Strictness is studied in the context of algebraic languages
where functions exhibit ``computational'' behaviour such as
partiality, failure or side effects. We propose a general approach
to modelling strictness in function application based on Moggi's
computational types. In this context, the notion of strictness can
be applied to any kind of behaviour, of which partiality is just a
special case. For instance, a function f is strict with respect to
failure if f(FAIL) = FAIL.  The power of the approach that we present
derives from the possibility of breaking the notion of computation
involved in the evaluation of terms down to elementary components and
considering strictness with respect to each component separately.
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We consider semantic structure for relating computational types, which
we call ``computational legs,'' of which composition of monads is a
special case. This allows arbitrary nonstrict functions to be treated
with the same degree of abstraction that monads introduce in the
treatment of strict program composition. Techniques for modularisation
can then be applied.