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: Mathematics can get limitlessly sophisticated. How can the
principles of basic algebra possibly take us to all of that?
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.