  Intersection type systems have been independently applied to different
evaluation strategies, such as call-by-name (CBN) and call-by-value (CBV).
These type systems have been then generalized to different subsuming paradigms
being able, in particular, to encode CBN and CBV in a unique unifying
framework. However, there are no intersection type systems that explicitly
enable CBN and CBV to cohabit together without making use of an encoding into a
common target framework. This work proposes an intersection type system for PCF
with a specific notion of evaluation, called PCFH. Evaluation in PCFH actually
has a hybrid nature, in the sense that CBN and CBV operational behaviors
cohabit together. Indeed, PCFH combines a CBV-like operational behavior for
function application with a CBN-like behavior for recursion. This hybrid nature
is reflected in the type system, which turns out to be sound and complete with
respect to PCFH: not only typability implies normalization, but also the
converse holds. Moreover, the type system is quantitative, in the sense that
the size of typing derivations provides upper bounds for the length of the
reduction sequences to normal form. This type system is then refined to a tight
one, offering exact information regarding the length of normalization
sequences. This is the first time that a sound and complete quantitative type
system has been designed for a hybrid computational model.
