%------------------------------------------------------------------------------ % Arithmetic Expressions % % All references are to HR and F Nielson "Semantics with Applications: % A Formal Introduction", John Wiley & Sons, 1992. (revised edition % available: http://www.daimi.au.dk/~hrn ) % % Author: David Lester, Manchester University, NIA, Université Perpignan % % Version 1.0 25/12/07 Initial Version %------------------------------------------------------------------------------
AExp[V:TYPE+]: THEORY
BEGIN
IMPORTING State[V]
AExp: DATATYPE BEGIN
N(n:int) : N?
V(x:V) : V?
Add(a1,a2:AExp) : Add?
Sub(a1,a2:AExp) : Sub?
Mul(a1,a2:AExp) : Mul? END AExp
s: VAR State
A(a:AExp) : RECURSIVE [State->int] = LAMBDA s: cases a of
N(n) : n,
V(x) : s(x),
Add(a1,a2) : A(a1)(s) + A(a2)(s),
Sub(a1,a2) : A(a1)(s) - A(a2)(s),
Mul(a1,a2) : A(a1)(s) * A(a2)(s) endcases MEASURE a by <<
END AExp
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