src/Provers/Arith/extract_common_term.ML
author wenzelm
Sun Mar 07 12:19:47 2010 +0100 (2010-03-07)
changeset 35625 9c818cab0dd0
parent 30649 57753e0ec1d4
child 35762 af3ff2ba4c54
permissions -rw-r--r--
modernized structure Object_Logic;
     1 (*  Title:      Provers/Arith/extract_common_term.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   2000  University of Cambridge
     5 
     6 Extract common terms in balanced expressions:
     7 
     8      i + u + j ~~ i' + u + j'  ==  u + (i + j) ~~ u + (i' + j')
     9      i + u     ~~ u            ==  u + i       ~~ u + 0
    10 
    11 where ~~ is an appropriate balancing operation (e.g. =, <=, <, -) and 0 is a
    12 suitable identity for +.
    13 
    14 This massaged formula is then simplified in a user-specified way.
    15 *)
    16 
    17 signature EXTRACT_COMMON_TERM_DATA =
    18 sig
    19   (*abstract syntax*)
    20   val mk_sum: typ -> term list -> term
    21   val dest_sum: term -> term list
    22   val mk_bal: term * term -> term
    23   val dest_bal: term -> term * term
    24   val find_first: term -> term list -> term list
    25   (*proof tools*)
    26   val prove_conv: tactic list -> Proof.context -> thm list -> term * term -> thm option
    27   val norm_tac: simpset -> tactic                (*proves the result*)
    28   val simplify_meta_eq: simpset -> thm -> thm -> thm (*simplifies the result*)
    29   val simp_conv: simpset -> term -> thm option  (*proves simp thm*)
    30 end;
    31 
    32 
    33 functor ExtractCommonTermFun(Data: EXTRACT_COMMON_TERM_DATA):
    34   sig
    35   val proc: simpset -> term -> thm option
    36   end
    37 =
    38 struct
    39 
    40 (*a left-to-right scan of terms1, seeking a term u that is also in terms2*)
    41 fun find_common (terms1,terms2) =
    42   let val tab2 = fold (Termtab.update o rpair ()) terms2 Termtab.empty
    43       fun seek [] = raise TERM("find_common", [])
    44         | seek (u::terms) =
    45               if Termtab.defined tab2 u then u
    46               else seek terms
    47   in seek terms1 end;
    48 
    49 (*the simplification procedure*)
    50 fun proc ss t =
    51   let
    52     val ctxt = Simplifier.the_context ss;
    53     val prems = prems_of_ss ss;
    54     val ([t'], ctxt') = Variable.import_terms true [t] ctxt
    55     val export = singleton (Variable.export ctxt' ctxt)
    56 
    57     val (t1,t2) = Data.dest_bal t'
    58     val terms1 = Data.dest_sum t1
    59     and terms2 = Data.dest_sum t2
    60 
    61     val u = find_common (terms1,terms2)
    62     val simp_th =
    63           case Data.simp_conv ss u of NONE => raise TERM("no simp", [])
    64           | SOME th => th
    65     val terms1' = Data.find_first u terms1
    66     and terms2' = Data.find_first u terms2
    67     and T = Term.fastype_of u
    68 
    69     val reshape =
    70       Data.prove_conv [Data.norm_tac ss] ctxt prems
    71         (t', Data.mk_bal (Data.mk_sum T (u::terms1'), Data.mk_sum T (u::terms2')))
    72   in
    73     Option.map (export o Data.simplify_meta_eq ss simp_th) reshape
    74   end
    75   (* FIXME avoid handling of generic exceptions *)
    76   handle TERM _ => NONE
    77        | TYPE _ => NONE;   (*Typically (if thy doesn't include Numeral)
    78                              Undeclared type constructor "Numeral.bin"*)
    79 
    80 end;