latte-kernel

The (very) small kernel of the LaTTe proof assistant in Clojure(script)

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Overview

LaTTe is a proof assistant based on a type theory (a dependently-typed proof theory). This repository contains the source code of its small trusted kernel, developed as a Clojure(script) library. Its design has been driven by the following criterion:

A Mathematical Assistant satisfying the possibility of independent checking by a small program is said to satisfy the de Bruijn criterion.

see: "The Challenge of Computer Mathematics", http://www.cs.ru.nl/~freek/notes/RSpaper.pdf

It is also optimized for readability rather than efficiency, but it has been tested heavily and performs quite "acceptably".

Organization

Each source file (extension .cljc) in the source directory src/latter_kernel is accompanied by its literate programming companion (extension .cljc.md).

The following files compose the kernel:

• presyntax.cljc[.md]: the user-facing syntax and the translation (parsing) to the internal syntax
• syntax.cljc[.md]: the internal syntax of lambda-terms plus syntax-level utilities (term substitution, alpha-normalization, alph-equivalence)
• norm.cljc[.md]: the (beta/delta)-reduction rules, normal forms and equivalences
• typing.cljc[.md]: the type inference algorithm
• proof.cljc[.md]: the internal representation of declarative proofs, and the proof checker implementation

Some auxiliary files are also used (in non-literate forms):

• utils.cljc: misc. utilities
• defenv.cljc: the representation of named abstractions (mathematical definitions, theorems, etc.)
• unparser.cljc: the regeneration of surface syntax for (proof) debugging purpose

Usage

The kernel is a basis to develop proof assistants, not to be "consumed" directly. The literate files also explain how to develop such a kernel.

The (several) unit tests (in test/latte_kernel) can be executed using the following command:

lein test

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This software is Copyright (C) 2018 Frederic Peschanski, under the MIT License (cf. LICENSE file)