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Tag Archives: Functional programming
Python in Functional Programming Style
Functional Programming has the following key styles:
1) Lambda function:
2) Map, Filter, Reduce
Knowing Monads Through The Category Theory
https://dev.to/juaneto/knowing-monads-through-the-category-theory-1mea
While Mathematicians like to talk non-sensical abstract idea, Informaticians want to know how to apply the idea concretely:
Mathematical Parlance:
Monad = Monoid +Endofunctor
Monoid = Identity + Associative
Endo-functor = functor between 2 same categories
IT Parlance:
Monad is a ‘function’ to wrap the ‘side effects’ (exception errors, I/O,… ) so that function composition in ‘pipeline‘ chained operation sequence is still possible in pure FP (Functional Programming, which forbids side-effects).
Some common Monads: ‘Maybe’, ‘List’, ‘Reader’…
This allows monads to simplify a wide range of problems, like handling potential undefined values (with the Maybe monad), or keeping values within a flexible, well-formed list (using the List monad). With a monad, a programmer can turn a complicated sequence of functions into a succinct pipeline that abstracts away additional data management, control flow, or side-effects.[2][3]
Exploring Monads in Scala Collections
The Evolution of Software
Monads – FP’s answer to Immutability
Introduction:
- The curse of Immutability in Functional Programming – no “Looping” (recursion ok), no Date, no Random, …no I/O …
- Monad is the Savior of “No Side Effect: IO Monads
Promise of Monads (A)
Promise of Monads (B)
Alejandro Serrano: Category Theory Through Functional Programming
(Part 1/3) – λC 2017
What is Category ?
Objects
Morphism (Arrows )
Rule1: Associative
Rule 2: Identity
A <– C –> B
Product of Categories : A x B
Unique
Sum of Categories: A + B
Unique
(Either a b)
Co-Product
Reverse all arrows.
Unique
Functor F: C-> D
Mapping of all objects (A, B) in categories C,D
Mapping of arrows f
f : A -> B
Ff : FA -> FB (preservation)
F Id = Id
F (f。g) = Ff。Fg
Example:
Constant C -> F
FC = k
Ff = Id
Arrow Functor F: C -> D
For any object A in C,
F A = D -> A
(Functional Type is also Type)
Functors compose !
Category of categories:
Objects: categories
Arrows : Functors
Haskell Category (Hask) is always Endo-Functor, ie Category Hask to itself.
Mapping of arrows.
Mapping of Objects = predefined
(Part 2/3) – λC 2017
(part 3/3) – λC 2017
