#category-theory

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Why Isomorphism Plays Significant Role in Self-Referential Types

Self-referential types and isomorphism illustrate that recursive data structures can be understood through structural equivalence in type theory.

The Modern Mathematics of Tiling a Bathroom Floor

Modern mathematics is an uncharted frontier where new discoveries are continuously made.
Math is more recent than traditionally understood, evolving with current explorations.
#functional-programming

Eugenio Moggi, monads, and functional programming

Moggi's work on monads introduced a foundational concept for functional programming.
Monads provide a way to structure and control computational effects in a pure and compositional way.

Monads!

Monads are fundamental in functional programming but can be intimidating; understanding the basic concepts is key for developers to embrace them.

Functional Containers Summary: Functor vs Applicative vs Monad

Functors represent mapping between categories, can be viewed as util class for mapping over values, prevalent in functional languages like Scala and Haskell.
Applicatives generalize Functors, operate not just on values but also on functions within a context, less powerful than Monads but more versatile.

Monads!

Monads are fundamental in functional programming but can be intimidating; understanding their basic concepts is key.

Eugenio Moggi, monads, and functional programming

Moggi's work on monads introduced a foundational concept for functional programming.
Monads provide a way to structure and control computational effects in a pure and compositional way.

Monads!

Monads are fundamental in functional programming but can be intimidating; understanding the basic concepts is key for developers to embrace them.

Functional Containers Summary: Functor vs Applicative vs Monad

Functors represent mapping between categories, can be viewed as util class for mapping over values, prevalent in functional languages like Scala and Haskell.
Applicatives generalize Functors, operate not just on values but also on functions within a context, less powerful than Monads but more versatile.

Monads!

Monads are fundamental in functional programming but can be intimidating; understanding their basic concepts is key.
morefunctional-programming

Functional Containers Summary: Functor vs Applicative vs Monad

Functor represents the mapping between two categories in category theory
Applicative is a concept that generalizes a Functor by allowing for operations on functions within a context
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