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- Jul 20, 2025
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- #1
Functions
In math, we know something like $f(x) = x + 1$ and we'd get Input `3' to Output `4' . Then: What is a function?
A function is a rule that makes inputs into outputs.
Functions can represent behavior:
Things get messy
Lets say now we want to do
Notice how they all operate on the same thing: radius.
Functions cluster around data?
We now have our circles radius, and functions that act on that. The radius is data, and those functions add on it. We have: data + functions that act on it. This is what a class brings together
So what is a class?
A class is a bundle of data and functions that operate on the data. So instead of circleArea(radius) we write circle.area(). We attach the function to the data.But, radii of circles does not really demonstrate my point properly. I will switch.
Can we express a class in math?
A class can be a pair?:
$C = (S,M)$
Where: $S$ is the data and $M$ is a set of methods that transform the state. Each method is a function. For example we have a bank account:
\begin{equation}
S = \{ bank balance, account owner \}
F = \{ deposit,withdraw \}
\end{equation}
and each function looks something like
\begin{equation}
deposit: S \times amount \to S
\end{equation}
So, the class transfors the state. So a class is a state space + state transition functions
What do classes do?
Classes let us make many states that have the same rules. Say we have three bank accounts with their own states. They will share the same functions. [therefore] classes separate rules and instances.
So then a class defines state machine?
Yes. methods are transitions. Each method moves the bank account from one state to another, and an object is an instance running that.
In math, we know something like $f(x) = x + 1$ and we'd get Input `3' to Output `4' . Then: What is a function?
A function is a rule that makes inputs into outputs.
Functions can represent behavior:
Haskell:
circleArea :: Double -> Double
circleArea radius = 3.14 * radius ^ 2Things get messy
Lets say now we want to do
Haskell:
circleArea :: Double -> Double
circleArea radius = 3.14 * radius ^ 2
circleCircumference :: Double -> Double
circleCircumference radius = 2 * 3.14 * radius
circleDiameter :: Double -> Double
circleDiameter radius = 2 * radius
radius :: Double
radius = 1.0
circleDiameter radius
circleCircumference radius
circleArea radiusNotice how they all operate on the same thing: radius.
Functions cluster around data?
We now have our circles radius, and functions that act on that. The radius is data, and those functions add on it. We have: data + functions that act on it. This is what a class brings together
So what is a class?
A class is a bundle of data and functions that operate on the data. So instead of circleArea(radius) we write circle.area(). We attach the function to the data.But, radii of circles does not really demonstrate my point properly. I will switch.
Can we express a class in math?
A class can be a pair?:
$C = (S,M)$
Where: $S$ is the data and $M$ is a set of methods that transform the state. Each method is a function. For example we have a bank account:
\begin{equation}
S = \{ bank balance, account owner \}
F = \{ deposit,withdraw \}
\end{equation}
and each function looks something like
\begin{equation}
deposit: S \times amount \to S
\end{equation}
So, the class transfors the state. So a class is a state space + state transition functions
What do classes do?
Classes let us make many states that have the same rules. Say we have three bank accounts with their own states. They will share the same functions. [therefore] classes separate rules and instances.
So then a class defines state machine?
Yes. methods are transitions. Each method moves the bank account from one state to another, and an object is an instance running that.
