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Homotopy type theory
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Merge pull request #756 from JasonGross/more-robust-equiv-induction

Make [equiv_induction] a bit more robust
latest commit babaf2181a
@mikeshulman mikeshulman authored
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contrib Move [proof_admitted] out of the standard library
coq-HoTT @ eaa3d0b Bump Coq version to 8.5-β₁
coq Move [proof_admitted] out of the standard library
etc Also build HoTT with the tip of v8.5 and trunk
theories Merge pull request #756 from JasonGross/more-robust-equiv-induction
.gitignore add more coq/ symlinks to .gitignore
.gitmodules Move to trunk
.mailmap Update .mailmap
.travis.yml Also build HoTT with the tip of v8.5 and trunk
CREDITS.txt Update CREDITS.txt Apparently sometimes 9 spaces
LICENSE.txt Added legaleze Make the clean target a bit quieter A naive coreflective subuniverse is uniquely determined by an hprop Updating readme, closing #729 Rebuild TOCs (auto)
UNICODE.txt Add unicode instructions Update submodules in Don't run coqdep when we run `make clean` Fix hoqide on Windows
hoqc Use ${BASH_SOURCE[0]} instead of $0
hoqdep Use ${BASH_SOURCE[0]} instead of $0
hoqide Use ${BASH_SOURCE[0]} instead of $0
hoqtop Use ${BASH_SOURCE[0]} instead of $0
hoqtop.byte Use ${BASH_SOURCE[0]} instead of $0

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Homotopy Type Theory is an interpretation of Martin-Löf’s intensional type theory into abstract homotopy theory. Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence. Logical constructions in type theory then correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning. As the natural logic of homotopy, type theory is also related to higher category theory as it is used e.g. in the notion of a higher topos.

The HoTT library is a development of homotopy-theoretic ideas in the Coq proof assistant. It draws many ideas from Vladimir Voevodsky's Foundations library (which has since been incorporated into the UniMath library) and also cross-pollinates with the HoTT-Agda library.


Installation details are explained in the file


It is possible to use the HoTT library directly on the command line with the hoqtop script, but who does that?

It is probably better to use Proof General and Emacs. When Proof General asks you where to find the coqtop executable, just point it to the hoqtop script. If Emacs runs a coqtop without asking, you should probably customize set the variable proof-prog-name-ask to nil (in Emacs type C-h v proof-prog-name-ask RET to see what this is about).

At the moment there is no hoqide equivalent of coqide, but getting one is high on our to-do list.


Contributions to the HoTT library are very welcome! For style guidelines and further information, see the file


The library is released under the permissive BSD 2-clause license, see the file LICENSE.txt for further information. In brief, this means you can do whatever you like with it, as long as you preserve the Copyright messages. And of course, no warranty!

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