My Own Private Automath: the Lestrade Type Inspector

This page provides resources related to a current little project of mine, whose motivation is actually philosophical. I have in mind a view of the philosophy of mathematics under which the objects of classical, nonconstructive, impredicative mathematics with higher orders of infinity are naturally accessible by finitary means, all the infinities being merely potential. This view exploits the Curry Howard isomorphism and some thoughts of mine about the nature of abstraction, and if it is to be taken seriously should be implementable on a computer. The implementation (given the intellectual ingredients I have mentioned) should resemble Automath. And it does.

An implementation is now found here with documentation and examples.

The name is admittedly a bit of mischief: I am Holmes, I already have a prover called Watson, and my son suggested that I call this one Lestrade...

Here is the source for the implementation in Moscow ML 2.01 of the Lestrade Type Inspector.

Here is the manual (which I have updated; it does not say everything that the paper below says, but it has a different emphasis and I think it is still useful).

Here is the source for the implementation in Poly/ML of the Lestrade Type Inspector.

Here is the source for the implementation in Moscow ML 2.10.1 of the Lestrade Type Inspector.

Here is a paper I am working on in summer 2016, containing an outline of the philosophical approach, an account of the commands and the formal language of Lestrade, and extensive sample Lestrade books.

Here is another paper I am working on in summer 2016, focussed more narrowly on the philosophical approach.

And here is another paper I am working on in fall 2016, which pretends to be an initial segment of an elementary discrete math test supported by Lestrade text.

Here is the source for the implementation in Moscow ML 2.01 of a version of Lestrade without the new type inference capabilities, which I will continue to maintain. I'll leave this up, but maintenance of it is suspended: the main version now supports a command basic() which will give this behavior, and fullversion() to restore type inference functions.

Here are the slides for a talk I am giving locally on October 25th 2016. Here is the supporting Lestrade script file.

Script files

Lestrade scripts have the extension .lti and should be opened with a text editor. They are executable by Lestrade itself using the readfile command, and they are produced by Lestrade as log files. Some of these files are things I am working on which will continue to be updated.

Classical Automath resources

Here is Freek Wiedijk's Automath site, including the only currently available implementation of standard Automath (as far as I know). What I present here is not standard Automath!

Here is the official Automath archive site.