Books about Type

flag flag flag flag flag flag Computation and Reasoning - This book is about type theory. Although it is very technical it is aimed at computer scientists, so it has more discussion than a book aimed at pure mathematicians. It is especially useful for the coverage of dependant types.

Type Theory and Category Theory

flag flag flag flag flag flag Categorical Logic and Type Theory - This book is about logic, type theory and category theory. It assumes the reader is familiar with category theory concepts such as adjunctions, limits and CCCs.
flag flag flag flag flag flag Categories for Types - The book has some introductory material including a chapter about category theory (although it would be a steep learning curve with no other sources). Then the book shows how to represent category theory in type theory.

 

 

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Youtube video

Advanced Topics in Programming Languages Series: Parametric Polymorphism and the Girard-Reynolds Isomorphism. This talk is based on a series of papers by Philip Wadler, a principal designer of the Haskell programming language. Featured are a number of double-barreled names in computer science:

  • Hindley-Milner (Strong typing without having to type the types)
  • Wadler-Blott (Making ad-hoc polymorphism less ad-hoc with parametricity)
  • Curry-Howard (Isomorphism between types and theorems, terms and proofs)
  • Girard-Reynolds (Isomorphism between types and terms in the presence of parametricity)

For Djinn code see here.

Parametricity
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