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Constrain continuation of computation based on Boolean expression

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The notion of guard is pretty general as it occurs in different ways in programming languages which is why we do not attempt a comprehensive description here. Instead, we explain guards in Haskell; they are helpful here for adding more control on pattern matching.

Guards in Haskell

Consider the following function for finding the minimum in a list:

findmin (x:xs) = findmin' x xs
  where
    findmin' m [] = m
    findmin' m (y:ys) =
      if m < y
        then findmin' m ys
        else findmin' y ys

Arguably, it may be preferable to decompose the second case for non-empty list into two cases: one for each branch of the if-then-else. We can guard the equations for the two cases accordingly.

findmin (x:xs) = findmin' x xs
  where
    findmin' m [] = m
    findmin' m (y:ys) | m < y = findmin' m ys
    findmin' m (y:ys) | m >= y = findmin' y ys

Arguably, the guard for the last equation is not needed because the equation would only be tried in a case where the condition must evidently hold. So we may want to simplify as follows.

findmin (x:xs) = findmin' x xs
  where
    findmin' m [] = m
    findmin' m (y:ys) | m < y = findmin' m ys
    findmin' m (y:ys) = findmin' y ys

Arguably, we do not want to use guards at all, as we may be even more concise (without guards) as follows.

findmin (x:xs) = findmin' x xs
  where
    findmin' m [] = m
    findmin' m (y:ys) = findmin' (min m y) ys

The guards of Haskell provide yet additional expressiveness that we omit here for brevity.

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