Implement a proper 'numerical tower' in core or std

[brendanzab]

I'm not sure how feasible this currently is. We would have to think in terms of compile-time, zero-cost abstractions. On #rust:

erickt: once we get default methods we can make proper mathematical groups, semigroups, rings, and etc

Relevant articles on Wikipedia:

• Numerical Tower
• Group
• Ring

Other things to consider in the same vein are units of measure, range types and mod types. Perhaps these could be implemented via traits and default methods.

• Units of measure (F#)
• F Sharp Programming/Units of Measure
• Physical Units – HaskellWiki
• Data types in Ada

[brendanzab]

An interesting paper on numerical towers in Typed Racket: http://www.ccs.neu.edu/racket/pubs/padl12-stff.pdf

[erickt]

A couple more links for interesting algebraic systems from Haskell [1], [2] and Felix [3] that I think would be pretty straightforward to migrate over to Rust:

1: Haskell Numeric Classes
2: Haskell Constructive Algebra
3: Felix Algebraic Typeclasses

[emberian]

@bjz default methods have mostly arrived!

[glaebhoerl]

another Haskell algebra package

[catamorphism]

This doesn't seem to have been nominated properly. Nominating in order to clear the milestone. I don't think this blocks production-readiness.

[catamorphism]

We agreed that if this is going to be a milestone bug, it should be more specific. De-nominating.

[metajack]

Triage bump.

Work is ongoing on cleaning up the traits in libstd.

[thestinger]

I think we're in agreement that this should be done out-of-tree. Once there's a fleshed out library, proposing an inclusion of it in the standard library via an RFC would make sense.

[ticki]

I would love to see this reopened. This would definitely boost the abilitiy to write generic code (without external libraries). Though there are some caveats.

[brendanzab]

I think this would be better off as a third-party lib first. Then it can be combined at a later date if it is deemed good enough.