In Lambda Calculus, natural numbers, boolean values, list processing functions, recursion, if function are defined in terms of lambda terms. For example, natural numbers are defined as Church numerals, and recursion is defined in terms of a fixed point of a function.
Functional languages are said to be based on Lambda Calculus.
Who shall be concerned about the above concepts in terms of lambda terms: the implementer/designer of the languages, and/or programmers in the languages?
Do functional programming languages define/implement the above concepts in terms of lambda terms?
As programmers in regular functional programming languages (such as Haskell, Lisp, ML), is it correct that the above concepts are always given in the same way as in imperative languages, and we never have to understand or deal with their definitions in terms of lambda terms?