(* Title: Provers/Arith/extract_common_term.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 2000 University of Cambridge
Extract common terms in balanced expressions:
i + u + j ~~ i' + u + j' == u + (i + j) ~~ u + (i' + j')
i + u ~~ u == u + i ~~ u + 0
where ~~ is an appropriate balancing operation (e.g. =, <=, <, -) and 0 is a
suitable identity for +.
This massaged formula is then simplified in a user-specified way.
*)
signature EXTRACT_COMMON_TERM_DATA =
sig
(*abstract syntax*)
val mk_sum: typ -> term list -> term
val dest_sum: term -> term list
val mk_bal: term * term -> term
val dest_bal: term -> term * term
val find_first: term -> term list -> term list
(*proof tools*)
val prove_conv: tactic list -> Sign.sg ->
thm list -> string list -> term * term -> thm option
val norm_tac: tactic (*proves the result*)
val simplify_meta_eq: thm -> thm (*simplifies the result*)
end;
functor ExtractCommonTermFun(Data: EXTRACT_COMMON_TERM_DATA):
sig
val proc: Sign.sg -> simpset -> term -> thm option
end
=
struct
(*Store the term t in the table*)
fun update_by_coeff (tab, t) = Termtab.update ((t, ()), tab);
(*a left-to-right scan of terms1, seeking a term u that is also in terms2*)
fun find_common (terms1,terms2) =
let val tab2 = foldl update_by_coeff (Termtab.empty, terms2)
fun seek [] = raise TERM("find_common", [])
| seek (u::terms) =
if is_some (Termtab.lookup (tab2, u)) then u
else seek terms
in seek terms1 end;
(*the simplification procedure*)
fun proc sg ss t =
let
val hyps = prems_of_ss ss;
(*first freeze any Vars in the term to prevent flex-flex problems*)
val (t', xs) = Term.adhoc_freeze_vars t;
val (t1,t2) = Data.dest_bal t'
val terms1 = Data.dest_sum t1
and terms2 = Data.dest_sum t2
val u = find_common (terms1,terms2)
val terms1' = Data.find_first u terms1
and terms2' = Data.find_first u terms2
and T = Term.fastype_of u
val reshape =
Data.prove_conv [Data.norm_tac] sg hyps xs
(t',
Data.mk_bal (Data.mk_sum T (u::terms1'),
Data.mk_sum T (u::terms2')))
in
apsome Data.simplify_meta_eq reshape
end
handle TERM _ => None
| TYPE _ => None; (*Typically (if thy doesn't include Numeral)
Undeclared type constructor "Numeral.bin"*)
end;