In Scheme, source code is data. Every non-atomic expression is written as a Scheme list, so we can write procedures that manipul
ate other programs just as we write procedures that manipulate lists. Rewriting programs can be useful: we can write an interpreter that only handles a small core of the language, and then write a procedure that converts other special forms into the core language before a program is passed to the interpreter.
For example, the let special form is equivalent to a call expression that begins with a lambda expression. Both create a new frame extending the current environment and evaluate a body within that new environment. Feel free to revisit Problem 15 as a refresher on how the let form works.
(let ((a 1) (b 2)) (+ a b))
;; Is equivalent to:
((lambda (a b) (+ a b)) 1 2)
These expressions can be represented by the following diagrams:
Let Lambda
let lambda
Use this rule to implement a procedure called let-to-lambda that rewrites all let special forms into lambda expressions. If we quote a let expression and pass it into this procedure, an equivalent lambda expression should be returned: pass it into this procedure:
scm> (let-to-lambda '(let ((a 1) (b 2)) (+ a b)))
((lambda (a b) (+ a b)) 1 2)
scm> (let-to-lambda '(let ((a 1)) (let ((b a)) b)))
((lambda (a) ((lambda (b) b) a)) 1)
In order to handle all programs, let-to-lambda must be aware of Scheme syntax. Since Scheme expressions are recursively nested, let-to-lambda must also be recursive. In fact, the structure of let-to-lambda is somewhat similar to that of scheme_eval--but in Scheme! As a reminder, atoms include numbers, booleans, nil, and symbols. You do not need to consider code that contains quasiquotation for this problem.
(define (let-to-lambda expr)
(cond ((atom? expr) )
((quoted? expr) )
((lambda? expr) )
((define? expr) )
((let? expr) )
(else )))
CODE:
; Returns a function that checks if an expression is the special form FORM
(define (check-special form)
(lambda (expr) (equal? form (car expr))))
(define lambda? (check-special 'lambda))
(define define? (check-special 'define))
(define quoted? (check-special 'quote))
(define let? (check-special 'let))
;; Converts all let special forms in EXPR into equivalent forms using lambda
(define (let-to-lambda expr)
(cond ((atom? expr)
; BEGIN PROBLEM 19
'replace-this-line
; END PROBLEM 19
)
((quoted? expr)
; BEGIN PROBLEM 19
'replace-this-line
; END PROBLEM 19
)
((or (lambda? expr)
(define? expr))
(let ((form (car expr))
(params (cadr expr))
(body (cddr expr)))
; BEGIN PROBLEM 19
'replace-this-line
; END PROBLEM 19
))
((let? expr)
(let ((values (cadr expr))
(body (cddr expr)))
; BEGIN PROBLEM 19
'replace-this-line
; END PROBLEM 19
))
(else
; BEGIN PROBLEM 19
'replace-this-line
; END PROBLEM 19
)))
