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Computer Science in Algebra

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Contracts

Understanding what functions should do and how to make them do it

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Vocab

Contract - a statement of the name, domain, and range of a function
Domain - the type of a data that a function expects
Range - the type of data that a function produces

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What's in a Function?

What does the '+' function do?

What does it take as input?
What does it return as output?

How about the 'triangle' function?
What do these different functions have in common?
Let's look at a simple way to describe any function

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Signing the Contract

What is a Contract?

A formal agreement
A description of expected behavior

Why do Contracts tell us?

What a function should do
What inputs a function needs
What a function returns

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The 3 Parts of a Contract

Name

A descriptive name to tell us what a function does

Domain

The data types that a function takes as input

Range

The data type that a function will return

We write contracts in the form:

Name: Domain -> Range

The Name of a function briefly describes what the function does.

The Domain of a function is the data that the function expects.

The Range of a function is the data that the function produces.

By keeping a list of all the functions in a language, and their Domains, programmers can easily look up how each function is used. However, it’s also important to keep track of what each function produces! For example, a program wouldn’t use "star" if they were trying to produce a Number, because “star” only produces Images.

Domains and Ranges help programmers write better code, by preventing silly mistakes and giving themselves hints about what to do next. A programmer who wants to use "star" can look up the Domain and immediately know that the first input has to be a Number (like 100), without having to remember it each time. Instead of writing a single value there, a programmer could write a whole expression, like (25 * 4). We know this code will return an appropriate value (Number) by looking at the Range for *; therefore, the result of * can be used in place of any Number value.

When programmers write down the Domains and Ranges of each function, they write what are called contracts, to keep track of what each function needs.

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Contract Examples

+: Number Number -> Number

What is this function's Name?
What is this function's Domain?
What is this function's Range?

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Contract Examples

triangle: Number String String -> Image

What is this function's Name?
What is this function's Domain?
What is this function's Range?

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Contract Examples

rotate: Number Image -> Image

What is this function's Name?
What is this function's Domain?
What is this function's Range?

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Writing Contracts

We will write a contract for every function we use

This will be helpful reference when we write code
Keep this reference with you at all times

Start your contract reference by writing contracts for:

+
-
*
/

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Contracts from Blocks

Evaluation Blocks give us some hints for contracts

The Name of each function is at the top
There will be a slot for each Domain element
The color of each slot tells you Domain type
The color of the whole block tells you Range
Color codes: Number String Image .

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Writing Contracts

What is the Name of this function?
What is the Domain of this function?
What is the Range of this function?
Add this function's contract to your reference

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Writing Contracts

What is the Name of this function?
What is the Domain of this function?
What is the Range of this function?
Add this function's contract to your reference

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Writing Contracts

What is the Name of this function?
What is the Domain of this function?
What is the Range of this function?
Add this function's contract to your reference

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Keep up your Contracts

As you continue programming, make sure you write a contract for every new function you encounter or write!