(* Title: HOL/Reconstruction.thy
ID: $Id$
Author: Lawrence C Paulson and Claire Quigley
Copyright 2004 University of Cambridge
*)
(*Attributes for reconstructing external resolution proofs*)
structure Reconstruction =
struct
(**************************************************************)
(* extra functions necessary for factoring and paramodulation *)
(**************************************************************)
fun mksubstlist [] sublist = sublist
| mksubstlist ((a, (_, b)) :: rest) sublist =
let val vartype = type_of b
val avar = Var(a,vartype)
val newlist = ((avar,b)::sublist)
in mksubstlist rest newlist end;
(**** attributes ****)
(** Binary resolution **)
fun binary_rule ((cl1, lit1), (cl2 , lit2)) =
select_literal (lit1 + 1) cl1
RSN ((lit2 + 1), cl2);
val binary = Attrib.syntax
(Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
>> (fn ((i, B), j) => Thm.rule_attribute (fn _ => fn A => binary_rule ((A, i), (B, j)))));
fun inst_single sign t1 t2 cl =
let val ct1 = cterm_of sign t1 and ct2 = cterm_of sign t2
in hd (Seq.list_of(distinct_subgoals_tac
(cterm_instantiate [(ct1,ct2)] cl)))
end;
fun inst_subst sign substs cl =
if (is_Var (fst(hd(substs))))
then inst_single sign (fst (hd substs)) (snd (hd substs)) cl
else if (is_Var (snd(hd(substs))))
then inst_single sign (snd (hd substs)) (fst (hd substs)) cl
else raise THM ("inst_subst", 0, [cl]);
(** Factoring **)
fun factor_rule (cl, lit1, lit2) =
let
val prems = prems_of cl
val fac1 = List.nth (prems,lit1)
val fac2 = List.nth (prems,lit2)
val sign = sign_of_thm cl
val unif_env = Unify.unifiers (sign, Envir.empty 0, [(fac1, fac2)])
val newenv = ReconTranslateProof.getnewenv unif_env
val envlist = Envir.alist_of newenv
in
inst_subst sign (mksubstlist envlist []) cl
end;
val factor = Attrib.syntax (Scan.lift (Args.nat -- Args.nat)
>> (fn (i, j) => Thm.rule_attribute (fn _ => fn A => factor_rule (A, i, j))));
(** Paramodulation **)
(*subst with premises exchanged: that way, side literals of the equality will appear
as the second to last premises of the result.*)
val rev_subst = rotate_prems 1 subst;
fun paramod_rule ((cl1, lit1), (cl2, lit2)) =
let val eq_lit_th = select_literal (lit1+1) cl1
val mod_lit_th = select_literal (lit2+1) cl2
val eqsubst = eq_lit_th RSN (2,rev_subst)
val newth = Seq.hd (biresolution false [(false, mod_lit_th)] 1 eqsubst)
val newth' = Seq.hd (flexflex_rule newth)
in Meson.negated_asm_of_head newth' end;
val paramod = Attrib.syntax (Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
>> (fn ((i, B), j) => Thm.rule_attribute (fn _ => fn A => paramod_rule ((A, i), (B, j)))));
(** Demodulation: rewriting of a single literal (Non-Unit Rewriting, SPASS) **)
fun demod_rule ((cl1, lit1), (cl2 , lit2)) =
let val eq_lit_th = select_literal (lit1+1) cl1
val mod_lit_th = select_literal (lit2+1) cl2
val (fmod_th,thaw) = Drule.freeze_thaw_robust mod_lit_th
val eqsubst = eq_lit_th RSN (2,rev_subst)
val newth = Seq.hd(biresolution false [(false, fmod_th)] 1 eqsubst)
val offset = #maxidx(rep_thm newth) + 1
(*ensures "renaming apart" even when Vars are frozen*)
in Meson.negated_asm_of_head (thaw offset newth) end;
val demod = Attrib.syntax (Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
>> (fn ((i, B), j) => Thm.rule_attribute (fn _ => fn A => demod_rule ((A, i), (B, j)))));
(** Conversion of a theorem into clauses **)
(*For efficiency, we rely upon memo-izing in ResAxioms.*)
fun clausify_rule (th,i) = List.nth (ResAxioms.meta_cnf_axiom th, i)
val clausify = Attrib.syntax (Scan.lift Args.nat
>> (fn i => Thm.rule_attribute (fn _ => fn th => clausify_rule (th, i))));
(** theory setup **)
val setup =
Attrib.add_attributes
[("binary", binary, "binary resolution"),
("paramod", paramod, "paramodulation"),
("demod", demod, "demodulation"),
("factor", factor, "factoring"),
("clausify", clausify, "conversion to clauses")];
end