Re: [Axiom-developer] Axiom Sane musings (SEL4)

2019-09-20 Thread Tim Daly
Axiom has type information everywhere. It is strongly dependently typed. So give a Polynomial type, which Axiom has, over a Ring or Field, such as Polynomial(Integer) or Polynomial(Fraction(Integer)) we can use theorems from the Ring while proving properties of Polynomials. Axiom has a deep type h

Re: [Axiom-developer] Axiom Sane musings (SEL4)

2019-09-20 Thread Henri Tuhola
I doubt it does cover that. And I think there would be at least two approaches to implement GCD for polynomials in Idris. Obvious approach would be to construct a type that represents polynomials on some base number and variables. For example, (Polynomial Nat [X]). You would then prove GCD for thi

Re: [Axiom-developer] Axiom Sane musings (SEL4)

2019-09-20 Thread Tim Daly
Does the Idris code cover GCD for polynomials? On 9/20/19, Henri Tuhola wrote: > You can already define and prove gcd in idris/agda/coq. It's not too hard > either. > > This weekend I am trying to prove transitive closure can be computed in > Idris. The way I represent it is that I have f:(a ->

Re: [Axiom-developer] Axiom Sane musings (SEL4)

2019-09-20 Thread Henri Tuhola
You can already define and prove gcd in idris/agda/coq. It's not too hard either. This weekend I am trying to prove transitive closure can be computed in Idris. The way I represent it is that I have f:(a -> a -> Type), this forms a type that is inhabited when a statement is true. I can wrap this i