# Logimat

Logimat is an esoteric programming language created by User:Uellenberg which allows compiling code similar to conventional programming languages into math functions and expressions (such that they can be evaluated by a scientific calculator). Its output is in the form of LaTeX, and it supports compiling to format uses by the Desmos graphing calculator. Logimat's syntax is inspired by TypeScript and Rust. Files containing Logimat code end with the extension .lm.

## Description

A program in Logimat consists of a series of functions, constants, and expressions. Each item of this type will be compiled to math syntax and appear as a line in the compiler's output. Programs in Logimat resemble those written in languages like TypeScript, but there are two important differences: mutability and iteration aren't possible in standard math notation, and so aren't possible in Logimat. There are tricks that can be used to remedy this, but do to these restrictions many programs cannot be expressed in Logimat, or need to be approached from a completely (often inefficient) angle.

## Examples

### Basic Example

Here is a simple program written in Logimat. It defines a constant s set to 5, as well as a function a(x) that will output sin(x) if the whole number part of x is odd, and cos(x) if it is even.

export const s = 5;

export function a(x){
if(floor(x/s) % 2 == 1) {
sin(x)
} else {
cos(x)
}
}


The compiler will give the following output:

s=5
a(x)=\operatorname{floor}\left({2}^{-\operatorname{abs}\left(\operatorname{mod}\left(\operatorname{floor}\left(\frac{x}{s}\right),2\right)-1\right)}\right)\operatorname{sin}\left(x\right)+\left(1-\operatorname{floor}\left({2}^{-\operatorname{abs}\left(\operatorname{mod}\left(\operatorname{floor}\left(\frac{x}{s}\right),2\right)-1\right)}\right)\right)\operatorname{cos}\left(x\right)


Rendered:

${\displaystyle s=5}$
${\displaystyle a(x)=\operatorname {floor} \left({2}^{-\operatorname {abs} \left(\operatorname {mod} \left(\operatorname {floor} \left({\frac {x}{s}}\right),2\right)-1\right)}\right)\operatorname {sin} \left(x\right)+\left(1-\operatorname {floor} \left({2}^{-\operatorname {abs} \left(\operatorname {mod} \left(\operatorname {floor} \left({\frac {x}{s}}\right),2\right)-1\right)}\right)\right)\operatorname {cos} \left(x\right)}$

### More Examples

More examples for Logimat can be found here.

## Usage

### Setting up

The easiest way to use Logimat is to install it through npm. If you have node installed, you can run npx logimat to run Logimat's command-line. This command-line has many options, the most important of which are -p and -s. -s helps prevent mistakes by adding strict variable checking, and -p allows exporting with piecewise output, which should be used if you are planning to use the output in Desmos (as it's a Desmos-specific feature that makes logical operations faster).

### Language

One important thing to keep in mind with Logimat is that it is based on Javascript, and a lot of its language features are built to emulate how the same thing would be handled in Javascript.

#### Blocks

One term used frequently in Logimat is a block. A block is simply a {} with something inside of it. For example, the following is a block:

{
1
}


Blocks are found as function bodies, if statement bodies, sum bodies, and many more things. Also, blocks can be used directly as expressions, so

const val = {
1
};


is perfectly valid.

#### State, early returns, and other restrictions

Because Logimat compiles to math, there are a few restrictions that it has. Namely, it has no ability for early returns. In order to return a value, you must set the state. The state is a variable that can be read and written to, as opposed to constants, which can only be written to. At the end of a block (something inside {}), the state must be set, or else a compile error will be thrown. Below is an example of setting the state:

state = 1;


It's also possible to avoid the state variable entirely by using constants and implicitly returning. This is a syntax ver similar to rust. For example, the following are equivalent:

const v = {
if(x == 1) {
state = 7;
} else {
state = 5;
}
};

state = v * 10;

const v = {
if(x == 1) {
7
} else {
5
}
};

v * 10


Whether you use state or not is up to you. It can be nicer when dealing with more complicated functions (you can change its value), but everything that can be done with state can also be done with implicit returns (that's when we write an expression with no semicolon) and consts. Basically, state is more powerful (but isn't always needed), while consts + implicit returns looks prettier. I'll be using implicit returns and consts here, but state syntax works as well.

Here's another example of state:

state = x * 10;
state = state + 1;
state = state / 5;


These will chain together and are equivelent to:

((x * 10) + 1) / 5


There are some restrictions on what you can do, but the syntax exists to guide you into not needing to worry about it. If something looks like it works within the valid syntax, it probably does.

### Divide By Zero

One thing to be aware of is that if you have a divide by zero anywhere in your code, everything will be undefined (this goes for other undefined operations as well). Even if the divide by zero happens somewhere in an if statement that doesn't run, it will still return undefined. There are ways to get around this. Take a look at the quadratic-factor example for more info.

#### Names

In Logimat, there are two types of names: inlined and exported names. Inlined names don't actually appear anywhere in the output, so they can be less restrictive than exported names. Inlined names are found on inline consts/functions (and their args), or consts defined inside of blocks. An inlined name must start with a letter, but it can have letters, digits, or underscores after it (for example, valid_inlined_name1). An exported name (found in exported consts/functions (and their args), and map variables), on the other hand, must either be a single letter, or it must be a letter, followed by an underscore and letters/digits/underscores (for example, v_alid_exported_name1). All names cannot contain spaces.

#### Imports

Imports are statements that import something (currently just templates) from a library. They follow the following format:

import templates from "PATH_HERE";


Where PATH_HERE is either a file path, or a npm package. This will make all templates in that library accessible to your file.

#### Outer Declarations

Logimat is split up into outer declarations. These outer declarations are things that will be output when it is compiled, or things that will be globally available. Below are the different kinds of outer declarations that exist.

##### import!

Import is technically a template, but it's common enough that it deserves its own section. Import is a template that imports other files. It is important to note that import works relative to the file running it, and not the main file. Here's how import is used:

import!("PATH.lm");


Where PATH.lm is a path to a file.

##### function

Functions are standard functions. They take in some inputs and return an output. Additionally, functions can be either exported or inlined, where exported means that they will appear as part of the output, and inlined means that they will not be. Exported functions' names can only be a single character long, with multi-character names being achieved using an underscore (for example, m_ethod). Inlined functions, on the other hand, have access to multi-character names.

An important feature of functions is that they return a value. In order to facilitate this, somewhere in the function the state must be set.

Here are a few examples of functions:

export function a_function(a, b) {
a * b
}

inline function an_inline_function(arg1, arg2) {
arg1 + arg2
}

##### const

Consts are variables. When used in outer declarations, they are accessible everywhere. Like functions, they can also be exported or inlined, and have a value attached to them. Here are a few examples of constants:

export const a_const = 1;

inline const an_inline_const = 2;


#### Inner Declarations

Inner declarations are things found inside of blocks. They include const, state, if statements, and many more. Below is an overview of them.

##### state

This section is just about state. Please see the section on state above before looking through this.

Inside of blocks, the state can and must be set. You can think of the state like a return statement, except it does not stop the block from running. At the end of the block, whatever the state was last set to will be the result. Below is an example of setting the state inside a function:

export function a() {
state = 1;
}

##### const

Consts can also appear inside of blocks. They are identical to outer declaration consts, except they are not exported/inlined (and they have the same naming rules as inlined consts). As their name implies, constants are constant, and cannot be modified. The only variable that can be modified is the state. Below is an example of a const inside a function:

export function a() {
const val = 1;
val
}

##### let

Variables can be created using the let keyword. Unlike constants, variables can be modified. It is extremely important to keep in mind that variables are only a convenience provided by the compiler, and do not allow actual mutability. Variables from inside of a sum/product/derivative/integral cannot be written from inside of it. For this reason, and because they can easily create duplicated code, variables are not recommended. They are, nonetheless, a useful feature that can simplify certain scenarios. Below is an example of a variable inside a function:

export function a(x) {
let val = 1;
if(x == 0) {
val = 2;
}

val
}

##### if

One very important statement in Logimat is the if statement. It acts as a normal if statement, except that an if statement must be paired with an else statement, unless the state was set prior to the if statement running. Else can also be paired with if with an else if.

Below is an example of its usage (both functions return the same value):

export function a() {
const val = 1;

if(val == 1) {
1
} else {
0
}
}

export function b() {
// This is an example of where state can be useful.
// We can declare a "fallback value" using state, so that if the
// if statement doesn't run, 0 is returned.
state = 0;

const val = 1;

if(val == 1) {
1
}
}


As a side note, the == 1 shown above can be omitted, as the if statement treats 1 as true.

## Graphgame

Graphgame is an extension to Logimat (used through the import keyword) that provides a game/animation engine. Documentation for Graphgame can be found on its GitHub Page and can be used through an online editor, and a full-featured example game is available here.