Compositive Objectives
Two evaluation algebras can be combined, as explained in the Initial Reading section. Review?
Formally, this is a product operation on two evaluation algebras:
Definition (Product operation on evaluation algebras):
Let M and N be evaluation algebras over Σ. Their product M***N is an evaluation algebra over Σ and has the functions
f_M***N((m1,n1)...(mk,nk)) = (f_M(m1,...,mk), f_N(n1,...,nk)) for each f in Σ,
and the objective function
h_M***N([(m1,n1)...(mk,nk)]) = [(l,r) | l ∈ L,
r <- h_N([r' | (l',r') <- [(m1,n1)...(mk,nk)], l' = l],
where L = h_M([m1,...,mk]).
Above, ∈ denotes the membership and hence ignores duplicates. In contrast <- denotes list membership and respects duplicates. Implementing set membership may require some extra filtering effort, but when the objective function h_M, which computes L, does not produce duplicates anyway, it comes for free.
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