fixpoint love

# fixpoint

## Definitions

• noun A fixed point.

## Etymologies

Shortening of fixed point.

## Examples

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

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• 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.

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

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

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• 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:

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

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• 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.

• 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