# Difference between revisions of "Let vs. Where"

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= let a = w x |
= let a = w x |
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in case () of |
in case () of |
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− | _ | cond1 x |
+ | _ | cond1 x -> a |

− | | cond2 x |
+ | | cond2 x -> g a |

− | | otherwise |
+ | | otherwise -> f (h x a) |

</haskell> |
</haskell> |
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## Revision as of 22:21, 23 October 2012

Haskell programmers often wonder whether to use `let`

or `where`

.
This seems to be only a matter of taste in the sense of "Declaration vs. expression style", however there is more to it.

It is important to know that `let ... in ...`

is an expression, that is, it can be written wherever expressions are allowed. In contrast, `where`

is bound to a surrounding syntactic construct, like the pattern matching line of a function definition.

## Advantages of let

Suppose you have the function

```
f :: s -> (a,s)
f x = y
where y = ... x ...
```

and later you decide to put this into the `Control.Monad.State`

monad.
However, transforming to

```
f :: State s a
f = State $ \x -> y
where y = ... x ...
```

will not work, because `where`

refers to the pattern matching `f =`

,
where no `x`

is in scope.

In contrast, if you had started with `let`

, then you wouldn't have trouble.

```
f :: s -> (a,s)
f x =
let y = ... x ...
in y
```

This is easily transformed to:

```
f :: State s a
f = State $ \x ->
let y = ... x ...
in y
```

## Advantages of where

Because "where" blocks are bound to a syntactic construct, they can be used to share bindings between parts of a function that are not syntactically expressions. For example:

```
f x
| cond1 x = a
| cond2 x = g a
| otherwise = f (h x a)
where
a = w x
```

In expression style, you might use an explicit `case`

:

```
f x
= let a = w x
in case () of
_ | cond1 x -> a
| cond2 x -> g a
| otherwise -> f (h x a)
```

or a functional equivalent:

```
f x =
let a = w x
in select (f (h x a))
[(cond1 x, a),
(cond2 x, g a)]
```

or a series of if-then-else expressions:

```
f x
= let a = w x
in if cond1 x
then a
else if cond2 x
then g a
else f (h x a)
```

These alternatives are arguably less readable and hide the structure of the function more than simply using `where`

.

## Lambda Lifting

One other approach to consider is that let or where can often be implemented using lambda lifting and let floating, incurring at least the cost of introducing a new name. The above example:

```
f x
| cond1 x = a
| cond2 x = g a
| otherwise = f (h x a)
where
a = w x
```

could be implemented as:

```
f x = f' (w x) x
f' a x
| cond1 x = a
| cond2 x = g a
| otherwise = f (h x a)
```

The auxiliary definition can either be a top-level binding, or included in f using `let`

or `where`

.

## Problems with where

If you run both

```
fib = (map fib' [0 ..] !!)
where
fib' 0 = 0
fib' 1 = 1
fib' n = fib (n - 1) + fib (n - 2)
```

and

```
fib x = map fib' [0 ..] !! x
where
fib' 0 = 0
fib' 1 = 1
fib' n = fib (n - 1) + fib (n - 2)
```

you will notice, that the second one runs considerably slower than the first one.
You may wonder, why just adding the explicit argument to `fib`

(known as eta expansion)
reduces the performance dramatically.

You might see the reason better, if you rewrite this code using `let`

.
Compare

```
fib =
let fib' 0 = 0
fib' 1 = 1
fib' n = fib (n - 1) + fib (n - 2)
in (map fib' [0 ..] !!)
```

and

```
fib x =
let fib' 0 = 0
fib' 1 = 1
fib' n = fib (n - 1) + fib (n - 2)
in map fib' [0 ..] !! x
```

. In the second case `fib'`

is (re-)defined for every argument `x`

,
thus it cannot be floated out.
In contrast to that, in the first case `fib'`

can be moved to the top level by a compiler.
The `where`

clause hid this structure
and made the application to `x`

look like a plain eta expansion, which it is not.

- Haskell-Cafe on Eta-expansion destroys memoization?