src/Provers/Arith/extract_common_term.ML
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(*  Title:      Provers/Arith/extract_common_term.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   2000  University of Cambridge
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Extract common terms in balanced expressions:
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     i + u + j ~~ i' + u + j'  ==  u + (i + j) ~~ u + (i' + j')
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     i + u     ~~ u            ==  u + i       ~~ u + 0
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where ~~ is an appropriate balancing operation (e.g. =, <=, <, -) and 0 is a
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suitable identity for +.
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This massaged formula is then simplified in a user-specified way.
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*)
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signature EXTRACT_COMMON_TERM_DATA =
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sig
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  (*abstract syntax*)
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  val mk_sum: typ -> term list -> term
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  val dest_sum: term -> term list
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  val mk_bal: term * term -> term
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  val dest_bal: term -> term * term
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  val find_first: term -> term list -> term list
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  (*proof tools*)
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  val mk_eq: term * term -> term
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  val norm_tac: simpset -> tactic                (*proves the result*)
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  val simplify_meta_eq: simpset -> thm -> thm -> thm (*simplifies the result*)
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  val simp_conv: simpset -> term -> thm option  (*proves simp thm*)
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end;
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functor ExtractCommonTermFun(Data: EXTRACT_COMMON_TERM_DATA):
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  sig
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  val proc: simpset -> term -> thm option
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  end
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=
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struct
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(*a left-to-right scan of terms1, seeking a term u that is also in terms2*)
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fun find_common (terms1,terms2) =
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  let val tab2 = fold (Termtab.update o rpair ()) terms2 Termtab.empty
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      fun seek [] = raise TERM("find_common", [])
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        | seek (u::terms) =
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              if Termtab.defined tab2 u then u
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              else seek terms
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  in seek terms1 end;
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(*the simplification procedure*)
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fun proc ss t =
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  let
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    val ctxt = Simplifier.the_context ss;
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    val prems = Simplifier.prems_of ss;
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    val ([t'], ctxt') = Variable.import_terms true [t] ctxt
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    val export = singleton (Variable.export ctxt' ctxt)
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    val (t1,t2) = Data.dest_bal t'
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    val terms1 = Data.dest_sum t1
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    and terms2 = Data.dest_sum t2
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    val u = find_common (terms1,terms2)
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    val simp_th =
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          case Data.simp_conv ss u of NONE => raise TERM("no simp", [])
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          | SOME th => th
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    val terms1' = Data.find_first u terms1
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    and terms2' = Data.find_first u terms2
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    and T = Term.fastype_of u
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    val t'' = Data.mk_bal (Data.mk_sum T (u::terms1'), Data.mk_sum T (u::terms2'))
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    val reshape =
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      Goal.prove ctxt [] [] (Data.mk_eq (t', t'')) (K (Data.norm_tac ss))
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  in
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    SOME (export (Data.simplify_meta_eq ss simp_th reshape))
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  end
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  (* FIXME avoid handling of generic exceptions *)
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  handle TERM _ => NONE
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       | TYPE _ => NONE;   (*Typically (if thy doesn't include Numeral)
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                             Undeclared type constructor "Numeral.bin"*)
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end;