This lab is designed to help you begin to understand how to design and implement an interpreter for a simple language. The concepts you will practice here will be foundation to further labs!
You will need to download and install Julia for this lab.
Note: if you are using Ubuntu 14.04, do not use the
apt version of Julia (it's too old!). You should use at least Julia 0.6.
Note that the lexer required for this lab is available on LearningSuite, in the “Content” section, under the “Interpreters” subsection, on the page titled “Base Interpreter”.
You will also need the
Error.jl file. You may choose to poke around with
Repl.jl, which provides an interactive lisp-style REPL.
For this lab, you will create a simple interpreter for a language we call OWL (“Our Widdle Language”). You need to create a Julia module that implements all requisite functionality.
Your module should export
Remember that you will use multiple dispatch to implement different “versions” of
calc, based on the input type.
An important difference between the code that you will implement for this lab, and the code we went through in class, is that your code should properly abstract multiple binary AST nodes into a single class we'll call
Please name your module RudInt.
Define a data-structure to contain a mapping from operator symbols to the functions that actually implement that symbol. For example:
Dict(:+ => +)
Write the following function(s):
expr will always be the output of the lexer, and will consist of numbers, symbols, and lists of numbers and symbols.
expr into an OWL datastructure according to this grammar:
<AE> ::= number | (+ <AE> <AE>) | (- <AE> <AE>) | (* <AE> <AE>) | (/ <AE> <AE>) | (mod <AE> <AE>) | (collatz <AE>) | (- <AE>)
where number is a Julia real number literal.
You should have test cases for all legal and illegal types of expressions. For example, the expression
(+ 1 2 3) will pass the lexer just fine, but it is not accepted by our grammar – our grammar can only handle two arguments, not three!
If you are given invalid input, you must throw an error, such as
throw( LispError(“Whoa there! Unknown operation!”) ). This is defined in
Error.jl. Do not just print an error message, as this will not by caught by the autograder's
You must parse
expr into the following types (copy and paste this to the top of your code):
abstract type AE end type Num <: AE n::Real end type Binop <: AE op::Function lhs::AE rhs::AE end
Plus any other subtypes you deem necessary.
Write the following function:
Consumes an OWL abstract syntax tree representing an expression and computes the corresponding numerical result.
It should throw a Lisp error if division by zero or collatz of a negative number or zero is attempted.
This interpreter has another binary operation called
mod, similar to other binary operations. You should implement it in Julia using Julia's built-in
mod function (note that this is not the same as the
% in-line operator, at least for negative numbers!).
One of the fundamental “primitives” in our language is a function called
collatz. This function is commonly used as an example of a function that is simple to write, but which cannot be analyzed – illustrating the difficulty of the general problem of program analysis. It comes from the
Collatz conjecture. Our collatz function returns the number of times the function recurses. Note that for some numbers, such as
n=28, the function returns quite quickly – only 18 iterations – but for neighboring numbers, such as
n=27, the function takes 111 iterations!
The function is defined as:
function collatz( n::Real ) return collatz_helper( n, 0 ) end function collatz_helper( n::Real, num_iters::Int ) if n == 1 return num_iters end if mod(n,2)==0 return collatz_helper( n/2, num_iters+1 ) else return collatz_helper( 3*n+1, num_iters+1 ) end end
Note that the
- operator has two distinct usages: as a binary operation (the “minus” operation) and as a unary operation (“negation”). You should create a distinct class to handle unary operations.
If you change a module, it can sometimes be tricky to convince Julia to reload it. I have found that the following two commands work:
workspace() reload("RudInt") ... using RudInt
In order for your code to work with the solo-grader you will need to do following:
JULIA_LOAD_PATH=PATH python ….or you can add