Functional Algebra by Example

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FUNCTIONAL ALGEBRA BY EXAMPLE

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Credit http://www.flickr.com/photos/slambo_42

Susan Potter @SusanPotter CodeMesh December 2013 1

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OBVIOUS FACE

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LESS OBVIOUS FACE

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MANUFACTURED FACE

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SQUINT FACE

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MAYBE FACE

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OO PATTERNS VS FP ABSTRACTIONS

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More (Subjective -> Objective)

→

More (Ambiguous -> Precise)

→

"Fluffy" Interfaces -> Generic Functions

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OO PATTERNS VS FP ABSTRACTIONS

→

More (Subjective -> Objective)

→

More (Ambiguous -> Precise)

→

"Fluffy" Interfaces -> Generic Functions

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OO PATTERNS VS FP ABSTRACTIONS

→

More (Subjective -> Objective)

→

More (Ambiguous -> Precise)

→

"Fluffy" Interfaces -> Generic Functions

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LAYING BRICKS

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WARNING

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Abstract Algebra -> (Continuous, Infinite)

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Real World -> usually (Discrete, Finite)

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WARNING

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Abstract Algebra -> (Continuous, Infinite)

→

Real World -> usually (Discrete, Finite)

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CODE

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EXAMPLE UNIX PIPE

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find . -name "*. rb" \ | xargs egrep "#.*? TODO:" \ | wc -l Character-based, through file descriptors

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EXAMPLE FUNCTION COMPOSITION

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( length . mapToUpper . sanitize ) input Value based, through functions

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VALUING VALUES IN REAL WORLD 1 2

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sealed trait PossiblyMaybe [+A] final case class Somefink [A](a: A) extends PossiblyMaybe [A] final case object Nowt extends PossiblyMaybe [ Nothing ]

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object PossiblyMaybeOps { def noneDefault [A](pm: PossiblyMaybe [A])(a: A): A = pm match { case Somefink (x) => x case _ => a } } Note _ in second match, caters for nulls 15

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FUNCTOR

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class Functor f where fmap � (a → b) → f a → f b

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SBT CONSOLE

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CONTRAVARIANT FUNCTOR

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class Contravariant f where contramap � (b → a) → f a → f b

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BI FUNCTOR

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class Bifunctor f where bimap � (a → c) → (b → d) → f a b → f c d

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PRO FUNCTOR

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class Profunctor f where dimap � (c → a) → (b → d) → f a b → f c d

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SAME TYPE, MANY INTERFACES

A type defined as a Monad can also be →

An Applicative

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A Functor

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And possibly many others :)

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SAME TYPE, MANY INTERFACES

A type defined as a Monad can also be →

An Applicative

→

A Functor

→

And possibly many others :)

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SAME TYPE, MANY INTERFACES

A type defined as a Monad can also be →

An Applicative

→

A Functor

→

And possibly many others :)

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APPLICATIONS

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KNOWN USES

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Monoids:

Accumulators are everywhere, almost

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Functors:

Lots of places (endo, contravariant, bi, pro)

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Monads:

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Applicatives:

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More … e.g. Arrows, Zippers, Lenses, etc.

Effects, "Linear Happy Path", and more "validations", and more

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THINKING ALGEBRAICALLY

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Properties:

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Data Types:

property based testing: quickcheck, scalacheck

start closed, extend using "type classes", dependent types, etc when relevant

→ Abstractions: build small building blocks, use motar to build solid walls → Dist Systems: using algebraic abstractions, properties to build more useful distributed systems

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ROYAL FAIL

http://www.flickr.com/photos/dadavidov/

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QUESTIONS

Questions?

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