# User:WillNess

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Monad is composable computation descriptions.

I like *this one-liner*:

```
-- infinite folding due to Richard Bird
-- double staged primes production due to Melissa O'Neill
-- tree folding idea Heinrich Apfelmus / Dave Bayer
primes = 2 : _Y ((3:) . gaps 5
. foldi (\(x:xs) -> (x:) . union xs) []
. map (\p-> [p*p, p*p+2*p..]))
_Y g = g (_Y g) -- multistage production via Y combinator
gaps k s@(c:t) -- == minus [k,k+2..] (c:t), k<=c,
| k < c = k : gaps (k+2) s -- fused for better performance
| otherwise = gaps (k+2) t -- k==c
```

`foldi`

is on Tree-like folds page. `union`

and more at Prime numbers.

The constructive definition of primes is the Sieve of Eratosthenes, **P** = **N**_{2}\**N**_{2}_{*}**N**_{2} = **N**_{2}\**P**_{*}**N**_{2} :

using standard definition

- . . . or, .

Trial division sieve is:

If you're put off by self-referentiality, just replace or on the right-hand side of equations with , as the ancient Greeks might or mightn't have done, as well.