In this section we will make an Ampersand script that is based on an existing spreadsheet. This technique is useful for quickly adding population to an information system. Ampersand has a facility that allows you to import existing .xlsx files with minimal changes.

## Theory: tables vs. binary relations

We can consider Ampersand as a finite system of relations. Every relation is a set of (ordered) pairs and each pair contains two atoms. However, in the real world we also store information in wider tables, as we do in spreadsheets and relational databases. Here is the trick. If we have two pairs that share the same left atom, e.g. (1, Abraham) and (1, Lincoln), we can put them in the same row. Using the same trick, we can interpret a row in a spreadsheet as a number of pairs.

### Example

Let us look at an example:

firstname lastname birth
1 Abraham Lincoln February 12, 1809
2 Barack Obama August 4, 1961
3 Calvin Coolidge July 4, 1872
4 Dwight Eisenhower October 14, 1890

Since Ampersand works with relations, it must represent this table as relations. Three relations can do the job in the following manner:

POPULATION firstname[President*Name] CONTAINS
[ ("1", "Abraham")
, ("2", "Barack")
, ("3", "Calvin")
, ("4", "Dwight")
]

POPULATION lastname[President*Surname] CONTAINS
[ ("1", "Lincoln")
, ("2", "Obama")
, ("3", "Coolidge")
, ("4", "Eisenhower")
]

POPULATION birth[President*Date] CONTAINS
[ ("1", "February 12, 1809")
, ("2", "August 4, 1961")
, ("3", "July 4, 1872")
, ("4", "October 14, 1890")
]


Notice that the column names in the table correspond with the relation names in Ampersand. In the table we call them "attributes". So it makes sense to say that a relation in Ampersand can correspond with an attribute in a table.

## Practice: how to prepare a spreadsheet

In theory, the population of the Hawaii-script might just as well be given in a spreadsheet. This works in practice too. It looks like this:

[Subject] pass required
Subject Student Destination
Surfing Brown Hawaii
Surfing Conway
Latin Brown Rome
World Religions Applegate
World Religions Brown Rome

Please copy this in a spreadsheet of your own. The element in the first column with square brackets tells Ampersand that a new table starts1. The first row contains relation names. The second row contains concept names. The rows that follow contain pairs. Ampersand reconstructs those pairs as in the example above.

## Reusing existing data

In practical applications, you might want to reuse data from existing spreadsheets. People tend to have lots of "informal administration" in spreadsheets, which gives you access to authentic population. Surely you need that data organized in rows, but fortunately that is reasonably common. In such cases, you just add two lines above each table to inform Ampersand about the relations that are populated. In other cases, you have some work organizing the spreadsheet for importing it.

You will find the Excel import function in the menu bar on the top right of your screen2.

## Assignment

Make a population of your own for the Hawaii-script and put it in a .xlsx spreadsheet. As described above. Make sure to delete the population statements from your Hawaii source code, to make sure that you get to see the population from your .xlsx-file. Generate a prototype from your Hawaii-application, upload your population in Excel and play around with the results.

## What have you learned?

After finishing your assignment, you have learned:

• to understand how a POPULATION-statement relates to the contents of a spreadsheet;