Groovy Monads

Yetanotherpresentationon MONADS
MarcinGryszko
@mgryszko

whyam I doingthis?

accordingto Brian Marick…
http://www.vimeo.com/20717301

Thereisanancient Mayan profecy
thatstatesthatsomedayevery single human onearthwillhave done a tutorial aboutmonads
and onthatpointthepurpose of theuniversewillhavebeenachieved
and allhumanswillascenttoparadise

I’ll try to do my bit
so thathumanity can reach nirvana

origins

XVIII century

Gottfried
1714
Monadologie

eternal
indecomposable
individual
hierarchical and aggregated
autonomic and independent
can change itself according to some intrinsic laws
infinite
space, time matter, and motion are phenomenal
atom
human being
soul
god – first monad
ultimate elements of the universe

XX century

categorytheory

abstractview of mathematical concepts (which are already quite abstract )

categories have:
objects
morphisms or maps or arrows
see a relationship with
classes, objects and methods?

defines monad
howitisrelatedtofunctionalprogramming?

functionalprogramming

what are monads?

containers
generalized interface for sequential computations
pattern for transmitting state using functions without mutation

what defines a monad?

monadictypeM
java.util.List
unitoperation
value -> monad
constructor/factory method
[1, 2, 3] (Integer -> List<Integer>)
bindoperation
monad -> next monad, exposing its internal value for a transformation function
any method in Groovy taking a closure as param
[1, 2, 3].bind({ x -> [x, x + 1] })
== [1, 2, 2, 3, 3, 4]

what does bind?
(typically)

Take a function and apply it to all values inside the monad
Each invocation returns monad M<U>
defintermediateMonads =
collect { x -> f(x) }
Extract U values from all intermediate M<U> monads and assemble the final M<U> monad
intermediateMonads.flatten()

monadic laws
(or when a monad is a monad)

1. identity
m.bind { x -> unit(x) } ≡ m
transforming to unit doesn’t change a monad

2. unit
unit(x).bind(f) ≡ f(x)
unit must preserve the value inside the monad

3. associativity
m.bind(f).bind(g) ≡
m.bind{ x -> f(x).bind(g) }
order of monad composition doesn’t matter

monadic zeros
(optional, empty monad)
[]

1. bindingwithzero
m.flatMap({ x -> mzero})≡ mzero
2. unit
mzero.bind(f) ≡ mzero
3. plus
mzero.plus(m) ≡ m
m.plus(mzero) ≡ m

examples
ListAsMonad
IO
State
Result

sources
https://github.com/dsrkoc/monadologie
http://james-iry.blogspot.com/2007/09/monads-are-elephants-part-1.html

Thank you!

Groovy Monads

by Marcin Gryszko

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