fixpoint

Action signature, we'll call a fixpoint method called Fix:

B# .NET Technical Community Homepage bart 2010

Reiter 1980 use fixpoint definitions to solve the problem.

Logic and Artificial Intelligence Thomason, Richmond 2008

Reiter 1980 provides a fixpoint definition of the extensions of such a theory, and develops the theoretical groundwork for the approach, proving a number of the basic theorems.

Logic and Artificial Intelligence Thomason, Richmond 2008

The solution to the functional equation is a fixpoint where the expectation function and the pricing function coincide.

The Scientific Contributions of Robert E. Lucas, Jr. 1995

Y combinator , a fixpoint combinator created by lambda calculus high priests.

B# .NET Technical Community Homepage bart 2010

To write an anonymous recursive function, we use the same fixpoint technique as we saw before.

B# .NET Technical Community Homepage bart 2010

The type of the intermediate function definition is quite impressive due to the fixpoint structure, but the essence of the function is quite easy to grasp:

B# .NET Technical Community Homepage bart 2010

We have a generic fixpoint method called "Fix", allowing us to define the factorial function (amongst others of course) as follows:

B# .NET Technical Community Homepage bart 2010

Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact that the identity is the limit of a sequence of projection terms.

Lambda the Ultimate - Programming Languages Weblog 2009

Although McDermott and Doyle's terminology is different from Reiter's, the logical ideas are very similar ” the essence of their approach, like Reiter's, is a fixpoint definition of the extensions of a nonmonotonic logic.

Logic and Artificial Intelligence Thomason, Richmond 2008