Pi-type

A Pi-type, in the context of logic and type theory, is a way to represent functions that depend on a parameter. Think of it as a rule that assigns a specific type (or category) to each element of a set. For example, if you have a set of objects, a Pi-type describes a family of types where each object has its own associated type. It generalizes the idea of functions by allowing the output type to vary based on the input. Essentially, Pi-types enable precise modeling of functions whose output types change depending on the input, providing a flexible and powerful framework for formal reasoning.