Is there a fully functional paradigm language that transpiles to JavaScript?

If you are looking to stay at the .NET platform, and would want to use F# as your language to transpile to JavaScript, then I recommend looking at the following:

1.) Fable - Fable brings together the power of the F# compiler and Babel to make JavaScript a true backend for F#. It works directly on F# source code, no compilation needed.

2.) WebSharper - A fundamentally different web framework for developing functional and reactive .NET applications

If you like F# you might like OCaml via js_of_ocaml (better OCaml compatibility) or BuckleScript (better JS interop) or even Reason ML (more modern syntax, including JSX).

If you like Haskell better, you could use GHCJS (it's Haskell, targeting JS), Purescript (strict evaluation means simpler JS), or Elm (who needs type classes anyway).

I'm less sure about Erlang. There seem to have been some attempts (possibly somewhat successful) at targeting JS, but I'm not at all familiar with any of them.

Check out Scala.js, Elm or PureScript.

Other languages include ClojureScript (Clojure) and Funscript (F#)

Of those, I've only really used Scala.js and Elm, both of which work extremely well in my opinion.

Currying

In Elm and PureScript functions are curried by default. In Scala Currying can be done very easily by using multiple parameter lists:

def curried(param1: Int)(param2: Int): Int = ...