Verifikation reaktiver Systeme - Universität Kaiserslautern

252
A.3 fractionLib
structure fractionLib :> fractionLib =
struct
open HolKernel boolLib Parse bossLib;
(* interactive mode
app load ["integerTheory","intLib","ringLib",
"integerRingTheory","integerRingLib"];
*)
open
pairTheory arithmeticTheory ringTheory ringLib
integerTheory intLib integerRingTheory integerRingLib
fractionTheory;
val ARW_TAC = RW_TAC int_ss;
val frac_bij = DB.fetch "fraction" "frac_tybij";
(*--------------------------------------------------------------------------
* FRAC_EQ_TAC : tactic
*
* A ?- abs_frac(a1,b1) = abs_frac(a2,b2)
* ========================================= FRAC_EQ_TAC
* A ?- a1=a2 | A ?- b1=b2
*
* Two fractions are equal, if the nominator and the denominator are
* equal.
*--------------------------------------------------------------------------*)
val FRAC_EQ_TAC:tactic = fn (asl,w) =>
let
val (lhs,rhs) = dest_eq w
in
let
val (lhc, lha) = dest_comb lhs;
val (rhc, rha ) = dest_comb rhs;
in
let
val [a1,b1] = strip_pair lha;
val [a2,b2] = strip_pair rha;
in
let
val sg1 = mk_eq(a1,a2);
val sg2 = mk_eq(b1,b2);
in
(
[(asl,sg1), (asl,sg2)],
fn [thm1,thm2] => MP