**PROJECT AUTOPIA**

**Mathematical Notation**

**Abstract**

(WARNING: this system is currently in development and might differ from the final one)

*The official international standard of mathematical notation of the Universal Selfederation.It is also intended to be used in scientific equations and formulas. *

**Syntax**

*In the autopian mathematical notation, every expression has the same basic form;
any given function application is represented by an horizontal line (called "application line") separating the function operator from its arguments; the first is placed above the line, the latter are arranged horizontally below it.*

Examples of basic expressions: generic function "a" applied on an increasing number of generic arguments ("b", "c" and "d").

*Expression can be nested: if a function application is in turn an argument of another function, the other arguments of the latter are lined next to the former one's operator, outside the range of its line.*

Example of a nested expression: function "a" applied on the arguments "b", "c" and a third argument that's the result of the function "d" applied on the arguments "e", "f" and "g".

*If a function application is in turn the function of another application (i.e.: the first one is an higher-order function), the whole expression of the former is used as the latter's operator, and therefore it lies above the arguments of the latter.*

Example of a nested expression: higher-order function "a" applied on the arguments "b", "c" and "d", resulting in another function applied on the arguments "e", "f" and "g".

*The system features some rules for simplifying complex expressions:
1) An application line does not need to span the entirety of its arguments' expressions: it only needs to be long enough to barely reach (width-wise) all the symbols involved in its expression who are immediately above it or immediately below it*

Examples showing how certain expressions can be simplified.

**Examples**

Examples of mathematical expressions written with the syntax of the autopian notation.

**Symbology**

*(work in progress...)*

**Return**