COCYTUS
An esoteric programming language with exact dyadic-rational arithmetic and a self-hosting compiler that must reproduce its own binary image byte-for-byte before a release.
Cocytus is an esoteric programming language, presented as a successor to Malbolge in a sustained literary framing built around Dante's ninth circle of Hell. Its numeric domain represents finite values exactly as a dyadic fraction (an integer over a power of two) in canonically normalized form, with exact addition and multiplication inside the representable range; a result that cannot be represented becomes explicitly unresolved rather than silently approximated. It also implements bounded, well-founded Conway cuts that can be validated, compared, negated, added and multiplied, each carrying both a value and a construction history (a birthday).
Its compiler is designed to be self-verifying: the native Cocytus compiler's own source is passed through Cocytus repeatedly until the resulting compiler image stops changing byte-for-byte, rather than trusting a bootstrap step or a hidden host compiler.
It is written in C and released under the Apache-2.0 license; release 0.2.1 is in preparation.