# Alpha Language Specification - Compute Engine

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# Introduction

What is the best way to express and deliver our ideas?

## Types

Complex Number. Real number. Rational number. Integer number. Natural number. $x:X$ï»¿ such that $X=\{...\}$ï»¿, $x\in X$ï»¿. Char. Array.

All types are *first-class.*

# Expressions

Should expressions admit whitespaces in names?

Closure.

## Some expressions

`$ +(||(0.7,0.2)-(0.2,0.3)||_2)`

`$ + . ||(0.7,0.2)-(0.2,0.3)||_2`

`$ ||(0.7,0.2)-(0.2,0.3)||_2 | +`

```
$ (x => x+1)(1)
1
```

`$ interval(1000) | reduce(p => [p[1],p[0]+p[1]],[0,1])`

```
$ connect(protocol=WebRTC) | chat
abc
```

```
connect(protocol=WebRTC, key="abc") |
interval(1000) |
reduce(p => [p[1],p[0]+p[1]],[0,1]) |
echo
```

## Comments

## Declarations and assignments

You can declare new terms but alpha doesnâ€™t allow assignments.

## Expressions

Alpha follows the convention that every expression has a value. The declarations or definitions return their references such that

```
x=6
// x
f(x)=x
// f
```

## Functions

The type of argument is by default real numbers.

`f(x)=x^2`

```
f (a,b,c) = (x1, x2) where
expressions
```

## Pattern matching

## Regular expressions

a ~ /REGULAR_EXPRESSION/g

# Program

UTF-8

Programs are not evaluated on the fly.

Every expression can ask about itself (quine and operational quine).

```
f(x) = x^2
f.self
// f(x)=x^2 : self
f.self.body.self
// x^2 : self
f.self.body.self.evaluate({"x": 1})
// 1^2
f.self.body.self.evaluate({"x": 1}).apply()
// 1
```

# Streams, composition, and pipes

The means of combinations are streams, composition ($f.g$ï»¿), and pipes (g|f).

# Lexical Structure

id: Unicode symbols

# Syntax

# Type rules

# Operational semantics

## Environment

# Commands

# Examples

## Grammar

```
Consider a grammar G4 where its production rules are
S: `X`*
what is its type?
```

```
Consider G4:Grammar where its production rules are
S: X*
what is its type?
```

```
Consider G4:Grammar where we have a environment e and its production rules are
S: X* {x=$$1}
W
```

```
graph TD
G --> Expr
Expr --> Expr+Expr
Expr+Expr --> Expr
Expr+Expr --> Expr
Expr --> 1
```

G â€”> Expr â€”> 1

G â€”> Expr â€”> Expr+Expr â€”>

**Readâ€“evalâ€“print loop and notebook**

## Kernels

```
%% html
%% prolog
%% alpha
```

## Modes

Authoring

Interactive

## References

https://www.npmjs.com/package/react-terminal#features

Jupyter

Wolfram Alpha