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Thomas de Grivel <thoxdg@gmail.com>

https://kmx.io/

2020-05-17

# Language

## Structure

### Three components

Any formal language usable with a model is composed of three things :

 - A schema (or grammar)
 - Semantics
 - Data

### Schema

In model theory a schema allows you to define an ontology,
that is a definition of what can and cannot be expressed in your
language.

It is a set of rules which make any pattern part of the language or not.

The most used schemas for formal language definition are grammars.

The schema is a generalistic view of all the data that can be
expressed in the language.

It can be a relative process where parts of the structure of the
language are combined to form a more complex schema, e.g. a
grammar made of simpler rules.

### Semantics

Semantics tell you the meaning of the language. They describe
how to translate your language into another one.

This is a relative process : a semantic is from a language to another,
even if it is the same language acting as source and destination
language.

Semantics give meaning to your language which otherwise is just another
data model.

A number of programming languages also export the semantics of
lower-level constructs such as mathematical operations from the processor
or disk access from the kernel.

Semantics tells you how your language relates to other languages.
It is a connection to other languages.

### Data

Data is valid use of the language for reasons pertaining to its
semantics.

It is a direct application of the language schema.

Semantics are appliable to all data.

Data is a choice from the possibilities of the language schema
driven by the semantics of the language.

Each datum represents a single valid use of the language and can
be uniquely identified.