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algorithms and models of computation in fstar

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// repository documentation

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Mechanizing Theory of Computation
---------------------------

This is a presentation in [F*](https://www.fstar-lang.org/) of some theory about decidable
   languages, and Deterministic Finite-state Automata (DFAs).

It is intended as supplementary material for a Models of Computation
   course, meant to provide a gentle introduction to mechanized proofs.

- _[Strings.fst](Strings.fst):_ (easy)
     Define strings as inductive types, and give some simple
     inductive proofs.
     The difficulty is similar to Section 4 in the F* tutorial[2], and
     includes some lemmas and exercises from Ch. 1 of Models of
     Computation [1].

- _[DFAs.fst](DFAs.fst):_ (medium)
     Defines DFAs and gives a few inductive proofs as well as
     the product construction for intersection of languages.
     Corresponds to Ch. 3 of Models of Computation [1].

- _[MyhillNerode.fst](MyhillNerode.fst):_ (hard)
      This gives a presentation of the Myhill Nerode theorem, based
      on the notions of "fooling sets" Ch.3 [1] and "classifiers" [1].

[1] Models of Computation. Jeff Erickson.
   http://jeffe.cs.illinois.edu/teaching/algorithms/models/all-models.pdf

[2] F* Tutorial. https://www.fstar-lang.org/tutorial/

[3] Regular Language Representations in the Constructive
   Type Theory of Coq
   Christian Doczkal, Gert Smolka
   https://hal.archives-ouvertes.fr/hal-01832031/document

Running Instructions
====================
Instructions for installing F* are found here:
https://www.fstar-lang.org/#download

The code here was developed in the [fstar-emacs](https://hub.docker.com/r/fstarlang/fstar-emacs) docker environment.

I run it like:
    ```
    docker run -it -v $PWD:/home/build/fstar374 fstarlang/fstar-emacs bash

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