# Formal Languages

% Remco Bloemen % 2014-02-27

## Classical languages

Classically formal languages are serial. Using brackets the language can express hiearchical structures. Using bound variables the languages can contain arbitrary expressions?

Problem areas: complex structures, reflection, self-reference.

Lambda calculus: one can dispense entirely with multiple inputs and multiple outputs by currying the inputs. However, I think this is unnatural.

## Proposed alternative

Concepts, applications and definitions.

The fundamental entity of the language is understood as an application (as in "a concept that is applied" not as in a piece of software). An application has a number of arguments and results. Sentences can be constructed by composing applications, one connects all the inputs of the algorithms to the outputs of others.

Well-formed sentences have exactly one output assigned to every input and contain no cycles.

Now that the concept of application is understood, there is a second concept required, that of definition.

A concept

Remco Bloemen
Math & Engineering
https://2π.com