You must do this assignment solo. We know that some of you are not yet comfortable with Racket; 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
- Write a parser and interpreter for the extended CFWAE language, as described below. Your interpreter should have eager application semantics and use deferred substitution. Call the new language CFWAE (conditionals, functions, with, and arithmetic expressions).
- 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 grammar 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
. Please include a contract for every function that you
write and include test cases that amply exercise all of the code you’ve
written.
Features to Implement
- Conditionals
-
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 thatif0
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.
Syntax of CFWAE
The syntax of the CFWAE language with these additional features can be captured with the following EBNF:
<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}
Testing Your Code
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 full credit to untested functionality, even if it is correct! Refer to the syllabus for style requirements.
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.
test/exn
. test/exn
tests
for errors, but only succeeds on errors that you explicitly signal.
Support Code
Your code must adhere to the following template, without any changes:
#lang plai (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 [mtEnv] [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 closuerV or a numV) (define (interp expr) ...)
However, 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
xinterp-lazy.rkt
should read:
(define-type CFWAE-Value [numV (n number?)] [closureV (params (listof symbol?)) (body CFWAE?) (env Env?)] [exprV (expr CFWAE?) (env Env?)])
Handin
You should turn in two Racket programs where each contains all of the code needed to run your parser and interpreter. One should be for the eager evaluation, called "xinterp.rkt", and the other for the lazy evaluation, called "xinterp-lazy.rkt". You can also include a readme or other relevant files. From the directory containing the files for the assignment you wish to hand in, execute
/course/cs173/bin/cs173handin xinterp