es:ES, A, T:Type, X:AbsInterface(A), base:T, f:(TAT), e:E.
local-state(f;base;X;e)
=
if e  X
ifthen f(if e  prior(X) then local-state(f;base;X;prior(X)(e)) else base fi ,X(e))
if e  prior(X) then local-state(f;base;X;prior(X)(e)) else base fi 
 T 

latex

Definitions

Unit, , p q, p  q, p  q, e = e', deq-member(eq;x;L), a = b, a = b, qeq(r;s), q_less(a;b), q_le(r;s), eq_atom$n(x;y), [d], a < b, x f y, a < b, null(as), x =a y, (i = j), i z j, i <z j, p =b q, P  Q, P & Q, case b of inl(x) => s(x) | inr(y) => t(y), x  dom(f), P  Q, strong-subtype(A;B), f(a), a:A fp B(a), x:A. B(x), tt, b, ff, prior-state(f;base;X;e), if b then t else f fi , e  X, local-state(f;base;X;e), X(e), prior(X), t.1, let x,y = A in B(x;y), left + right, b, x:A  B(x), , , <a, b>, A, E, x:AB(x), AbsInterface(A), Type, ES, s = t, t  T

Lemmas

assert of bnot, eqff to assert, iff transitivity, bool wf, not wf, assert wf, eqtt to assert, es-interface-local-state-prior, ifthenelse wf, es-interface-local-state wf, es-E wf, es-interface wf, event system wf, es-interface-val wf