@lelf The ∘ (called Jot) is an operator, not a function. It binds tighter than a train, and it forms a single function from its left and right operands. So (f∘h) works differently from f g h. "⍺(f∘h)⍵ is ⍺f(h ⍵)" is just the definition of Jot.
@lelf (f+g)(x) in Traditional Mathematical Notation (TMN) is (f+g)(x) in APL. (f∘g)(x) in TMN is (f∘g)(x) in APL. Now we add a left argument (using dot notation): (f+g)(x) ⇔ f(x)+g(x) → x.(f+g)(y) ⇔ x.f(y)+x.g(y) which in APL is (x f y)+(x g y). Similarly, (f∘g)(x) ⇔ f(g(x)) → x.(f∘g)(y) ⇔ x.f(g(y)) which in APL is x f g y.
a simpler model outputting the result in reverse would be {{⎕←⍺|⍵ ⋄ ⌊⍵÷⍺}/⍺,⍵} (which would be more prettily describable as a loop with an accumulator but apl doesn't really make that easy)
now trying it, gnu apl accepts pretty much everything… both alphas, omegas, even minuses (ascii hyphen & mathematical minus U+2212). Edit: ah, it's all in the pdf you posted
@lelf And yes, two to be precise, that one and ∧ vs ^.
I personally think that if Dyalog wants to position itself as the ultimate APL for the future, it should eat all the synonyms (but normalise immediately).