It is well known that all computable functions can be expressed as terms of the lambda calculus and computed according to its rules. It is also more or less obvious that many classical formal languages (i.e. languages with formalized semantics) can be translated into the lambda calculus (e.g. using a Church encoding). I am, however, pretty sure that there are languages where such a translation is not possible, the simplest example would be a language with a builtin primitive that solves the Halteproblem.
That makes me wonder if there is an established terminus for the languages that can be translated.
Is there a name for the class of languages that can be translated (correctly, completely) into the lambda calculus?