Don’t fear the Monad

Brian Beckman: 

You can understand Monad without too much Category Theory.

Functional Programming = using functions to compose from small functions to very complex software (eg. Nuclear system, driverless car software…).

Advantages of Functional Programming:

  • Strong Types Safety: detect bugs at compile time. 
  • Data Protection thru Immutability: Share data safely in Concurrent / Parallel processing.
  • Software ‘Componentisation’  ie Modularity : Each function always returns the same result, ease of software reliability testing.

Each “small” function is a Monoid.
f : a -> a (from input of type ‘a‘ , returns type ‘a’)
g: a -> a

compose h from f & g : (strong TYPING !!)
h = f。g : a -> a

[Note] : Object in Category, usually called  Type in Haskell, eg. ‘a’ = Integer)

You already know a Monoid (or Category in general) : eg Clock

  1. Objects: 1 2 3 …12 (hours)
  2. Arrow (Morphism): rule “+”: 
    • 7 + 10 = 17 mod 12 = 5
  3. Law of Associativity:
    x + (y + z) = (x + y) + z
  4. Identity (or “Unit”):  (“12”):
    x + 12 = 12 + x = x

More general than Monoid is a “Monoidal” Category where: (instead of only single object ‘a’, now more “a b c…”)
f : a -> b
g: b -> c
h = f。g : a -> c

Function under composition Associative rule and with an Identity => Monoid

Monad (M): a  way to manage  the side-effects (I/O, exception , SQL Database, etc) within the Functional Programming way like monoidal categories: ie associative composition, identity.

Remark: For the last 60 years in Software, there have been 2 camps: 

  1. Bottom-Up Design: from hardware foundation,  build performance-based languages: Fortran, C, C++, C#, Java…
  2. Top-Down Design: from Mathematics foundation, build functional languages (Lambda-Calculus, Lisp, Algo, Smalltalk, Haskell…). 
  3. F# (Microsoft) is the middle-ground between 1 & 2.

Ref: What is a Monad ?

Monad = chaining operations with binding “>>=”

  • Possible use: allows to write mini-language, parser…

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