Let vs. Where

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?