I defined a function that computes sqrt and converts argument from and to Integral class:

isqrt :: Integral i => i -> i
isqrt = floor . sqrt . fromIntegral

I don't understand why that compiles. If we write out signatures of the individual functions we get:

fromIntegral :: (Num b, Integral a) => a -> b
sqrt :: Floating a => a -> a
floor :: (RealFrac a, Integral b) => a -> b

So "sqrt" takes something of Floating type but it is supplied with Num. If you take a look at class hierarchy, you can see that Floating "inherits" from Num but not the other way around. I would understand if Floating could be implicitly treated as Num because it is a more "specialized" type. Why this is ok for the compiler ?

CodePudding user response：

So sqrt takes something of Floating type but it is supplied with Num.

No. The fromIntegral guarantees that it can convert any number with a type that is a member of the Integral typeclass to any Num type, not to a Num type.

Since sqrt needs an number that is a member of the Floating typeclass, for that specific case, fromIntegral will specialy to return something of a type that is a member of the Floating typeclass.

CodePudding user response：

No, sqrt is not supplied with any Num.

Its supplier fromIntegral is able to produce any Num indeed as needed, whereas sqrt demands a Floating as its input. And Floating is a subclass of Num.

So fromIntegral happily obliges. Since it can produce any Num, surely it can produce any type in its subclass. So whatever the specific concrete type it ends up to be, it is in Floating, and necessarily it is in Num.

Thus fromIntegral has no problem to provide it.