https://github.com/jozefg/blott
An experimental type checker for a modal dependent type theory.
https://github.com/jozefg/blott
Last synced: about 2 months ago
JSON representation
An experimental type checker for a modal dependent type theory.
- Host: GitHub
- URL: https://github.com/jozefg/blott
- Owner: jozefg
- License: mit
- Created: 2019-01-22T10:42:08.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2020-05-09T00:38:40.000Z (about 5 years ago)
- Last Synced: 2025-04-12T18:14:48.721Z (about 2 months ago)
- Language: OCaml
- Size: 135 KB
- Stars: 110
- Watchers: 16
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
## blott
An implementation of normalization by evaluation (nbe) & semantic type checking for Martin-Löf Type
Theory with dependent products, dependent sums, natural numbers, id, box, and a cumulative hierarchy
of universes. This implementation supports eta-rules for box, pi, and sigma.
For examples, see the `test/` directory.
The type theory underlying `blott` as well as the implementation is described in
[Implementing a Modal Dependent Type Theory](https://doi.acm.org/10.1145/3341711).
## building
blott has been built with OCaml 4.06.1 and 4.07.1 with [opam 2.0](https://opam.ocaml.org/). Once
these dependencies are installed blott can be built with the following set of commands.
```
$ opam update
$ opam pin add -y blott . # first time
$ opam upgrade # after packages change
```
After this, the executable `blott` should be available. The makefile can be used to rebuild the
package for small tests. Locally, blott is built with [dune](https://dune.build), running the above
commands will also install dune. Once dune is available the executable can be locally changed and
run with the following:
```
$ dune exec ./src/bin/main.exe # from the `blott` top-level directory
```
## syntax
This experimental proof assistant supports the following top-level declarations:
- A definition, written `let NAME : TYPE = TERM`
- A command to normalize a definition `normalize def NAME`
- A command to normalize an expression `normalize TERM at TYPE`
Unlike in the paper, names instead of indices are used for the surface syntax. The following are
the valid expressions in blott.
``` ocaml
(* Let bindings *)
let NAME = TERM in TERM
let NAME : TYPE = TERM in TERM
(* Natural numbers *)
nat, 0, 1, 2...
(* Recursion on natural numbers *)
rec NUMBER at x -> MOTIVE with
| zero -> TERM
| suc n, ih -> TERM
(* Functions *)
(NAME : TP) -> TP
fun NAME -> TERM
TERM TERM
(* Pairs *)
(NAME : TP) * TP
fst TERM
snd TERM
(* The box modality *)
[box TP]
[lock TERM]
[unlock TERM]
(* Universes *)
U<0>,U<1>,...
(* Identity types *)
Id TYPE TERM TERM
refl TERM
match PRF at x y prf -> MOTIVE with
| refl x -> TERM
```
A small collection of example programs is contained in the `test/` directory. See `test/README.md`
for a brief description of each program's purpose.