Contents

• Introduction
• Definition
• History
• Taxonomy
• Features
• Functional concepts
• When to use it?
• When not to use it?
• Resources

Introduction

• Disclaimer
• Inventory
• Anecdote
• About
  • GFDL
  • on github
  • libre tools

Definition

• Functions are central construct
• Functions are regular values
  • passed around
  • returned
  • composed
  • (partially) applied
• No variables but binding of values
  • all variables are immutable

Definition of a Function

• Functions are mathematical

Example

Non-example

Definition of a Function

• Same input -> same output
• No side effects, pure

History

• Lambda calculus
  • Alonzo Church 1930s
  • untyped lambda calculus
  • simply typed lambda calculus

Taxonomy

• Group functional languages across several axis:
  • Statically typed / Dynamically typed
  • Strong typing / Weak typing
  • Lazy / Eager
  • Single paradigm / Multi paradigm

Taxonomy

Taxonomy

Features

• Read Eval Print Loop (REPL)
• Type inference (var on steroids)
• Pattern matching
• Algabraic data types
• Function composition
• Anonymous functions (lambda expressions)
  • Closure

Features

• Sequence Epressions (List Comprehensions)
• Partial function application (currying)
• Higher order functions (map, fold, filter)

Funtional concepts

• Tail Recursion
• Continuation passing style
• Memoization

Computation Expressions (Monads)

• Concept from mathematics, Category theory
• A triple:
  • type constructor
  • bind aka chain operation
  • return aka inject operation

Category

• a collection of elements
• a collection of morphisms (think function)
• a notion of composition of these morphisms
• Example Grp, Set, Hask

Functor

• Transformation between categories
• Given category C, D, functor F
  • F : C -> D
  • f: A -> B then F(f) -> F(A) -> F(B)
• Examples: F: Grp -> Set, forgetful functor

Monad

• Functor: M: C -> C
• unit: X -> M(X)
• join: M(M(X)) -> M(X)

Monads

class Monad m where
    (>>=) :: m a -> (a -> m b) -> m b
    return :: a -> m a

instance Monad [] where
    return x = [x]
    xs >>= f = concat (map f xs)

When to use it?

• stateless
• data-transformations
• calculation /scientific computing
• parrallellism

When not to use it?

• a lotta state
• gui's

Resources

• F#
  • Expert F#
  • Wikibook
  • Developer Center
  • HubFs
• Haskell
  • Real World Haskell (book)
  • Real World Haskell online
  • Haskell.org
  • Haskell lectures Erik Meijer
  • Yet another Haskell tutorial

Labs

• Haskell
• F#
• fix code such that quickcheck/fscheck succeeds
• solutions on solution branch
• try euler project