src/Provers/Arith/assoc_fold.ML
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Mon, 15 Sep 2014 10:49:07 +0200
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(*  Title:      Provers/Arith/assoc_fold.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1999  University of Cambridge
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Simplification procedure for associative operators + and * on numeric
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types.  Performs constant folding when the literals are separated, as
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in 3+n+4.
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*)
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signature ASSOC_FOLD_DATA =
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sig
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  val assoc_ss: simpset
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  val eq_reflection: thm
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  val is_numeral: term -> bool
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end;
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signature ASSOC_FOLD =
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sig
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  val proc: Proof.context -> term -> thm option
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end;
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functor Assoc_Fold(Data: ASSOC_FOLD_DATA): ASSOC_FOLD =
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struct
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exception Assoc_fail;
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fun mk_sum plus []  = raise Assoc_fail
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  | mk_sum plus tms = foldr1 (fn (x, y) => plus $ x $ y) tms;
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(*Separate the literals from the other terms being combined*)
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fun sift_terms plus (t, (lits,others)) =
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  if Data.is_numeral t then (t::lits, others) (*new literal*) else
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  (case t of
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    (f as Const _) $ x $ y =>
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      if f = plus
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      then sift_terms plus (x, sift_terms plus (y, (lits,others)))
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      else (lits, t::others)    (*arbitrary summand*)
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  | _ => (lits, t::others));
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(*A simproc to combine all literals in a associative nest*)
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fun proc ctxt lhs =
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  let
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    val plus = (case lhs of f $ _ $ _ => f | _ => error "Assoc_fold: bad pattern")
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    val (lits, others) = sift_terms plus (lhs, ([],[]))
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    val _ = length lits < 2 andalso raise Assoc_fail (*we can't reduce the number of terms*)
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    val rhs = plus $ mk_sum plus lits $ mk_sum plus others
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    val th = Goal.prove ctxt [] [] (Logic.mk_equals (lhs, rhs))
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      (fn _ => rtac Data.eq_reflection 1 THEN simp_tac (put_simpset Data.assoc_ss ctxt) 1)
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  in SOME th end handle Assoc_fail => NONE;
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end;