Without trying to speak to why "katlang" does what it does, there are other languages that do this and I can speak to how useful it is when you already prefer functions of low arity: It repeatedly demonstrates a substantial improvement in bug/defect reduction and code.
APL does this; a function like {ω×α+ω} and assigns omega to the right-argument, and alpha to the left-argument. They also have ωω for the right-side function and αα for the left-hand function for writing higher-order functions. Dyadic expressions tend to modify their right-hand argument, and not the left, so for the times that the arguments are "backwards" this can usually be fixed with the commute operator (⍨) which looks similar to katlang's "grace" operator (~) so I assume at least some influence.
k/q does something more similar: a function like {x*y+x} assigns the first argument to x, the second to y, the third to z. The author seems inspired by this behaviour (even mentioning it in a linked paper). In q, when the function is in the q context, x is the left-argument and y is the right-argument when called dyadically. Sadly, q and k don't have commute.
APL does this; a function like {ω×α+ω} and assigns omega to the right-argument, and alpha to the left-argument. They also have ωω for the right-side function and αα for the left-hand function for writing higher-order functions. Dyadic expressions tend to modify their right-hand argument, and not the left, so for the times that the arguments are "backwards" this can usually be fixed with the commute operator (⍨) which looks similar to katlang's "grace" operator (~) so I assume at least some influence.
k/q does something more similar: a function like {x*y+x} assigns the first argument to x, the second to y, the third to z. The author seems inspired by this behaviour (even mentioning it in a linked paper). In q, when the function is in the q context, x is the left-argument and y is the right-argument when called dyadically. Sadly, q and k don't have commute.