[Haskell-cafe] Generalized partial application (again)

[Peter Verswyvelen]

Please correct me if I'm wrong in any of the reasoning below.

Haskell provides the ability the perform partial application on the
rightmost arguments.
I learned from some pretty smart guys that partial application cannot be
emulated with lambas, because they behave differently operationally, e.g.

e = trace "e"
op = (+)

a1 = let f = (op (e 1)) in (f 10, f 100)
a2 = let f = (\x -> op (e 1) x) in (f 10, f 100)

a1 and a2 are operationally not the same: a1 will evaluate (e 1) once, a2
will evaluate it twice.

However, Haskell also allows to partially apply the second argument of
binary functions (using sections)

b1 = let f = (`op` (e 1)) in (f 10, f 100)
b2 = let f = (\x -> (e 1) `op` x) in (f 10, f 100)

Again, b1 evaluates (e 1) once, b2 twice.

b1 is actually the same as

c1 = let f = ((flip op) (e 1)) in (f 10, f 100)

So for ternary functions we could write more permutations of flip:

flip3_12 f a1 a2 a3 = f a2 a1 a3
flip3_13 f a1 a2 a3 = f a3 a2 a1
flip3_23 f a1 a2 a3 = f a1 a3 a2

And use these to partially apply any argument

e1 x = trace "e1" x
e2 x = trace "e2" x

op2 :: Int -> Int -> Int -> Int
op2 x y z = x+10*y+100*z

z1 = let f = (flip3_12 op2) (e1 1) (e2 2) in (f 3, f 4)
z2 = let f = (flip3_13 op2) (e1 1) (e2 2) in (f 3, f 4)
z3 = let f = (flip3_23 op2) (e1 1) (e2 2) in (f 3, f 4)

This could be extended to N-ary functions. Haskell doesn't give any special
syntactic support for this, but it surely is possible.

Am I missing something here? Is there any easier way to perform "generalized
partial application"?
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