Local Definitions

We already saw how we can use where to define local helper expressions, but there is another way. The let-in construct also allows us to define local expressions with the syntax let <declarations> in <expression>:
sumSquares2 x y =
  let
    a = x ^ 2
    b = y ^ 2
  in
    a + b
    
ghci> sumSquares 2 5
29
ghci> sumSquares2 2 5
29
We can also use let-in and where in combination – for example, let's write a function that checks whether the sum of squares of two numbers is a multiple of five:
sumSquaresM5 x y =
  let
    sum = a + b
  in
    mod sum 5 == 0 -- (mod) is the modulo operator 
  where
    a = x ^ 2
    b = y ^ 2
We know a number is a multiple of five if the remainder of its division by five is zero. A thing to note here is the difference betweenlet-inandwhere. What we define in the where declarations is accessible to any code above it, however, the declarations from the let block are only accessible in the in block of the let-in clause. For example, we could try to calculate the remainder from the division by five in the where clause using the sumfrom the let clause, but it will not work:
sumSquaresM5 x y =
  let
    sum = a + b
  in
    res == 0
  where
    a = x ^ 2
    b = y ^ 2
    res = mod sum 2 -- the sum expression is not accessible here
The compilation of the above would result in an error as sum is only accessible in the in clause of the code. This means that with let-in we can create super-localised expressions that aren't accessible anywhere outside the in code block.

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The Infix Operator

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