## CS 3520 Homework 5

Due: Wednesday, October 2nd, 2019 11:59pm

Difficulty: ★★☆☆

Start with `lambda+if0.rkt`, which doesn’t already include recursive binding and also doesn’t include `*` for multiplication.

### Part 1 — Syntactic Sugar for Recursive Bindings

Extend the `parse` function so that it supports a `letrec` form for recursive function bindings.

<Exp> = ...
| {letrec {[<Symbol> <Exp>]} <Exp>}

You should not change the `interp` function at all.

The September 26 lecture slides spell out how to extend the parser to make `letrec` work, especially at the end of part 4. You may find the following definition useful:

(define mk-rec-fun
`{lambda {body-proc}
{let {[fX {lambda {fX}
{let {[f {lambda {x}
{{fX fX} x}}]}
{body-proc f}}}]}
{fX fX}}})

The above definition makes sense only if you can keep track of different languages and how they interact. The `mk-rec-fun` definition above is a Plait definition. The value of `mk-rec-fun` is a representation of the concrete syntax of a Curly expression. If you pass `mk-rec-fun` to `parse`, you get a Plait value that is an `interp`retable representation of a Curly expression.

Example:

(test (interp (parse `{letrec {[f {lambda {n}
{if0 n
0
{+ {f {+ n -1}} -1}}}]}
{f 10}})
mt-env)
(numV -10))

### Part 2 — Implementing a Two-Argument Function in Curly

Define the Plait constant `plus` as a representation of the concrete syntax of a Curly expression such that

(interp (parse (list->s-exp (list (list->s-exp (list plus `*n*)) `*m*))) mt-env)

produces the same value as

(interp (parse (list->s-exp (list `+ `*n* `*m*))) mt-env)

for any Plait number *n* and *m*.

In other words, you add a Plait definition

(define plus `{lambda ....})

to the interepreter program, replacing the `....` with somethig that creates the desired Curly function.

You should not change the `interp` or `parse` function for this part.

### Part 3 — Implementing a Recursive Function in the Curly

Define the Plait constant `times` such that

(interp (parse (list->s-exp (list (list->s-exp (list times `*n*)) `*m*))) mt-env)

produces the same value as `(numV (* `*n* *m*)) for any non-negative Plait integers *n* and *m*.

You should not change the `interp` or `parse` function for this part.

Last update: Monday, August 3rd, 2020mflatt@cs.utah.edu |