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I'm looking for the moral equivalent of ghci's:
Prelude> :t 1 + 2
1 + 2 :: Num a => a
502
A function f from X to Y is an object that, for each element x ∈ X, assigns an element y ∈ Y . We use the notation f : X → Y to denote a function as described. We write f(x) = y or f : x ↦→ y to denote that the element in Y assigned to x is y. We call X the domain of f, and we call Y the codomain of f.
Derivative as a functionLet f be a function that has a derivative at every point in its domain. We can then define a function that maps every point x to the value of the derivative of f at x. This function is written f′ and is called the derivative function or the derivative of f.
f, f′ and f″ Since (f′)′=f″, when f′ is increasing, f″ is positive. Similarly, when the slopes of tangent lines are decreasing, i.e. when f′ is decreasing, the function is concave down, as you can see in the second two graphs below. Since (f′)′=f″, when f′ is decreasing, f″ is negative.
In F# Interactive you get that after each execution:
> (+);;
val it : (int -> int -> int) = <fun:it@1>
> 1 + 2;;
val it : int = 3
> printfn "Hi";;
Hi
val it : unit = ()
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