Monads in 5 MinutesShay Elkin

image: Rodrigo Galindez cc-by

“All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor.”

Mac Lane, SaundersCategories for the Working Mathematician (2nd Ed.)

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Caveat Emptor(Questions? — Mention @srockets)

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Functional Programming

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function foo(x) {

…

return y

}

function M_foo(x) {

…

return [y, state]

}

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function foo(x) {

…

return y

}

function bar(x) {

…

return z

}

h = bar(foo(x))

function M_foo(x) {

…

return [y, state]

}

function M_bar(x) {

…

return [z, state]

}

t = M_foo(x)

if t[1] {

// handle state

} else {

t2 = M_bar(t[0])

if t2[1] // … statehttp://shayelk.in/5mm

a → Ma

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(Type constructor)

unitM(a value) → Ma

unitM(x) ~ [x, state]

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x → foo(x) → bar( foo(x) )

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(bar∘foo)(x) := bar(foo(x))

x → (unitM∘bar) ? foo

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x → (unitM∘bar) >>= foo

bindM(Ma value, Mb (*func)(a))

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x → (unitM∘bar) >>= foo

bindM(Ma value, Mb (*func)(a))

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The Maybe Monad

Ma := a | Nothing

function unitM(x) {

return { "isNothing": false, "value": x }

}

function bindM(mx, f) {

if (!mx["isNothing"]) {

return ["isNothing": false, "value": f(mx["value"])]

} else { return mx }

}

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(M, unitM, bindM)and the monad rules

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Moral: Monads are Easy!

Further reading:Philip Wadler,Monads for functional programming.

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