Homework #4 Solution

Description

How to Submit
• Submit one solution per team (each team can have 1–3 members), through TEACH. Put the names and ONID usernames of all team members as a comment at the top of the file.
• Your submission should consist of a file named HW4.<your-username>.hs, where <your-username> is the ONID username of the team member who submitted the file, and possibly an HTML file with your amazing picture (see below).
• Your Haskell file must compile without errors or warnings in GHCi. Put all non-working parts of your solution in comments! If your file does not compile, the TA will not evaluate it.
• Please preserve the existing doctest comments in the template (the lines starting with >>> and the results underneath). This will help the TA during grading.
• If you can’t solve a problem, you can get partial credit by describing in comments what you tried and where you got stuck.
Files
Template: HW4.template.hs
Support files (don’t edit or submit these):
• MiniMiniLogo.hs
• Render.hs
You should download both of these files and put them in the same directory as your HW4.<your-username>.hs file.
Description
MiniMiniLogo is a simplified version of the MiniLogo language that you worked with in HW3, which is itself a simplified version of the Logo language for programming simple 2D graphics.
MiniMiniLogo is like MiniLogo, except that it doesn’t have macros, variables, or addition. This leaves only a very simple syntax remaining.
int ::= (any integer)
prog ::= ε | cmd ; prog sequence of commands
mode ::= down | up pen status
cmd ::= pen mode change pen mode
| move ( int , int ) move pen to a new position
The following MiniLogo program (to draw a 2×2 square with its bottom-left corner at the origin) is also a valid MiniMiniLogo program.
pen up; move (0,0);
pen down; move (2,0); move (2,2);
move (0,2); move (0,0);
A Haskell implementation of the abstract syntax of MiniMiniLogo is already provided for you in the file MiniMiniLogo.hs. It also provides some functions to generate programs that draw simple shapes.
In this assignment, you will be implementing the semantics of MiniMiniLogo. The meaning of a MiniMiniLogo program is: (1) the change in the state of the pen and (2) a list of lines to draw.
Conceptually, the execution environment for a MiniMiniLogo program consists of two parts:
• a canvas rooted at position (0,0) and extending infinitely upward and to the right
• a pen which is always located at a certain absolute point on the canvas, and which can be in one of two states, either up or down
The move command moves the position of the pen from one absolute point to another. If the pen is down when it moves, it draws a straight line connecting the two points. If the pen is up, it just moves to the new point but does not draw a line. The state of the pen can be changed using the pen command as illustrated in the example program above.
The support file Render.hs defines types for representing the state of the pen, and provides a library for rendering the output of a MiniMiniLogo program as an SVG image in an HTML5 file.
Tasks
1. Implement cmd, the semantic function for MiniMiniLogo commands (Cmd). Note that a command updates the state of the pen and possibly draws a line. Therefore, the semantic domain is State -> (State, Maybe Line).
2. Implement prog, the semantic function for MiniMiniLogo programs (Prog). A program changes the state of the pen and may draw several lines. Therefore, the semantic domain is State -> (State, [Line]).
After you have implemented prog, you can use the draw function in the template to run a MiniMiniLogo program and render its output to HTML, which you can then load in your browser. To see if your semantics is working correctly, you can compare the result of running draw demo with this image: MiniMiniLogo-Demo.png
Extra credit
Use your creativity to produce a MiniMiniLogo program that draws an amazing picture! I will show off the most amazing pictures (anonymously) in class.
To get extra credit, you must do two things:
1. Define the amazing variable in the template file. This should be the MiniMiniLogo program that generates the amazing picture.
2. Submit the .html file produced by running draw amazing. To make things easier for me, first rename this file to reflect your amazing picture. For example, if your amazing picture is the Mona Lisa, name the file MonaLisa.html.
The amount of extra credit awarded will be proportional to the technical impressiveness and/or artistry of the amazing picture.
To make a truly amazing picture, you will probably need to define some helper functions that generate parts of your MiniMiniLogo program, similar to box, nix, and steps in MiniMiniLogo.hs. You are free to define as many of these helper functions as you wish.
In the past, some students have also modified the Render.hs file to make their pictures even more amazing. If you decide to go down the rabbit hole, please also submit your modified Render.hs file so that we can reproduce your amazing picture.