Re: [Axiom-developer] Proving Axiom Correct -- at the C level

2017-03-31 Thread Tim Daly
I previously mentioned the "proof tower" approach to the question of proving code at many different layers. Spad code proven in COQ, Lisp code in ACL2, and Intel code in CCAs. The missing step in the tower was C. Apparently there is work in COQ (http://robbertkrebbers.nl/research/ch2o/) on the CH2

Re: [Axiom-developer] Proving Axiom Correct

2017-03-31 Thread Tim Daly
>Perhaps there are issues around this that will matter? Given that there >are two formulations of each algebra, one like this: >zero: () -> $ >succ: ($) -> $ >and one like this: >+ ($,$) -> $ >If one form is needed for inductive proofs and the other form for >applied mathematics. Could Axiom ho

Re: [Axiom-developer] Proving Axiom Correct, "state of the art" report

2017-03-31 Thread Martin Baker
On 31/03/17 05:34, Tim Daly wrote: Consider the Axiom Domain NonNegativeInteger. NNI roughly corresponds to the Type theory "Nat" construction. They differ in that Axiom uses Lisp Integers whereas Type theory uses Peano arithmetic (a zero and a successor function) but for our purposes this does n