Currying with Mathematica

Question

One may implement a limited form of Currying in Mathematica, using this construct:

f[a_][b_][c_] := (a^2 + b^2)/c^2

Allowing one to do, for

Answer 1

Sorry for a probably unrelated comment. I just searched «currying with Mathematica» and this question was the first in Google list. Although, it is 1 year old and already got answer, I found that the solutions presented are not quite elegant imho. The simple modification of the initial code should be as follows:

ClearAll[f]
SetAttributes[f, HoldAllComplete]
f[a_, b_, c_] := {ToString@Unevaluated@a, ToString@Unevaluated@b,
ToString@Unevaluated@c}
f[a__] := Function[x, f[a, x], HoldAll]

It results in the desired carrying:

f[2+2][2+1] /@ Unevaluated@{1+1, 3+3} → {{2+2, 2+1, 1+1}, {2+2, 2+1, 3+3}}

It works fine for three possible partitions of arguments

f[1 + 1, 2 + 2, 6 + 1]
f[1 + 1, 2 + 2][6 + 1]
f[1 + 1][2 + 2][6 + 1]

and gives the correct result: {"1+1", "2+2", "6+1"}}, but it fails for f[1 + 1][2 + 2, 6 + 1]. For this one, one can use a little bit more advanced version:

ClearAll[f, g]
SetAttributes[f, HoldAllComplete]
SetAttributes[g, HoldAllComplete]
f[a_, b_, c_] := (ClearAll[g]; SetAttributes[g, HoldAllComplete]; 
  Thread[Hold[{a, b, c}]] /. {Hold[e_] :> ToString@Unevaluated[e]})
f[a__] := (g[x__] := f[a, x]; g)