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