bookshelf/README.md

bookshelf

A study of the books listed below. Most proofs are conducted in LaTeX. Where feasible, theorems are also formally proven in Lean.

• Apostol, Tom M. Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra. 2nd ed. Vol. 1. 2 vols. Wiley, 1991.
• Avigad, Jeremy. ‘Theorem Proving in Lean’, n.d.
• Axler, Sheldon. Linear Algebra Done Right. Undergraduate Texts in Mathematics. Cham: Springer International Publishing, 2015.
• Cormen, Thomas H., Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms. 3rd ed. Cambridge, Mass: MIT Press, 2009.
• Enderton, Herbert B. A Mathematical Introduction to Logic. 2nd ed. San Diego: Harcourt/Academic Press, 2001.
• Gries, David. The Science of Programming. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
• Gustedt, Jens. Modern C. Shelter Island, NY: Manning Publications Co, 2020.
• Ross, Sheldon. A First Course in Probability Theory. 8th ed. Pearson Prentice Hall, n.d.
• Smullyan, Raymond M. To Mock a Mockingbird: And Other Logic Puzzles Including an Amazing Adventure in Combinatory Logic. Oxford: Oxford university press, 2000.

Documentation

To generate documentation, we use bookshelf-docgen. Refer to this project on prerequisites and then run the following to build and serve files locally:

> lake build Bookshelf:docs
> lake run server

This assumes you have python3 available in your $PATH. To change how the server behaves, refer to the .env file located in the root directory of this project.

A color code is used on generated PDF headers to indicate their status:

• Cyan statements indicate axioms and definitions. There must exist a corresponding axiom or def in Lean.
• Teal statements indicate those with complete proofs in both LaTeX and Lean.
• Magenta statements indicate those that have not been completely proven in either LaTeX or Lean (or both). Progress is currently being made to correct this though.
• Red coloring is a catch-all for all statements that don't fit the above categorizations. Incomplete definitions, proofs only conducted in LaTeX, etc. belong here.