#### DocDiff

##### 1` `Introduction

Consider the problem of comparing two text documents. Why might you want to do this? Perhaps you want to check for plagiarism, search for articles similar to a particular one you’re studying, or have uncovered a new manuscript and want to know whether it’s a legitimate Shakespeare or a fake. All these require being able to determine the similarity between documents.

##### 2` `Theme Song

Changes by David Bowie

##### 3` `Definition

[list: "The", "quick", "brown", "fox", "jumps"]

In order to compute the similarity between two documents, we associate each document with a mathematical vector, which here we will represent using a list of numbers. The indices of the vector correspond to words that are found in either document. The value at each index is how many times the corresponding word occurs in the document.This is called the bag of words model. It’s a “bag” because, like a set, order doesn’t matter, but the count does.

For example, the documents [list: "a", "b", "c"] and [list: "d", "d", "d", "b"] would result in vectors of length 4, accounting for all unique words ("a", "b", "c", and "d"):

| "a" |
| "b" |
| "c" |
| "d" | |

[list: "a", "b", "c"] |
| 1 |
| 1 |
| 1 |
| 0 |

[list: "d", "d", "d", "b"] |
| 0 |
| 1 |
| 0 |
| 3 |

Therefore, the two documents will respectively have the representations [list: 1, 1, 1, 0] and [list: 0, 1, 0, 3].

Note: When comparing two documents, the same length vector is used for both documents because the vector accounts for all the words across both documents.

We assume that two words are the same if they have the same characters in the same order, ignoring upper- and lower-case (Pyret has functions to upper- or lower-case a string, and for sorting; you can look up these functions in the string and list libraries.)

We define the overlap between two documents, represented this way, to be proportional (\(\propto\)) to the dot product of these two document vectors:

\[overlap(\vec{d_1}, \vec{d_2}) \propto \vec{d_1} \cdot \vec{d_2}\]

To obtain a formula, we normalize this dot-product. We will choose a simple method, which is to divide by the squared magnitude of the larger vector:

\[overlap(\vec{d_1}, \vec{d_2}) = \frac{\vec{d_1} \cdot \vec{d_2}}{max(\|\vec{d_1}\|^2,\|\vec{d_2}\|^2)}\]

where the magnitude of a vector \(\vec{x}\), denoted as \(\|\vec{x}\|\), is given by \(sqrt(\vec{x} \cdot \vec{x})\). Observe that this means every document will have an overlap of 1 with itself, and any two documents that have no words in common will have overlaps of 0 with each other.

##### 4` `Assignment

fun overlap(doc1 :: List<String>, doc2 :: List<String>) -> Number: ... end |

Note that we are not asking you to consider efficiency of implementation.

##### 5` `Language Use

You may not use built-in sets; everything in the list library is permitted.

##### 6` `Background

You will find this chapter useful in learning to convert from Racket to Pyret, and this one useful for learning more about lists in Pyret.

##### 7` `A Warning

You’ll be reusing DocDiff later in the semester! Therefore, if you falter in this assignment, you’ll want to make sure you understand what you did wrong.

##### 8` `Starter

##### 9` `Handing In

You will submit three separate files, named docdiff-code.arr, docdiff-tests.arr, and docdiff-common.arr (which may effectively be empty).