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 bartoszmilewski.com
Functors | Bartosz Milewski's Programming Cafe
| | serokell.io
Algebraic Data Types in Haskell
2.7 parsecs away

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| | In this article, we introduce you to the concept of algebraic data types and show how you can build your own data types in Haskell.
| | kuruczgy.com
Introduction to dependent types and the Curry-Howard isomorphism
2.2 parsecs away

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| | [AI summary] The article explores the intersection of functional programming and logic through the lens of dependent types. It begins with foundational concepts like type constructors and inductive types, then delves into the Curry-Howard isomorphism, which links programs to mathematical proofs. The discussion covers how types represent propositions, functions as implications, and inductive types as proof strategies. Examples include defining logical relations like less than or equal to and equality, and demonstrating how to prove properties like universal quantification and mathematical identities. The article concludes with an overview of resources for further study in proof assistants like Coq and Idris, emphasizing the practical applications of dependent...
| | www.jeremykun.com
Functoriality | Math Programming
2.6 parsecs away

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| | Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves?
| | blog.polybdenum.com
What are GADTs and why do they make type inference sad? | Considerations on Codecrafting
9.4 parsecs away

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| Back in 2020, I created Cubiml, a simple ML-like language that demonstrated how to extend the usual Hindley-Milner type system with subtyping while still having decidable full type inference. One question I got was whether it would be possible to support generalized algebraic data types (GADTs) in Cubiml. I had heard that GADTs break type inference and didn't see the point, so I didn't think much of it at the time.