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Lists can be encoded in the lambda calculus. A way to do this, is by defining a lambda term that, like a cons, inserts an

Lists can be encoded in the lambda calculus. A way to do this, is by defining a lambda term that, like a "cons", inserts an element at the head of a list, initially empty. Rather than showing the full lambda term, we introduce the defined term cons . For example, the result of reducing the encoding of the expression cons 3[7,8] will be the encoding for the list [3,7,8]. Assume that you have available the fixed-point operator Y and the terms cons , sqr and succ , respectively for list construction, square and successor functions. Which expressions will these terms define? Show your argument before the final answer.
1. Y\lambda l.(consxl)
2. Y(\lambda f.\lambda n.(cons(sqrn)(f(succn))))0

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