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