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ARO-0052: Numeric Separators

  • Proposal: ARO-0052
  • Author: ARO Language Team
  • Status: Implemented
  • Requires: ARO-0001

Abstract

This proposal extends numeric literal syntax to allow underscore (_) characters as visual separators in decimal integer and floating-point literals. This feature improves readability of large numbers by allowing grouping of digits, consistent with existing support for underscores in hexadecimal and binary literals.

1. Motivation

1.1 Problem

Large numeric literals are difficult to read without visual grouping:

Create the <budget> with 1000000000.
Create the <population> with 7900000000.
Create the <pi-precise> with 3.14159265358979.

These numbers require mental effort to count digits and understand magnitude.

1.2 Solution

Underscore separators allow natural digit grouping:

Create the <budget> with 1_000_000_000.
Create the <population> with 7_900_000_000.
Create the <pi-precise> with 3.141_592_653_589_79.

The underscores are purely visual and do not affect the numeric value.

1.3 Consistency

ARO already supports underscores in hexadecimal and binary literals:

Create the <color> with 0xFF_FF_FF.
Create the <flags> with 0b1010_1010.

This proposal extends the same convenience to decimal literals.

2. Syntax

2.1 Integer Literals

integer_literal = [ "-" ] , digit , { digit | "_" , digit } ;

Valid examples:

1_000
1_000_000
1_000_000_000
123_456_789

Invalid examples:

_1000       (* Cannot start with underscore *)
1000_       (* Cannot end with underscore *)
1__000      (* Cannot have adjacent underscores *)

2.2 Floating-Point Literals

float_literal = [ "-" ] , integer_part , "." , fraction_part , [ exponent ] ;

integer_part  = digit , { digit | "_" , digit } ;
fraction_part = digit , { digit | "_" , digit } ;
exponent      = ( "e" | "E" ) , [ "+" | "-" ] , digit , { digit | "_" , digit } ;

Valid examples:

1_234.567_890
3.141_592_653
1_000.00
1e1_0
1.5e1_000

Invalid examples:

1_.5        (* Underscore cannot be adjacent to decimal point *)
1._5        (* Underscore cannot be adjacent to decimal point *)
1.5_e10     (* Underscore cannot be adjacent to exponent marker *)
1.5e_10     (* Underscore cannot be adjacent to exponent marker *)

3. Semantics

3.1 Value Equivalence

Underscores do not affect the numeric value:

Literal Value
1_000_000 1000000
1000000 1000000
1_234.567_890 1234.56789
1234.56789 1234.56789

3.2 Grouping Freedom

Underscores can appear between any digits, not just at thousand separators:

(* All valid - grouping is flexible *)
Create the <binary-style> with 1111_0000_1111_0000.
Create the <phone-style> with 555_123_4567.
Create the <date-style> with 2024_01_15.

4. Implementation

4.1 Lexer Changes

The scanNumber() method in Lexer.swift is modified to:

  1. Accept _ characters between digits in the integer part
  2. Accept _ characters between digits after the decimal point
  3. Accept _ characters between digits in the exponent
  4. Filter out underscores before parsing with Int() or Double()

4.2 Validation Rules

The lexer enforces:

  • Underscore must be between two digits
  • No leading underscores (before first digit)
  • No trailing underscores (after last digit)
  • No adjacent underscores
  • No underscores adjacent to . or e/E

5. Examples

5.1 Financial Calculations

(Application-Start: Financial Demo) {
    Create the <principal> with 1_000_000.
    Create the <rate> with 0.05.
    Create the <years> with 10.

    Compute the <interest> from <principal> * <rate> * <years>.
    Log "Interest on $1,000,000: " to the <console>.
    Log <interest> to the <console>.

    Return an <OK: status> for the <demo>.
}

5.2 Scientific Notation

(Application-Start: Science Demo) {
    Create the <avogadro> with 6.022_140_76e23.
    Create the <planck> with 6.626_070_15e-34.

    Log "Avogadro's number: " to the <console>.
    Log <avogadro> to the <console>.

    Return an <OK: status> for the <demo>.
}

5.3 Large Integers

(Application-Start: Large Numbers) {
    Create the <billion> with 1_000_000_000.
    Create the <trillion> with 1_000_000_000_000.

    Log "One billion: " to the <console>.
    Log <billion> to the <console>.
    Log "One trillion: " to the <console>.
    Log <trillion> to the <console>.

    Return an <OK: status> for the <demo>.
}

6. Comparison with Other Languages

Language Syntax Example
ARO _ separator 1_000_000
Swift _ separator 1_000_000
Rust _ separator 1_000_000
Python _ separator 1_000_000
Java _ separator 1_000_000
JavaScript _ separator 1_000_000

ARO follows the widely-adopted convention of using underscores as numeric separators.

Summary

Aspect Description
Purpose Improve readability of large numeric literals
Syntax Underscore (_) between digits
Scope Decimal integers, floats, and exponents
Semantics Purely visual, no effect on value
Consistency Matches existing hex/binary underscore support

References

  • Sources/AROParser/Lexer.swift - Lexer implementation
  • Tests/AROParserTests/LexerTests.swift - Unit tests
  • Examples/NumericSeparators/ - Example usage
  • ARO-0001: Language Fundamentals - Number literal syntax