Axiom Interval

A PHP library that extends gosuperscript/axiom with support for Interval types: a Type that validates and coerces intervals, and an Extension that teaches the compiler to compare them.

Features

• Interval Type: Validate and coerce interval values at a program's boundary
• Operator rules: Compare an interval against a number (>, <, >=, <=) and two intervals for equality (==, !=), resolved and type-checked at compile time
• Type Safety: Built with PHP 8.4+ strict types
• Format Support: Parse intervals from string notation (e.g., [1,2], (1,2))

Requirements

• PHP ^8.4
• ext-intl
• gosuperscript/axiom
• superscript/interval ^1.0.4

Installation

Install via Composer:

composer require gosuperscript/axiom-interval

Usage

The interval type

IntervalType is an Axiom Type: it coerces and asserts interval values, formats them, and projects into the shape algebra as an opaque interval identity.

use Superscript\Axiom\Interval\Types\IntervalType;

$type = new IntervalType();

// Coerce from a string or an Interval object
$interval = $type->coerce('[1,2]')->unwrap()->unwrap();

// Assert an existing Interval object (strict membership)
$type->assert($interval)->isOk(); // true

// Format back to string notation
$type->format($interval); // "[1,2]"

Interval notation

• [1,2] — Closed interval (includes both endpoints)
• (1,2) — Open interval (excludes both endpoints)
• [1,2) — Half-open (includes left, excludes right)
• (1,2] — Half-open (excludes left, includes right)

The extension

IntervalExtension contributes the interval's operator rules and its literal registration. Compose it onto the core dialect and hand the dialect to an expression; the compiler resolves and type-checks every operator against it, and the compiled Program runs what it resolved — no runtime dispatch.

use Superscript\Axiom\Dialect;
use Superscript\Axiom\Expression;
use Superscript\Axiom\Interval\IntervalExtension;
use Superscript\Axiom\Interval\Types\IntervalType;
use Superscript\Axiom\Sources\InfixExpression;
use Superscript\Axiom\Sources\StaticSource;
use Superscript\Axiom\Sources\SymbolSource;

$dialect = Dialect::core()->with(new IntervalExtension());

$expression = new Expression(
    new InfixExpression(new SymbolSource('range'), '>', new StaticSource(1)),
    dialect: $dialect,
    declarations: ['range' => new IntervalType()],
);

$program = $expression->compile()->unwrap();

$program(['range' => '[2,3]'])->unwrap()->unwrap(); // true — [2,3] lies above 1

Supported operations

• Ordering against a number — interval > number, >=, <, <= → boolean. The interval is the left operand.
• Equality against another interval — interval == interval, != (and the =/===/!== aliases) → boolean. Core refuses equality on opaque operands, so the interval package owns its own.

Operand types that no rule accepts — interval == number, interval + interval — are refused at compile time with a named diagnostic, never at runtime.

Development

Testing

Run the full test suite:

composer test

Or run individual suites:

# Type checking with PHPStan
composer test:types

# Unit tests with PHPUnit (requires 100% code coverage)
composer test:unit

# Mutation testing with Infection
composer test:infection

Code Style

This project uses Laravel Pint for code formatting:

vendor/bin/pint

License

This project is licensed under the MIT License - see the LICENSE file for details.

Credits

• Built on superscript/interval
• Extends gosuperscript/axiom