[TYPES] Book on Category Theory

[Sean Leather]

Hi Aaron,

On Mon, Oct 23, 2017 at 4:56 PM, Aaron Gray wrote:
>
> Thanks everyone, but as far as I can tell none of these books give me any
> real stuff on covariance, contravariance, anamophisms and catamophisms.


Perhaps “Category Theory for Program Construction by Calculation” (1995) by
Lambert Meertens?

https://www.kestrel.edu/home/people/meertens/diverse/ct4pc.pdf

>From the Introduction:

Category theory is the theory of structure-preserving transformations. This
theory provides
us with a language for describing complex problems in an elegant way, and
tools
to give elegant, and above all simple, proofs. The language of category
theory allows
us to consider the essence of some problem, without the burden of—often
numerous and
complicated—non-essential aspects.

The constructive and universal character of category theory is an aid in
finding these
proofs. In these lecture notes we emphasise a calculational proof style, to
which category
theory lends itself well. Examples are drawn from functional
programming—and to a
lesser extent from lattice theory—and in fact the applicability to
calculational program
construction has influenced the choice of topics covered.

Regards,
Sean