isabelle

I did a proof for elliptic curves taking as a base field the reals. Now I want to change the reals by an arbitrary field which has characteristic different from 2, so that from the equation 2x = 0 one can deduce that x = 0. How does one phrase this in a proof assistant like Isabelle? In essence, you can use class ell_field = field + assumes zero_ne_two: "2 ≠ 0" For example, see The Group Law for Elliptic Curves by Stefan Berghofer . I assume that you wish to work with the class field from the main library of the object logic HOL. Unfortunately, I am not aware of a general treatment of the ring

I investigated Coq a little, with its dependent types. I have only the foggiest idea about it all, but now I have in mind that I want a bit vector as a bool list , in which the length of the vector is part of the type. (This question is the possible predecessor of another question. In the next question, if I ask it, I'll ask whether I can recover what I lose, when I use typedef as below.) (For this question, the question is at the bottom) Here are the requirements for the type I want: It has to use bool list , so that I can directly or indirectly do pattern matching and recursion on the list,

How can I use the find_theorems mechanism to search the whole Archive of Formal Proofs (AFP)? I have downloaded the archive to my machine, and I am able to import theories from it. For instance, if I write imports Kleene_Algebra.Kleene_Algebra_Models then all the theorems in that theory are successfully made available to me. But if I then type find_theorems <expression> , I only get search results from the specific theory I imported. What if I want to search the whole archive? For instance, perhaps somebody has proved a theorem that is useful to me, but I don't know what they called their

Let's assume I have a directory isabelle_afp where a lot of theories are stored. This directory is a library and I do not plan to change the files in it. I want to speed up the start-up time of Isabelle/jEdit (by default, all theories in isabelle_afp my current theory depends on are processed anew). How can I skip this step? The system manual tells me to build a persistent heap image . What is the easiest way to do so? And how can I tell Isabelle/jEdit to load this heap image? Isabelle/jEdit in Isabelle2013 already takes care of building your heap images, by a relatively basic mechanism that

Closed. This question is off-topic . It is not currently accepting answers. Want to improve this question? Update the question so it's on-topic for Stack Overflow. Closed 2 years ago . I am looking at creating an Eclipse PDE and need to communicate with with Isabelle. I do find some publication stating that Scala can be used to communicate to Isabelle. I am looking for an example how to use Scala to create proves in Isabelle. For posterity, quoting myself from an older answer : Isabelle itself is implemented in Standard ML, but for communicating with the external world, it uses a protocol

What are real_of_int , real and int in Isabelle? They sound a bit like types, but usually types are written something like x ::real and these are written like real x . I am having trouble proving the following statement, "S ((n*x)+(-x)) = S (n*x)*C (-x) + C (n*x)*S (-x)" and I noticed that Isabelle writes it as: S (real_of_int (int (n * x) + - int x)) = S (real (n * x)) * C (real_of_int (- int x)) + C (real (n * x)) * S (real_of_int (- int x)) so I'd like to be able to understand what these mean. Johannes When one uses Complex_Main (or a logic based on it like HOL-Analysis , HOL-Probability