In explaining fromIntegral, I want to say that it is really a collection of overloaded functions:
Integer -> Double
Int -> Float
...
When GHC compiles a line of code with fromIntegral it in, it must decide at compile time which of these overloaded functions to compile to. This is in contrast to saying that fromIngetral is a function of the type (Integral a, Num b) => a -> b. In reality there is no (single) function of the type (Integral a, Num b) => a -> b because (among other things) every function must map between actual types, but (Integral a, Num b) => a -> b does not say which actual types are mapped between.
Is the preceding a reasonable thing to say?
If so, can I say the same sort of thing about constants like 1 and []? In particular there is no single value []. Instead [] is a symbol which at compile time must be compiled to the empty list of some particular type, e.g., [Int]. There is no such Haskell value as [] :: [a] since [a] (as type) is not an actual type. I want to say the same thing about 1, i.e., that there is no such Haskell value as 1 :: (Num t) => t. When the symbol 1 appears in a program, the compiler must decide during compilation whether it is intended to be 1::Int or 1::Integer or 1::Double, etc.
-- Russ Abbott
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Professor, Computer Science
California State University, Los Angeles
Google voice: 424-242-USA0 (last character is zero)
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
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