If we've got this expression:


where F and G are functions (as well as a, of course; but let's treat a as a constant).

It must be understood that: first apply F taking G as input; then apply the previous result with a as input. This is

FGa = (FG)a

conventionally expressed:

( F(G) )( a )

Or is it this instead:

FGa == F(Ga) == F(G(a))


  • $\begingroup$ According to function composition rules, $F\circ G \circ a = F(G(a))$. I don't know if this applies to lambda calculus as well, but my best guess is that it does. $\endgroup$
    – nir shahar
    Commented May 12, 2021 at 13:33

1 Answer 1


It's the first one. Function application is left-associative.

$$FGa = (F G) a$$


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