I wanted to do this same problem that calculates the roots of a second degree function, but using let.
raizes2 :: Float -> Float -> Float -> (Float, Float)
raizes2 a b c
|delta < 0 = error "Delta nao pode ser menor que zero"
|a == 0 = error "A nao pode ser zero"
|otherwise = ((-b + (sqrt(delta)))/2*a, (-b - (sqrt(delta)))/2*a)
where
delta = (b^2 - 4*a*c)
You have to use case expressions. For example:
raizes2 :: Float -> Float -> Float -> (Float, Float)
raizes2 a b c = let delta = (b^2 - 4*a*c)
in case compare delta 0 of
LT -> error "Delta nao pode ser menor que zero"
_ -> if a == 0
then error "A nao pode ser zero"
else ( (-b + (sqrt(delta)))/2*a
, (-b - (sqrt(delta)))/2*a )
It's a little different because case only compares equalities. And what is compared is static, that is, it will always be the result of compare delta 0 , which can be LT , GT or EQ . Since its patterns involve the comparison not only of the delta value, it is necessary to use the _ (which accepts anything) case and within it to create a if (or other case ) to compare the value of a .
If you want to read a little about these structures, the page about case is translated into Wikibook in Portuguese .
You can not use guards inside the let directly. The guards come before the definition of the expression to be evaluated, and the let ja is that expression. But a way to solve (inelegantly) the problem is to define an auxiliary function inside the let, and in that definition to use the guards
raizes2 a b c = let delta = (b^2 - 4*a*c)
auxiliar
|delta < 0 = error "Delta nao pode ser menor que zero"
|a == 0 = error "A nao pode ser zero"
|otherwise = ((-b + (sqrt(delta)))/2*a, (-b - (sqrt(delta)))/2*a)
in auxiliar
As I said, it is inelegant ....