about the use of "case of" in Haskell-CodePudding

I think case of is quite straight forward, as i come from more imperative languages. Nevertheless, i have encountered a Kata where one of the solutions by another user, confuses me about the use of case and Data.List (sort)

import Data.List (sort)

isTriangle :: Int -> Int -> Int -> Bool
isTriangle a b c =
  case sort [a,b,c] of
     [min, middle, max] -> (min   middle) > max

By definition, 3 segments can make a triangle if the condition a b > c is met for the 3 permutations of [a,b,c] so, something more straight forward (my answer) would be:

isTriangle :: Int -> Int -> Int -> Bool
isTriangle a b c = a   b > c && b   c > a && a   c > b

My question is, in the case above, how is the case of testing that condition for the 3 combinations?

CodePudding user response：

Imagine that a b and c are ordered from small to large, then the algorithm tests that a b > c, which is what the first implementation checks.

If we know that a < b < c, and a b > c holds, then we know that a c > b holds. Indeed: a c > a b > c > b, hence a c > b holds because a b > c holds. Furthermore b c > a b > c > a holds, and thus b c > a holds as well.

This thus means that checking if it holds for a known minimum, maximum and value in between, the two other equations are implied.

What the case … of does here is sorting the list [a, b, c] and unpacking the sorted list in min, middle and max, it is thus a tool that is used to assign the smallest value to min, the largest value to max and the remaining value to middle. A where … or let … in … is probably more elegant, for example:

isTriangle :: Int -> Int -> Int -> Bool
isTriangle a b c = (min   middle) > max
  where [min, middle, max] = sort [a, b, c]