[ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]
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