File reconstruction.ML (Isabelle2005: October 2005)

# File reconstruction.ML

    (*  Title:      HOL/Reconstruction.thy
        ID: $Id: reconstruction.ML,v 1.14 2005/09/19 16:30:22 paulson Exp $
        Author:     Lawrence C Paulson and Claire Quigley
        Copyright   2004  University of Cambridge
    *)

    (*Attributes for reconstructing external resolution proofs*)

    structure Reconstruction =
    let open Attrib
    in
    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);

    fun binary_syntax ((i, B), j) (x, A) = (x, binary_rule ((A,i), (B,j)));

    fun gen_binary thm = syntax
          ((Scan.lift Args.nat -- thm -- Scan.lift Args.nat) >> binary_syntax);
    val binary_global = gen_binary global_thm;
    val binary_local = gen_binary local_thm;

    (*I have not done the MRR rule because it seems to be identifical to
    binary*)

    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;

    fun factor_syntax (i, j) (x, A) = (x, factor_rule (A,i,j));

    fun factor x = syntax ((Scan.lift (Args.nat -- Args.nat)) >> factor_syntax) x;

    (** 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;

    fun paramod_syntax ((i, B), j) (x, A) = (x, paramod_rule ((A,i), (B,j)));

    fun gen_paramod thm = syntax
          ((Scan.lift Args.nat -- thm -- Scan.lift Args.nat) >> paramod_syntax);
    val paramod_global = gen_paramod global_thm;
    val paramod_local = gen_paramod local_thm;

    (** 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;

    fun demod_syntax ((i, B), j) (x, A) = (x, demod_rule ((A,i), (B,j)));

    fun gen_demod thm = syntax
          ((Scan.lift Args.nat -- thm -- Scan.lift Args.nat) >> demod_syntax);
    val demod_global = gen_demod global_thm;
    val demod_local = gen_demod local_thm;

    (** 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)

    fun clausify_syntax i (x, th) = (x, clausify_rule (th,i));

    fun clausify x = syntax ((Scan.lift Args.nat) >> clausify_syntax) x;

    (** theory setup **)

    val setup =
      [Attrib.add_attributes
         [("binary", (binary_global, binary_local), "binary resolution"),
          ("paramod", (paramod_global, paramod_local), "paramodulation"),
          ("demod", (demod_global, demod_local), "demodulation"),
          ("factor", (factor, factor), "factoring"),
          ("clausify", (clausify, clausify), "conversion to clauses")]];

    end
    end