Isomorphism and Embedding

To me as a programmer, to write mathematical proofs that are mechanically checked by a computer feels empowering. To have these proofs as executable programs feels even more empowering. Therefore, our proofs have a computational aspect and vice-versa: our programs have a logical aspect. To be able to get an instant feedback while proving a theorem is amazing. With Agda, a dependently typed functional programming language, one can interactively write a proof by getting guidance from Agda as to what is left to prove. Furthermore, Agda checks the correctness of proofs by following a set of rules. Unlike with pen and paper proofs, proofs in Agda are much more rigorous because there is no room for hand-waving nor unwarranted claims for something to be trivial. An uninformed mathematician will likely find this comparison to Agda hard to believe.

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Gave a Talk: Terminating and Productive Functions

Courtesy of Tomislav Grospić

At the Lambda Zagreb Meetup this Monday I gave a talk on terminating and productive functions. It was an interesting discussion with questions that tied the topic and examples I had with natural numbers, linear types and communicating systems.

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Programming Lego Mindstorms EV3 in Haskell

Earlier this week I got a Lego Mindstorms EV3 robotics kit. I was aware there is a Haskell binding, but I didn’t know it is compatible only with the earlier NXT generation of the Mindstorms line, at least according to the Wikipedia page on EV3. I’m hoping to find out today if the NXT Haskell library can nevertheless be used with the EV3. If not, I’m likely to start writing a Haskell library for EV3.

Gave a Talk on Function Totality

As announced last week, yesterday I gave a talk on function totality at the Institute of Electrical and Electronics Engineers, Croatian Section. The talk was located at the University of Zagreb at the Faculty of Electrical Engineering and Computing. Slides used during the talk are freely available. The talk was in Croatian.

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Function Totality: Abstraction Tool in Programming

Edsger Dijkstra said the following of abstraction:

“The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.”

Abstraction is a cornerstone of programming a complex software system. Without it, a complex software system is a complicated software system. In this article I will explore an important tool in achieving abstraction in programming: function totality.

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Typed Functional Programming and Software Correctness

Software testing has been an important, if not prevalent way of checking software correctness. In this article I will tell how have my doctoral dissertation on testing and verification of imperative software as well as my work experience after the studies led me to typed functional programming, which consequently gave me a different perspective on automatic software testing. Furthermore, I’ll explain why functional programming and static type systems are important for software correctness.

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Less bad MTL

I stumbled upon a recording of a talk by George Wilson on the monad transformer library (MTL) in Haskell. He goes on to demonstrate how monad transformers can be made more composable by using constraints instead of directly putting a monad transformer in the return type of a function. What is presented there is definitely an improvement, however it is still unsatisfactory. In particular, in his examples there is no separation of describing and running a program, which means everything happens in the IO monad (the MonadIO constraint in function signatures in the examples). In other words, anything goes and such functions are again too powerful.

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