## Can Coq be used (easily) as a model checker?

As the title says, can Coq be used as a model checker? Can I mix model checking with Coq proving? Is this usual? Google talks about a “ยต-calculus”, does anyone have experience with this or something …

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coq

As the title says, can Coq be used as a model checker? Can I mix model checking with Coq proving? Is this usual? Google talks about a “ยต-calculus”, does anyone have experience with this or something …

I’m trying to (classically) prove

~ (forall t : U, phi) -> exists t: U, ~phi

in Coq. What I’m trying to do is prove it contrapositively:

1. Assume there is no such t (so ~(exists t: U, ~phi))

…

Ever since I learned a little bit of Coq I wanted to learn to write a Coq proof of the so-called division algorithm that is actually a logical proposition: forall n m : nat, exists q : nat, exists r : …

Here is a recursive function all_zero that checks whether all members of a list of natural numbers are zero:

Require Import Lists.List.

Require Import Basics.

Fixpoint all_zero ( l : list nat ) : …

As a rough and untutored background, in HoTT, one deduces the heck out of the inductively defined type

Inductive paths {X : Type } : X -> X -> Type :=

| idpath : forall x: X, paths x x.

which …

This question has to do with configuring the Coq mode within Proof General, in Emacs.

I’m trying to have Emacs automatically replace keywords and notation in Coq with the corresponding Unicode glyphs….

I am having trouble defining a tactic to recursively invert hypotheses in a proof context. For instance, suppose I have a proof context containing a hypothesis like:

H1 : search_tree (node a (node b …

I am implementing Algorithm W (the Hindley-Milner type system) in JavaScript:

The function which implements the above rules is typecheck and it has the following signature:

typecheck :: (Context, …

I can naively construct a hierarchy of algebraic structures in Coq using type classes. I’m having some trouble finding resources on Coq’s syntax and semantics for type classes. However, I believe the …

I see a couple of different research groups, and at least one book, that talk about using Coq for designing certified programs. Is there are consensus on what the definition of certified program is? …