Questions and answers

Q: Where is the set theory?

A: Like many modern proof assistants, Prooftoys is based on simple type theory rather than set theory. A big advantage for Prooftoys is that type theory enables us to get on very directly to talk about things like numbers without theorizing about sets first.

Q: How can the principles of basic algebra possibly handle advanced mathematics?

A: The power of simple principles to solve complex problems is part of the wonder of mathematics. In fact Prooftoys does employ just a couple of simple extensions to basic algebra, but mostly it applies the same principles in more general ways.

Q: Tell me more about this type theory.

A: See the technical notes for more information about type theory and Prooftoys’ use of it.

Q: Is there something weird about this logic? When I look at theorems with quantifiers for example, I see things like forall P. What’s up with that?

A: No, the principles behind Prooftoys are about as standard as can be. The notation is sometimes a bit different though. Anywhere you see something like forall P you can read it exactly as forall x. P x in a more traditional notation.

Q: Some theorems have curly braces in them. What do they mean?

A: The curly braces are the Prooftoys notation for on of the main innovations of type theory. See the technical notes.

Q: I have a different question. What can I do?

A: Contact the author by email, or better yet file an issue or a question on GitHub, perhaps with the “question” label.