# BYU CS classes

cs330_f2016:laby

### Objective:

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!

### Prerequisite:

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 “Julia” subsection, on the page titled “Arithmetic expression interpreter and lexer”.

You can also find these files in Dr. Wingate's home directory:

/users/faculty/wingated/cs330/julia_interpreters

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 code development, you may wish to use the IJulia plugin for Jupyter (which we used in class), or another IDE of your choice.

### Deliverable:

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 parse and calc functions, and a single type, Num.

Remember that you will use multiple dispatch to implement different “versions” of parse and 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 BinOp.

#### Operator Table

Define a data-structure to contain a mapping from operator symbols to the functions that actually implement that symbol. For example:

Dict(:+ => +)

#### Parser

Write the following function(s):

function parse(expr)

expr will always be the output of the lexer, and will consist of numbers, symbols, and lists of numbers and symbols.

parse parses expr into an OWL datastructure according to this grammar:

  <OWL>	 	::=	 	number
|	 	(+ <OWL> <OWL>)
|	 	(- <OWL> <OWL>)
|	 	(* <OWL> <OWL>)
|	 	(/ <OWL> <OWL>)
|               (mod <OWL> <OWL>)
|               (collatz <OWL>)
|               (- <OWL>)

where number is a Julia number.

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 try…catch block.

You must parse expr into the following types (copy and paste this to the top of your code):

abstract type OWL end

type Num <: OWL
n::Real
end

type Binop <: OWL
op::Function
lhs::OWL
rhs::OWL
end

Plus any other subtypes you deem necessary.

#### Interpreter

Write the following function:

function calc(e)

Consumes an OWL representation of 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.

### Implementing mod

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!).

### Implementing collatz

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

### Hints:

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()
using ClassInt
3. Make sure the path for the Error and Lexer files are on you Julia path. To do this you can call JULIA_LOAD_PATH=PATH python …. or you can add push!(LOAD_PATH,pwd()) into your juliarc file.
4. Inside your module have the lines using Error and using Lexer.