CS 3540: Programming Languages and Paradigms

Homework 9
Boom, A Little Arithmetic Language

Due: Monday, April 21, at 11:59 PM

Introduction

This assignment gets you started on your work for the rest of the semester: an interpreter and other tools for processing a small language. This language may seem a bit more useful to you than the little language we have worked with up to now, because it will has real numbers and real operations, and it solves real problems.

Before going any farther, read the Boom language specification. It defines the language and talks about some of the Racket you can use to implement your homework.

Code and Files

For this assignment, you will implement the initial components of a Boom interpreter, including syntax procedures that define its abstract syntax, a pre-processor to eliminate syntactic abstractions, and an evaluator. Organize your code as follows.

Make sure that each file provides all of its public functions so that other files can require them. For example, interpreter.rkt will require syntax-procs.rkt and provide only the preprocessor and evaluator. Any file may want to require utilities.rkt in order to use one or more of its functions.

We will extend the Boom language and interpreter on future homework assignments. Please comment your source code so that you and I can easily find the various pieces.

Problems

  1. Define a complete set of syntax procedures for Boom.

    For each type of expression in the BNF description, define:
    • a type predicate,
    • a constructor, and
    • one or more access procedures that retrieve the relevant parts of the expression.
    The names you choose for your constructor and type predicate should be the same except for the type predicate's trailing "?". The names your choose for your accessors may be short, but they should be descriptive.

    Finally, create a general type predicate named (boom-exp? arg) that returns true if and only if arg is a legal expression in the language: a number, a unary expression, or a binary expression.

  2. Define a function named (preprocess sugared-exp).

    sugared-exp is a Boom expression from the full syntax of the language, which includes the operators sq and @.

    preprocess returns an expression in the core Boom language, with the syntactic abstractions translated into equivalent expressions, and all other expressions preserved. For example: 
    > (preprocess '(3 @ 9))
((3 + 9) / 2)

> (preprocess '(- (3 @ 9)))
(- ((3 + 9) / 2))

> (preprocess '((2 * 14) + (13 @ 29)))
((2 * 14) + ((13 + 29) / 2))

  3. Define a function named (eval-exp exp).

    exp is a Boom expression from the full syntax of the language. If exp is not a legal Boom expression, eval-exp signals an error. For example: 
    > (eval-exp '(4 sq 3))
boom: illegal expression -- (4 sq 3)
    eval-exp returns the value of exp as its result, according to the language's semantics.

    Note that exp can contain sugar, so eval-exp must pre-process its argument before evaluating it! You may want to make eval-exp an interface procedure that ensures its argument is a legal expression, preprocesses it, and calls a helper to evaluate the resulting core expression.

    For example: 
    > (eval-exp '(- 3))
-3

> (eval-exp '(sq 3))
9

> (eval-exp '(9 + 6))
15

> (eval-exp '((- 3) + (sq (4 * 2))))
61

> (eval-exp '(8 & 3))
boom: illegal expression -- (8 & 3)

> (eval-exp '(3 @ 9))
6

> (eval-exp '((2 * 14) + (13 @ 29)))
49

> (eval-exp '(((130 - 2) / 4) @ (15 / (17 % (sq 4)))))
23
    The language description provides more sample expressions for testing. You can also find other simple test expressions in the description of Boom's semantics. Be sure to test other expressions, including some that are more complex.

    Some notes on the use of Racket to implement the evaluator:
    • You may not use Racket's eval function in your solution. The job of your Boom evaluator is to handle all of it operations directly.
    • You may find Racket's quotient and remainder functions useful when implementing Boom's integer division operations.
    • You may find Racket's expt function useful when implementing Boom's ^ operation.

Deliverables

By the due time and date, use the course submission system to submit the following files electronically:

Be sure that your submission follows the submission requirements. As always, use the specified names for your files. This enables the auto-grader to find and run your code.