src/HOL/Tools/reconstruction.ML
author wenzelm
Thu Aug 03 17:30:36 2006 +0200 (2006-08-03)
changeset 20328 5b240a4216b0
parent 20258 4fe3c0911907
child 20762 a7a5157c5e75
permissions -rw-r--r--
RuleInsts.bires_inst_tac;
     1 (*  Title:      HOL/Reconstruction.thy
     2     ID: $Id$
     3     Author:     Lawrence C Paulson and Claire Quigley
     4     Copyright   2004  University of Cambridge
     5 *)
     6 
     7 (*Attributes for reconstructing external resolution proofs*)
     8 
     9 structure Reconstruction =
    10 struct
    11 
    12 (**** attributes ****)
    13 
    14 (** Binary resolution **)
    15 
    16 fun binary_rule ((cl1, lit1), (cl2 , lit2)) =
    17      select_literal (lit1 + 1) cl1
    18      RSN ((lit2 + 1), cl2);
    19 
    20 val binary = Attrib.syntax
    21   (Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
    22     >> (fn ((i, B), j) => Thm.rule_attribute (fn _ => fn A => binary_rule ((A, i), (B, j)))));
    23 
    24 
    25 (** Factoring **)
    26 
    27 (*NB this code did not work at all before 29/6/2006. Even now its behaviour may
    28   not be as expected. It unifies the designated literals
    29   and then deletes ALL duplicates of literals (not just those designated)*)
    30 
    31 fun mksubstlist [] sublist = sublist
    32   | mksubstlist ((a, (T, b)) :: rest) sublist =
    33       mksubstlist rest ((Var(a,T), b)::sublist);
    34 
    35 fun reorient (x,y) = 
    36       if is_Var x then (x,y)
    37       else if is_Var y then (y,x)
    38       else error "Reconstruction.reorient: neither term is a Var";
    39 
    40 fun inst_subst sign subst cl =
    41   let val subst' = map (pairself (cterm_of sign) o reorient) subst
    42   in 
    43       Seq.hd(distinct_subgoals_tac (cterm_instantiate subst' cl))
    44   end;
    45 
    46 fun factor_rule (cl, lit1, lit2) =
    47     let
    48        val prems = prems_of cl
    49        val fac1 = List.nth (prems,lit1)
    50        val fac2 = List.nth (prems,lit2)
    51        val sign = sign_of_thm cl
    52        val unif_env = Unify.unifiers (sign, Envir.empty 0, [(fac1, fac2)])
    53        val newenv = ReconTranslateProof.getnewenv unif_env
    54        val envlist = Envir.alist_of newenv
    55      in
    56        inst_subst sign (mksubstlist envlist []) cl
    57     end;
    58 
    59 val factor = Attrib.syntax (Scan.lift (Args.nat -- Args.nat)
    60   >> (fn (i, j) => Thm.rule_attribute (fn _ => fn A => factor_rule (A, i, j))));
    61 
    62 
    63 (** Paramodulation **)
    64 
    65 (*subst with premises exchanged: that way, side literals of the equality will appear
    66   as the second to last premises of the result.*)
    67 val rev_subst = rotate_prems 1 subst;
    68 
    69 fun paramod_rule ((cl1, lit1), (cl2, lit2)) =
    70     let  val eq_lit_th = select_literal (lit1+1) cl1
    71          val mod_lit_th = select_literal (lit2+1) cl2
    72          val eqsubst = eq_lit_th RSN (2,rev_subst)
    73          val newth = Seq.hd (biresolution false [(false, mod_lit_th)] 1 eqsubst)
    74          val newth' = Seq.hd (flexflex_rule newth)
    75     in Meson.negated_asm_of_head newth' end;
    76 
    77 
    78 val paramod = Attrib.syntax (Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
    79   >> (fn ((i, B), j) => Thm.rule_attribute (fn _ => fn A => paramod_rule ((A, i), (B, j)))));
    80 
    81 
    82 (** Demodulation: rewriting of a single literal (Non-Unit Rewriting, SPASS) **)
    83 
    84 fun demod_rule ctxt ((cl1, lit1), (cl2 , lit2)) =
    85     let  val eq_lit_th = select_literal (lit1+1) cl1
    86          val mod_lit_th = select_literal (lit2+1) cl2
    87          val ((_, [fmod_th]), ctxt') = Variable.import true [mod_lit_th] ctxt
    88          val eqsubst = eq_lit_th RSN (2,rev_subst)
    89          val newth =
    90            Seq.hd (biresolution false [(false, fmod_th)] 1 eqsubst)
    91            |> singleton (Variable.export ctxt' ctxt)
    92     in Meson.negated_asm_of_head newth end;
    93 
    94 val demod = Attrib.syntax (Scan.lift Args.nat -- Attrib.thm -- Scan.lift Args.nat
    95   >> (fn ((i, B), j) => Thm.rule_attribute (fn context => fn A =>
    96       demod_rule (Context.proof_of context) ((A, i), (B, j)))));
    97 
    98 
    99 (** Conversion of a theorem into clauses **)
   100 
   101 (*For efficiency, we rely upon memo-izing in ResAxioms.*)
   102 fun clausify_rule (th,i) = List.nth (ResAxioms.meta_cnf_axiom th, i)
   103 
   104 val clausify = Attrib.syntax (Scan.lift Args.nat
   105   >> (fn i => Thm.rule_attribute (fn _ => fn th => clausify_rule (th, i))));
   106 
   107 
   108 (** theory setup **)
   109 
   110 val setup =
   111   Attrib.add_attributes
   112     [("binary", binary, "binary resolution"),
   113      ("paramod", paramod, "paramodulation"),
   114      ("demod", demod, "demodulation"),
   115      ("factor", factor, "factoring"),
   116      ("clausify", clausify, "conversion to clauses")];
   117 
   118 end