1.1 Components
Components are the basic building blocks that we'll use to construct functions. A component has an output wire on its left side and a fixed number of input wires on its right side. Here are the addition, subtraction,
multiplication, and division components.
The squaring and cubing components each have one input wire,
as do the square root and cube root components.
Given values for each of its input wires, a component produces a single value for its output wire in a reproducible way. When we give the squaring component an input three, it will produce the output \( 3^2 = 9 \).
When a component has more than one input wire, we read its inputs from top to bottom. For example, when we give the subtraction component the inputs \( (8, 2) \), it will output the result \( 8 - 2 = 6 \).
A constant component takes no input and will always produce the same output.
Every number gets its own constant component.
Schematics
By connecting up the wires between several components, we can create a schematic. We can think of a schematic as a large component made up of smaller components.
A schematic may have multiple input wires and multiple internal wires, but we expect it to have a single output wire, only. We'll always attach wires compatibly: one component's output wire is another component's input wire.
Important.
We will never wire output to output nor input to input.
We evaluate a schematic by pushing the given input values across components from right to left. Let's see how this works with an example.
Example.
Let's evaluate the following schematic for the pair of inputs \( (4, 3) \). We start by placing the inputs on the right-most wires.
Pushing the values across the components, we find that schematic produces the output value five on its left-most wire.
A schematic can include components, wires, and one other kind of object: a splitter.
A splitter duplicates its input by producing the same value on each of its output wires. Since a splitter does not have a single output wire, it is not considered a component.
Example.
Let's evaluate the following schematic for the input three.
Our input is duplicated by the splitter, and the constant component introduces its value, one.
The schematic's output is three-quarters.