Holbert

Holbert is an interactive theorem prover, or proof assistant, based on higher order logic and natural deduction. Furthermore, Holbert is graphical. It presents proofs and rules using conventional inference rule notation and proof trees. It is designed to be used by students, without any expertise on using a theorem prover. It does not feature proof scripts (in the traditional sense), tactics, or other such complications.

You can try Holbert out by trying the live demo here (this version may not be the latest one available from GitHub). This Holbert instance explains more about the rationale behind its design and my intended goals with it.

Like Isabelle, Holbert is just a pure meta-logic. It does not define any connectives (like conjunction or disjunction) itself, although all can be defined within the system. For binding structures and quantifiers, higher order abstract syntax can be used.

Unlike conventional theorem provers, Holbert’s term language is just the untyped lambda calculus. While this technically makes the logic unsound, it is much simpler to use as a pedagogical tool.

Holbert is intended as a tool for education, and not as an industrial-strength proof assistant where theorems must be trusted. So, just avoid writing fixed point combinators and you should be fine.

Building, Installing

Holbert is written in GHC Haskell, intended to be compiled with ghcjs. It uses the Miso framework and the optics-core library. Acquiring GHCJS can be difficult, but I was able to follow the instructions on the Miso readme to install it using nix, and then I just used cabal from then on once I had the ghcjs binaries.

Once it is set up, make sure that the OUTPUT variable in the Makefile points to wherever cabal builds the jsexe directory for the compiled app. To find out what this is, you can type:

cabal configure --ghcjs
cabal build

The correct directory to set OUTPUT to will be listed as the last line in the build log (Linking ...), but you can also find it by typing:

find . | grep jsexe | head -1

Once the OUTPUT directory is set, you can build Holbert properly (including all resources) by typing:

make

And if you have python3 there is a shortcut to start a server with the app with

make server

Licenses

Holbert is released under the BSD3 license. It includes the following free projects:

• Computer Modern font families, released under the SIL Open Font License.
• The Neo Euler font, also released under the SIL Open Font License.
• The Typicons icon font, also released under the SIL Open Font License.

Some code for the unification engine were taken from Tobias Nipkow’s paper on the topic, as well as from Daniel Gratzer’s higher order unification implementation in Haskell.

The following MIT licensed JS libraries are used:

• Split.js by Nathan Cahill
• FileSaver.js by Eli Grey

Future work

• Support for deferred proof steps to lemmas.
• “Books”, multiple interlinked documents.
• (Built-in) support for equality
• (Built-in) support for induction
• And much much more!