# Idiom brackets

In July 2007, Conor McBride described `idiom brackets'.

See also the 2008 paper Applicative programming with effects by Conor Mcbride and Ross Paterson.

## Motivation

Using Control.Applicative you could write:

```
f <$> x <*> y
```

Since f is not a pure function, it's f :: x -> y -> m c. The correct form would be

```
join $ f <$> x <*> y
```

But maybe some type-class hackery can be used to eliminate the join.

## Idiom brackets

Type class hackery to eliminate the 'join':

```
class Applicative i => Idiomatic i f g | g -> f i where
idiomatic :: i f -> g
iI :: Idiomatic i f g => f -> g
iI = idiomatic . pure
data Ii = Ii
instance Applicative i => Idiomatic i x (Ii -> i x) where
idiomatic xi Ii = xi
instance Idiomatic i f g => Idiomatic i (s -> f) (i s -> g) where
idiomatic sfi si = idiomatic (sfi <*> si)
```

So that

```
iI f x y Ii = f <$> x <*> y
```

Now add

```
data Ji = Ji
instance (Monad i, Applicative i) => Idiomatic i (i x) (Ji -> i x) where
idiomatic xii Ji = join xii
```

and you've got

```
iI f x y Ji = join $ f <$> x <*> y
```

or, more flexibly,

```
data J = J
instance (Monad i, Idiomatic i f g) => Idiomatic i (i f) (J -> g) where
idiomatic fii J = idiomatic (join fii)
```

so you can insert joins wherever you like, thus:

```
iI f x y J z Ii = join (f <$> x <*> y) <*> z
= do {x' <- x; y' <- y; f' <- f x y; z' <- z; return (f' z')}
```

Of course, the implementation is an ugly hack, made uglier still by ASCII. Worse, for reasons I have never entirely understood, the type-class hackery doesn't allow these brackets to nest as they should. Even so, I find them a considerable convenience. I always assumed that was down to peculiarity on my part.

I thought I'd present it as a curio illustrating part of the design space, but I don't imagine there's that big a market for an "idiom brackets done properly" proposal.