);
fun make_banned_test xs =
let val ht = Polyhash.mkTable (Polyhash.hash_string, op =)
(6000, HASH_STRING)
fun banned s = isSome (Polyhash.peek ht s) orelse banned_theory s
in app (fn x => Polyhash.insert ht (x,())) (!blacklist);
app (insert_suffixed_names ht) (!blacklist @ xs);
banned
end;
(*Create a hash table for clauses, of the given size*)
fun mk_clause_table n =
Polyhash.mkTable (ResClause.hash_clause, ResClause.clause_eq)
(n, HASH_CLAUSE);
(*Use a hash table to eliminate duplicates from xs*)
fun make_unique ht xs =
(app (ignore o Polyhash.peekInsert ht) xs; Polyhash.listItems ht);
(*Write out the claset and simpset rules of the supplied theory.
FIXME: argument "goal" is a hack to allow relevance filtering.
To reduce the number of clauses produced, set ResClasimp.relevant:=1*)
fun get_clasimp_lemmas ctxt goal =
let val claset_thms =
map put_name_pair
(ReduceAxiomsN.relevant_filter (!relevant) goal
(ResAxioms.claset_rules_of_ctxt ctxt))
val simpset_thms =
if !use_simpset then
map put_name_pair
(ReduceAxiomsN.relevant_filter (!relevant) goal
(ResAxioms.simpset_rules_of_ctxt ctxt))
else []
val banned = make_banned_test (map #1 (claset_thms@simpset_thms))
fun ok (a,_) = not (banned a)
val claset_cls_thms = ResAxioms.clausify_rules_pairs (filter ok claset_thms)
val simpset_cls_thms = ResAxioms.clausify_rules_pairs (filter ok simpset_thms)
val cls_thms_list = make_unique (mk_clause_table 2200)
(List.concat (simpset_cls_thms@claset_cls_thms))
(* Identify the set of clauses to be written out *)
val clauses = map #1(cls_thms_list);
val cls_nums = map ResClause.num_of_clauses clauses;
(*Note: in every case, cls_num = 1. I think that only conjecture clauses
can have any other value.*)
val whole_list = List.concat
(map clause_numbering (ListPair.zip (cls_thms_list, cls_nums)));
in (* create array of put clausename, number pairs into it *)
(Array.fromList whole_list, clauses)
end;
end;