III. Semantic algebras:
Tr ...truth values
Id ...identifiers
Nat ...natural numbers
Store = Id -> Nat
update: Id -> Nat -> Store
-> Store
update i v s = [i ->v]s
Answer = P(Tr x
Store)
no-answer: Answer
no-answer = {}
join: Answer -> Answer -> Answer
a_1 join a_2 = a_1 union a_2
then: (Store -> Answer) ->
(Store -> Answer) -> (Store
-> Answer)
(f_1 then f_2)(s) = (g+
o f_1)(s)
where g(t, s) = t -> f_2(s) [] (t, s)