Proposal: indexed infinity for division by zero (RICIS-III ontology)

[A1Dmitry]

Current behavior

In Pony, integer division by zero returns 0:

let x = I64(1) / I64(0) // x = 0

This is pragmatic but loses provenance: 1/0 and 2/0 both return 0.

Proposal: indexed infinity (RICIS-III ontology)

RICIS-III (DOI: 10.5281/zenodo.17872755) defines F/0 = ∞_F — an indexed infinity that preserves the numerator as provenance.

Expression	Current Pony	Proposed
1/0	0	∞_1
2/0	0	∞_2
0/0	0	resolved via A4
∞_1/∞_2	NaN	1/2

This could be a fourth division mode (/? preserves the indexed structure) or a compile-time option.

Why

• Preserves information that Pony currently discards
• Allows structural cancellation: 0_F/0_G = F/G
• Prevents NaN cascade from inf/inf
• Already implemented in C# (Expression Trees): [link to your repo]

Questions for maintainers

1. Would a fourth division mode (/?i for indexed) be acceptable?
2. Could this be a compiler flag?
3. Interested in a proof-of-concept PR?

References

• DOI: 10.5281/zenodo.17872755
• Online calculator: https://remix-ricis-iii-501343051156.europe-west2.run.app/
• C# implementation: https://github.com/A1Dmitry/Ricis.Core.git

[SeanTAllen]

We have an RFC process for things like this: https://github.com/ponylang/rfcs. As part of the RFC, you'll need to provide at least one motivating example. I'm transfering this as an issue on the RFC repo that someone could write up an RFC for.