Modeling

Everything What Is is a sub-process and has a structure. Understanding of a structure is knowing. Otherwise that would be believing.

Mathematics is the language for capturing patterns and describing structures and processes.

Verbalized information is knowledge encoded for a communication, which uses a human language as a medium.

Every verbalization (a description or a formal model) is inevitably different (distant) from What Is, and is an adequate generalized over-simplification (an approximation). This is what we hope for.

A verbalization is not an actual experience, a “map” is not the territory.

Mathematical and programming language models are mere verbalizations too. It is a knowledge in a written form which uses some standard (agreed upon) notation which precise meaning (semantics).

Just like mathematical notation, formally defined pure-functional programming languages are the best for writing models.

A proper abstraction is a captured pattern - a generalized and over-simplified concept which abstracts our all the irrelevant details and particulars.

It has nothing to with abstractionism as an art-form, which is ephemeral and emphasize vagueness and unreality.

Simple geometric figures are the best example of proper abstractions, which capture and generalize essential patterns of certain shapes.

It is also a well-defined mapping to a simple, well-understood general concepts, such as a Sequence or a Set, or a Relation.

Simple models which capture and generalize actual (non-imaginary) patterns are the only useful.

A Set, a Function and a Sequence are probably the most used abstractions. No wonder they are at the core of Functional Programming.

Type-Traits and Type-Classes, which have more structure than mere Sets of Values are general ways of capturing and defining proper abstractions.

This is how one combines and nests simple types.

These are the fundamental building blocks of formal models in pure-functional languages.

This is how to model processes outside your head.