R5rs scheme (dr.racket) | Computer Science homework help

;; Towards a Scheme Interpreter for the Lambda Calculus — Part 1: Syntax

;; 5 points

;; , and pre-requisite for all subsequent parts of the project

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; All programming is to be carried out using the pure functional sublanguage of R5RS Scheme.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; You might want to have a look at http://www.cs.unc.edu/~stotts/723/Lambda/overview.html

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; 1. The lambda calculus is a particularly simple programming language consisting only of
;; variable references, lambda expressions with a single formal parameter, and function
;; applications.  A BNF definition of lambda calculus expressions is

;; <expr> ::= <variable> | (lambda ( <variable> ) <expr> )  |  ( <expr> <expr> )

;; Design a data type for the lambda calculus, with constructors, selectors, and classifiers.

;; For concrete representation, use Scheme, as follows:  an identifier should be represented as
;; a quoted Scheme variable, a lambda expression (lambda (x) E) as the quoted 3-element list
;; ‘(lambda (x) [list representing E]), and an application  (E1 E2) as the quoted 2-element list
;; ‘([list representing E1]  [list representing E2])

;; 2.  In (lambda (<variable>) <expr>), we say that <variable> is a binder that
;; binds all occurrences of that variable in the body, <expr>, unless some intervening
;; binder of the same variable occurs. Thus in (lambda (x) (x (lambda (x) x))),
;; the first occurrence of x binds the second occurrence of x, but not
;; the fourth.  The third occurrence of x binds the fourth occurrence of x.

;; A variable x occurs free in an expression E if there is some occurrence of x which is not
;; bound by any binder of x in E.  A variable x occurs bound in an expression E if it is
;; not free in E.  Thus x occurs free in (lambda (y) x), bound in (lambda (x) x), and both
;; free and bound in (lambda (y) (x (lambda (x) x))).

;; As a consequence of this definition, we can say that a variable x occurs free in a
;; lambda calculus expression E iff one of the following holds:

;;   (i) E = x
;;   (ii) E = (lambda (y) E’), where x is distinct from y and x occurs free in E’
;;   (iii) E = (E’ E”) and x occurs free in E’ or x occurs free in E”

;; Observe that this is an inductive definition, exploiting the structure of lambda calculus
;; expressions.

;; Similarly, a variable x occurs bound in a lambda calculus expression E iff one of the
;; following holds:

;;   (i) E = (lambda (x) E’) and x occurs free in E’
;;   (ii) E = (lambda (y) E’), and x occurs bound in E’: here, y may be x, or distinct from x
;;   (iii) E = (E1 E2) and x occurs bound in either E1 or E2

;; Develop and prove correct a procedure free-vars that inputs a list representing a lambda calculus
;; expression E and outputs a list without repetitions (that is, a set) of the variables occurring
;; free in E.

;; Develop and prove correct a procedure bound-vars that inputs a list representing a lambda calculus
;; expression E and outputs the set of variables which occur bound in E.

;; 3.  Define a function all-ids which returns the set of all symbols — free or bound variables,
;; as well as the lambda identifiers for which there are no bound occurrences — which occur in
;; a lambda calculus expression E.  

Get 20% Discount on The assignment
Pages (550 words)
Approximate price: -

Try it now!

Get 20% Discount on The Assignment

We'll send you the first draft for approval by at
Total price:
$0.00

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

EssayBrill has stood as the world’s leading custom essay writing services providers. Once you enter all the details in the order form under the place order button, the rest is up to us.

Essays

Essay Writing Services

At EssayBrill, we prioritize on all aspects that bring about a good grade such as impeccable grammar, proper structure, zero-plagiarism and conformance to guidelines. Our experienced team of writers will help you completed your essays and other assignments.

Admissions

Admission and Business Papers

Be assured that you’ll definitely get accepted to the Master’s level program at any university once you enter all the details in the order form. We won’t leave you here; we will also help you secure a good position in your aspired workplace by creating an outstanding resume or portfolio once you place an order.

Editing

Editing and Proofreading

Our skilled editing and writing team will help you restructure you paper, paraphrase, correct grammar and replace plagiarized sections on your paper just on time. The service is geared toward eliminating any mistakes and rather enhancing better quality.

Coursework

Technical papers

We have writers in almost all fields including the most technical fields. You don’t have to worry about the complexity of your paper. Simply enter as much details as possible in the place order section.