In this post we explore the equivalence between monoidal and applicative functors. Monoidal functors in Hask are functors which preserve the product (in some relaxed way), while applicative functors are ones that preserve application of lambdas. Monoidal functors have much more conincise laws, but at the end it turned out that the applicative formulation was very successful.

• code (literate haskell)

In this post we will discover that the imperative programming style leads to monoidal IO, while using recursive style, which is more natural for functional programming, leads to monadic IO.

• code (literate haskell)

In this post we will discover and describe categories which admits monadic effects, we will build a free object of this type and show how to use it to build a typed safe state machine that was presented by Edwin Brady.

• code (literate haskell)

In this short post we explore the interplay of free monads and Kleisli categories.

• code (literate haskell)

In this post I model finite state machines using free categories; you will also get a gentle introduction to Kleisli categories, folds on free categories and finally tagless style. Based on a simple example of an FSM by Oscar Wickström.

• code (literate haskell)

Introduction to the monadicity theory based on free-algebras Haskell package.

• code

Link to free-algebra package on hackage.

The post was re-published on iohk blog.

Introduction to Universal Algebra, a mathematical discipline that is hidden under many constructions in Haskell ecosystem. It is more concrete than Category Theory, and hence often easier to understand. It is also a very useful source of examples in Category Theory.

My talk at Monadic Warsaw Haskell meetup on PureScript type system and composition of cofree comonads.

• youtube
• slides
• gist

Workshop on Category Theory

Workshop I gave at Monadic Party. Unfortunatelly, first 30 minutes of the recording was lost...

• youtube: lectures 1 & 2
• youtube: lectures 3 & 4

My talk at PureScript Conf 2017 (a satelite event of Lambda Conf 2017) about routing frontend applications using coffree comonad and modelling DOM with Coffree [].

• youtube
• slides
• code

Fun with Peano axioms in Haskell.