By CodeJustin
via reperiendi.wordpress.com
Published: Jul 07 2009 / 05:41
In many languages you have type constructors; given a type A and a type constructor Lift, you get a new type Lift>. A functor is a type constructor together with a function
lift: (A -> B) -> (Lift> -> Lift>)
that preserves composition and identities. If h is the composition of two other functions g and f
h (a) = g (f (a)),
then lift (h) is the composition of lift (g) and lift (f)
lift (h) (la) = lift (g) (lift (f) (la)).
Similarly, if h is the identity function on variables of type A
h (a: A) = a,
then lift (h) will be the identity on variables of type Lift>
lift (h) (la : Lift>) = la.
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