Why these assignments produce different results?

Question

Why

let ab a b = a 5 + b

will produce

val ab : a:(int -> int) -> b:int -> int

and

let ab2 a b = a 5 +b

will produce

val ab2 : a:(int -> int -> 'a) -> b:int -> 'a

Why this one space between '+' and 'b' makes this difference?

Answer 1

It is all down to how the parser prioritises different syntactic options to avoid ambiguity.

+ is both the binary addition operator and the unary "positive"¹ operator. 5 + b is thus the application of addition to two arguments; but +b is the positive operator applied to some symbol b.

Thus

let ab a b = a 5 + b

is parsed as:

let ab a b = (a 5) + b

with a being a function of one integer argument returning an int so it can be added to b; but

let ab2 a b = a 5 +b

is parsed as:

let ab2 a b = a (5) (+b)

with a being a function of two arguments, with no way to infer the type it returns.

¹ I don't have an F# operator list to hand, so can't check the correct name. Edit: it appears I couldn't remember correctly: Arithmetic Operators (F#) :-).