# Difference between revisions of "Let vs. Where"

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If you run both |
If you run both |
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<haskell> |
<haskell> |
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fib = (map fib' [0 ..] !!) |
fib = (map fib' [0 ..] !!) |
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fib' n = fib (n - 1) + fib (n - 2) |
fib' n = fib (n - 1) + fib (n - 2) |
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</haskell> |
</haskell> |
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and |
and |
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<haskell> |
<haskell> |
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fib x = map fib' [0 ..] !! x |
fib x = map fib' [0 ..] !! x |
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fib' n = fib (n - 1) + fib (n - 2) |
fib' n = fib (n - 1) + fib (n - 2) |
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</haskell> |
</haskell> |
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⚫ | |||

⚫ | |||

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⚫ | |||

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Compare |
Compare |
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<haskell> |
<haskell> |
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fib = |
fib = |
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in (map fib' [0 ..] !!) |
in (map fib' [0 ..] !!) |
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</haskell> |
</haskell> |
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and |
and |
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<haskell> |
<haskell> |
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fib x = |
fib x = |
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in map fib' [0 ..] !! x |
in map fib' [0 ..] !! x |
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</haskell> |
</haskell> |
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− | . In the second case <hask>fib'</hask> is (re-)defined for every argument <hask>x</hask>, thus it cannot be floated out.<br><br> |
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+ | In the second case, <hask>fib'</hask> is redefined for every argument <hask>x</hask>. The compiler cannot know whether you intended this -- while it increases time complexity it may reduce space complexity. Thus it will not float the definition out from under the binding of x.<br><br> |
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− | The <hask>where</hask> clause hid this structure |
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and made the application to <hask>x</hask> look like a plain eta expansion, which it is not. |
and made the application to <hask>x</hask> look like a plain eta expansion, which it is not. |
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## Revision as of 23:34, 11 June 2014

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. You may wonder why simply adding an explicit argument to `fib`

(known as eta expansion) degrades performance so dramatically.

You might see the reason better if you rewrote 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 redefined for every argument `x`

. The compiler cannot know whether you intended this -- while it increases time complexity it may reduce space complexity. Thus it will not float the definition out from under the binding of x.

In contrast, in the first function, `fib'`

can be moved to the top level by the 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?