# HoTT/Coq-HoTT

A Coq library for Homotopy Type Theory

Repository: https://github.com/HoTT/Coq-HoTT
Canonical: https://ross.abutalabs.com/products/coq-hott
Homepage: http://homotopytypetheory.org/
Language: Rocq Prover
License: NOASSERTION
License Family: other
Topics: type-theory, homotopy-type-theory, univalent-foundations
Last push: 2026-08-22T12:57:31+00:00

## Health v2 (maintenance only)
Score: 85/100 (v2, computed 2026-09-02T17:46:02.011165+00:00)
- activity 99, release rhythm 58, longevity 100
- inputs: {"age_days": 5639, "days_push": 11, "days_rel": 70, "gap_med": 317.0, "n_releases_24m": 3}
- flags: no_license
- formula: round(0.45*activity + 0.35*rhythm + 0.20*longevity); archived -> min(score, 10)

## Adoption (not part of the score)
Stars 1403, forks 203 (observed 2026-08-28T04:04:37.807708+00:00)

## What it is
A Coq library for Homotopy Type Theory, interpreting Martin-Löf's intensional type theory into abstract homotopy theory. It provides formalizations of homotopy-theoretic ideas such as univalence and higher inductive types for use in the Coq proof assistant.

## Use cases
- formalize mathematics in homotopy type theory
- prove theorems using the univalence axiom in Coq
- experiment with higher inductive types
- study univalent foundations of mathematics
- develop homotopy-theoretic constructions in a proof assistant
- teach or learn homotopy type theory interactively

## When to choose
- you want to do formal proofs in homotopy type theory within Coq
- you need a mature, actively maintained HoTT library with Coq Platform support
- you want BSD-licensed formalization code you can reuse freely

## When to avoid
- you need standard Coq with classical mathematics rather than univalent foundations
- you prefer Agda or Lean-based HoTT developments
- you need a general-purpose programming library rather than a proof library

## Facets
- artifact type: library
- maturity: active
- function: type-system, interpreter, developer-tools
- domain: programming-languages, mathematics, education
- platform: cli, cross-platform
- tags: coq, homotopy-type-theory, univalent-foundations, proof-assistant, formalization, higher-inductive-types, algorithms

## Member repositories
- HoTT/Coq-HoTT (main) score 85

## Provenance
- Observed fields: from GitHub, fetched 2026-08-28T04:04:37.807708+00:00.
- Health v2: computed from the inputs above; adoption is never an input.
- Inferred fields (summary, facets, guidance): AI-extracted, prompt v1, taxonomy v1, on 2026-08-30T04:38:53.318081+00:00, confidence not recorded.
  - readme: https://github.com/HoTT/Coq-HoTT (fetched 2026-08-28T04:04:37.807708+00:00, sha 031dee4867f6)
  - homepage: http://homotopytypetheory.org/ (fetched 2026-08-29T11:52:41.673978+00:00, sha 03e4934b4412)
- Data as of 2026-08-30T08:39:29.467469+00:00.