Project 0 - First Interpreters

Project 0 - Implementing our First Interpreters EECS 662 - Programming Languages

The objective of this project is to develop your first rudimentary interpreters. You will extend with the AE language presented in class to get up-to-speed with Haskell and write three different interpreters using three different styles. For this project AE will be extended to include an if0 construct in addition to constructs discussed in class:

AE ::= Nat
        AE + AE |
        AE - AE |
        AE * AE |
        AE / AE |
        if0 AE then AE else AE

The new construct, if0, is an expression that evaluates its first argument and if it is 0 evaluates its second. If not it evaluates its third.

Assume that Nat represents the natural numbers as we have been discussing in class. You must add error handling for negative numbers.

To aid in your quest the file p0.hs implements the Haskell AE data type and a parser from strings to the data type. At the bottom of the file you will find signatures for the four functions required for the four exercises below. Take a careful look at this file before you begin.

Exercise 1

Write a function, evalAE::AE -> Int, that takes a AE data structure, evaluates it, and returns an Int. If your interpreter fails, it should throw an error using the error function discussed in class. Remember that Nat is a natural number and cannot be negative.

Exercise 2

Write a function, evalAEMaybe::AE -> Maybe Int, that takes the same AE data structure as Exercise 1, evalutes it, and returns a value. Use Just to return a number and Nothing to indicate an error. Do not use Maybe as a monad in this interpreter. Use if and/or case to process errors.

Exercise 3

Write a function, evalM::AE -> Maybe Int, that takes the same AE data structure as Exercises 1 & 2, evaluates it, and returns a number. This time, use the do notation to treat Maybe as a monad.

Exercise 4

Write a function, interpAE that combines the AE parser and evalM into a single operation that parses and then evaluates an AE expression. You will be provided a parser and must integrate it with your interpreter.

Notes

Most if not all the code for the AE interpreter can be found in our text. I would encourage you to try to write as much of it as possible without referring to the textbook examples.

The evalM function closely resembles the interpreters we will write for the remainder of the semester. The do notation and monads make things much easier and make our code look more like its formal representation. You don’t have to deeply understand monads to use them. The Maybe monad in this project is an example of that.

To give you an idea of the effort required for this project, my code is about 100 lines long and took me roughly an hour to write and debug. I view this as an easy project at this point in the semester. Do not put it off as most of you haven’t used Haskell in some time. Additionally, you’ll need to figure out how to use the Haskell tools installed on EECS machines or install them on your own.