The word processor that can check your math

Detailed About Page

This page assumes you’ve read the simple introduction on the About page, and it wasn’t enough for you. Here is a deeper introduction to the aim, structure, and design of Lurch.

What is Lurch?

Lurch is a math word processor that checks the steps of the user’s work.

What is a step?

A step is any part of a Lurch document (but usually a single mathematical expression) to which a reason is attached (regardless of whether that reason is correct, or even left blank).

What is a reason?

A reason is a reference to a “grading procedure,” a method by which Lurch can check whether the reason justifies the step to which it is attached. Theorems are a common mathematical example of reasons; you cite one, and then the reader (or the software) can check whether you’ve used the theorem correctly. A more computer-oriented example would ask Lurch to use its internal computer algebra system to grade the step of work.

What does it mean to check a step?

“Check” is the informal way to say “validate.” The brains of Lurch is its validation engine.

Different contexts call for different types of validation. Since Lurch is designed for educational use, different learning goals in different courses will dictate different styles of interacting with the program.

Also, there may be varying amounts of validation, from none to very strict.

Can you give some examples?

Word processing in Lurch Lite

Word processing (no validation)

Yes, but these examples are from our last release, Lurch Lite.  A new and much improved version is on its way in early 2012.

Lurch validating algebra with its built-in CAS

Validation using a computer algebra system

One of the topics built into the current version of Lurch Lite is a simple math word processor. It does no validation at all. This is the base on which Lurch is built; think of it as the trivial example (validation amount equals zero).

Simple theorem validated in Lurch

Validating each step of a proof (next release)

A broadly applicable topic is one that validates all steps of work based on an internal computer algebra system. It can check algebra and calculus work.

Our next release will drop the “Lite” and simply be called Lurch, because it will have a much more rigorous mathematical foundation, capable of validating theorems, as shown below.

Furthermore, the next release is easy to customize for any mathematician. Just write the theorems and rules you want your students to have access to, and Lurch learns them just as your students would! They can then cite them by whatever names you use for them in your course.