Assignment 5, CSC430, Winter 2012

1 Guidelines

1.1 Contracts & Test Cases

For this and all remaining assignments, every function you develop must come with the following things:

• A commented header line that expresses the result of the function in terms of its inputs, written in English. Be as precise as you can within the space of a line or two.

• A commented contract line that gives the types of the inputs and the output. The contract should have the form <in-type> ... -> <out-type>. So, for instance, a numerical square function might have the contract line:

  ; number -> number

• Test cases. A function without test cases is incomplete. Write the test cases first, please.

1.2 Handling errors

Your parser and interpreter must detect errors and explicitly signal them by calling (error ...). We will consider an error raised internally by Racket to be a bug in your code.

For example, Racket signals a "divide by zero" error if you attempt to evaluate (/ 1 0). Since we use Racket’s division function to implement division in CFWAE, you may be tempted to leave it to Racket to signal division by zero errors for you. However, you must signal the error yourself by explicitly testing for division by zero before calling Racket’s division procedure.

Note that you may assume that your contracts are respected. That is, if your interp function’s contract indicates that it expects an OCFAE, you do not need to worry about miscreants that call it with a number or a string or another surprising value.

1.3 Language Level & File Format

Your solution should take the form of a single file. Solve each problem separately, and make sure that each solution appears in a separate part of the file, with comments separating each problem’s solution.

Hand in your solution using the handin server. For help with the handin server, please see the course web page.

2 Pair Programming

This assignment is a pair programming assignment. This means that you may work with at most one other person. You are not required to do so, but I strongly encourage it; if you don’t feel that you need the help, then work with someone who does.

To declare partners, both you and your partner must send me e-mail indicating this fact, at least three days before the assignment is due. In order to submit a pair programming assignment, use the string formed by joining your individual ids with a "+" in between. So, if my login is "clements" and my partner’s is "wilson", then we would submit as "clements+wilson". Don’t submit by yourself if you’re planning to work with a partner; an individual submission will prevent a later pair submission.

3 The Assignment

This assignment requires you to implement recursive first-class functions, and structures.

3.1 Laziness?

This assignment’s interpreter should not be lazy. Make it eager again, and make sure that all of your old test cases pass before beginning the rest of the assignment.

3.2 Recursive Functions

For this assignment, you must implement recursive functions using the withrec form. It binds a (possibly recursive) function in the environment, and then evaluates the body. Here’s a simple example:

{withrec {countDown {fun {x} {switch x [0 => 0] [else {countDown {- x 1}}]}}}

{countDown 13}}

As in lecture, the environment contained in the newly formed closure must contain the binding for the closure itself. You may use a box (as discussed in class) to represent this circular binding.

Note that you are not required to extend the withrec form to handle multiple bindings. You might like to think about how this might work....

3.3 Removing List Primitives

The pair and related forms are now redundant, as they can be implemented using objects. Remove all of them, including all of the related operators.

3.4 Objects

The assignment requires you to implement objects much as we did in class. Specifically, you must implement the new form and object reference using the ref operator.

Here are some examples:

{new {author

{new {firstname "Herbert"} {surname "Simon"}}}

{title

"The Sciences of the Artificial"}

{year 1994}}

The outer object has author, title, and year fields. The inner object has firstname and surname fields.

4 Syntax of OCFAE

The syntax of the OCFAE language with these additional features can be captured with the following EBNF:

OCFAE		=		num
		|		string
		|		true
		|		false
		|		{operator OCFAE *}
		|		id
		|		{switch CFWAE [CFWAE => CFWAE] * [else CFWAE]}
		|		{with {{id = OCFAE}*} OCFAE}
		|		{withrec {id OCFAE} OCFAE}
		|		{fun {id *} OCFAE}
		|		{OCFAE OCFAE *}
		|		{new {id OCFAE}*}
		|		{ref OCFAE id}

with

operator		=		+
		|		-
		|		*
		|		/
		|		and
		|		or
		|		equal?
		|		<=
		|		not
		|		number?
		|		string?

where an id is not true, false, with, switch, else, fun, withrec, ref, new, or one of the operator names

and num is a number.

If a fun or a with expression has duplicate identifiers, we consider it a syntax error. Therefore, such errors must be detected in parse-exp. For example, parsing the following expressions must signal errors:

{with {{x 10} {x 20}} 50}

{fun {x x} 10}

...

5 Support Code

Your code must adhere to the following template, without any changes. Note that the code below uses the list/c contract, which denotes a list of a fixed length containing elements matching the given sub-contracts. Also, the hash/c contract indicates a hash from a given kind of key to a given kind of value.

; represents an expression

(define-type OCFAE

[num (n number?)]

[bool (b boolean?)]

[str (s string?)]

[unop (op symbol?) (arg OCFAE?)]

[binop (op symbol?) (lhs OCFAE?) (rhs OCFAE?)]

[varref (name symbol?)]

[switch (val OCFAE?) (clauses (listof SClause?)) (elseval OCFAE?)]

[fun (params (listof symbol?)) (body OCFAE?)]

[withrec (name symbol?) (rhs OCFAE?) (body OCFAE?)]

[app (f OCFAE?) (args (listof OCFAE?))]

[newexp (fields (listof (list/c symbol? OCFAE?)))]

[objref (obj OCFAE?) (field symbol?)])

; represents a 'switch' clause

(define-type SClause

[clause (patval OCFAE?) (result OCFAE?)])

; represents a possible result of evaluation

(define-type OCFAE-Value

[numV (n number?)]

[boolV (b boolean?)]

[strV (s string?)]

[closureV (params (listof symbol?))

(body OCFAE?)

(env (hash/c symbol? valbox?))]

[objectV (fields (hash/c symbol? OCFAE-Value?))])

; a box containing false or a value:

(define (valbox? b)

(box/c (or/c false? OCFAE-Value?)))

; parse-exp : s-exp -> OCFAE?

;  consumes an s-expression and produces the corresponding

;  expression.

(define (parse-exp sexp)

...)

;  This procedure interprets the given OCFAE and produces a result

;  in the form of an OCFAE-Value

;  interp : OCFAE? hash? -> OCFAE-Value?

(define (interp expr env)

...)