You must do this assignment solo. We know that some of you are not yet comfortable with Scheme; for that reason, we will weight this assignment very, very low in the overall score. Doing poorly on it will not at all damage your course grade. But, you should exploit this opportunity to become familiar with the style of programming you will do in the rest of the semester.

Extended Interpreter

  1. Write a parser and interpreter for the CFWAE language we've discussed in class, extended with the language features described below. Your interpreter should have eager application semantics and use deferred substitution.

  2. After completing the first part of the assignment, copy the resulting interpreter and modify it so that it has lazy application semantics. (We strongly recommend that you not attempt this part of the assignment until you've gotten the first interpreter done, thoroughly tested, and debugged!) Ensure you don't miss the change you must make to the type definitions for this part.

In each part of the assignment, implement the function parse, which consumes an expression in the language's concrete syntax and returns the abstract syntax representation of that expression. parse must accept only expressions in the syntax of the language.

In addition to parse, you must implement the function interp, which consumes an abstract syntax expression (as returned by the parse function) and returns a CFWAE-Value.

You must include a contract for every function that you write and include test cases that amply exercise all of the code you've written. We will not give any credit to untested functionality, even if it is correct! (Note that DrScheme will tell you if any of your code is untested.) Refer to the syllabus for style requirements.

Features to Implement


As the name suggests, your language should support conditionals, functions, with, and arithmetic expressions.


To save the trouble of having to add boolean values and operators over them, create the construct if0 using the syntax described by the EBNF below. Note that if0 has three branches:

  • A test expression
  • A "then" expression, which evaluates if the test expression evaluates to zero
  • An "else" expression, which evaluates for any other number.

Evaluation should signal an error for non-numeric test values.

Multi-argument fun

Extend the fun language feature described in lecture so that functions can accept a list of zero or more arguments instead of just one. All arguments to the function must evaluate with the same deferred substitutions. An example of a multi-argument fun:

{{fun {x y} {* x y}} 2 3}

This evaluates to 6.

As you did for multi-armed with, you must ensure that the arguments to a function have distinct names.


The syntax of the language you should implement can be captured with the following grammar:

<CFWAE> ::= <num>
    | {+ <CFWAE> <CFWAE>}
    | {- <CFWAE> <CFWAE>}
    | {* <CFWAE> <CFWAE>}
    | {/ <CFWAE> <CFWAE>}
    | <id>
    | {if0 <CFWAE> <CFWAE> <CFWAE>}
    | {with {{<id> <CFWAE>} ...} <CFWAE>}
    | {fun {<id> ...} <CFWAE>}
    | {<CFWAE> <CFWAE> ...}
where an id is not +, -, *, /, with, if0 or fun.

In this grammar, the ellipsis (...) means that the previous non-terminal is present zero or more times.

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

{with {{x 10} {x 20}} 50}

{fun {x x} 10}

Scheme's (match ...) Syntax

If you're feeling better with Scheme and think your rinterp parser is disgusting, now might be the time to take a look at Scheme's (match ...) syntax. But it is still (and always will be) not required.

Testing Your Code

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

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

If you are not sure if an error raised by your program constitutes a bug, search the DrScheme Help for test/exn. test/exn tests for errors, but only succeeds on errors that you explicitly signal.

Support Code

Use the "PLAI Scheme" language. Your code must adhere to the following template, without any changes:

(define-type Binding
  [binding (name symbol?) (named-expr CFWAE?)])

(define-type CFWAE
  [num (n number?)]
  [binop (op procedure?) (lhs CFWAE?) (rhs CFWAE?)]
  [with (lob (listof Binding?)) (body CFWAE?)]
  [id (name symbol?)]
  [if0 (c CFWAE?) (t CFWAE?) (e CFWAE?)]
  [fun (args (listof symbol?)) (body CFWAE?)]
  [app (f CFWAE?) (args (listof CFWAE?))])

(define-type Env
  [anEnv (name symbol?) (value CFWAE-Value?) (env Env?)])

(define-type CFWAE-Value
  [numV (n number?)]
  [closureV (params (listof symbol?))
            (body CFWAE?)
            (env Env?)])

;; parse : expression -> CFWAE
;; This procedure parses an expression into a CFWAE
(define (parse sexp)

;; interp : CFWAE -> CFWAE-Value
;; This procedure interprets the given CFWAE and produces a result
;; in the form of a CFWAE-Value (either a closureV or a numV)
(define (interp expr)

For the second part of the assignment (lazy application), you will need to add an exprV variant to CFWAE-Value. That is, CFWAE-Value for should read:

(define-type CFWAE-Value
  [numV (n number?)]
  [closureV (params (listof symbol?))
            (body CFWAE?)
            (env Env?)]
  [exprV (expr CFWAE?) (env Env?)]))

That said, note that interp should never return an exprV. The top-level is always a strictness point.


Turn in two files where each contains all of the code needed to run your parser and interpreter:

  1., which uses eager evaluation.
  2., which uses lazy evaluation.