# Blog Posts & Events

# Monoidal and applicative functors

Published 1 III 2019In 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.

# Why Monadic IO?

Published 8 II 2019In 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.

# Categories with Monadic Effects and State Machines

Published 1 II 2019In 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.

# Kleisli categories and free monads

Published 20 XII 2018In this short post we explore the interplay of free monads and Kleisli categories.

# Typed transitions, finite state machines and free categories

Published 25 VIII 2018In 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.

# Monadicity

*from algebras to monads and back to algebras*Published 9 VIII 2018Introduction to the monadicity theory based on free-algebras Haskell package.

# Free algebras

*haddock documentation*Link to

`free-algebra`

package on hackage.# From free algebras to free monads

Published 30 VII 2018The 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*.# Composing cofree intepreters

Published: 30 VIII 2018My talk at Monadic Warsaw Haskell meetup on PureScript type system and composition of cofree comonads.

# Workshop on Category Theory

Published: 12 VI 2018Workshop I gave at Monadic Party. Unfortunatelly, first 30 minutes of the recording was lost...

# Routing with cofree comonad

Published: 14 X 2017My talk at PureScript Conf 2017 (a satelite event of Lambda Conf 2017) about routing frontend applications using coffree comonad and modelling DOM with

`Coffree []`

.# Peano Algebras in Haskell

Published: 2017Fun with Peano axioms in Haskell.