# Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach

@inproceedings{MirandaPerea2012MendlerstyleIP, title={Mendler-style Iso-(Co)inductive predicates: a strongly normalizing approach}, author={Favio Ezequiel Miranda-Perea and Lourdes Del Carmen Gonz{\'a}lez-Huesca}, booktitle={Workshop on Logical and Semantic Frameworks with Applications}, year={2012} }

We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic includes primitive constructors of least and greatest fixed points of predicate transformers, but contrary to the common approach, we do not restrict ourselves to positive operators to ensure monotonicity, instead we use the Mendler-style, motivated here by…

## One Citation

### A realizability interpretation of Church's simple theory of types

- PhilosophyMathematical Structures in Computer Science
- 2016

A realizability interpretation of an intuitionistic version of Church's Simple Theory of Types which can be viewed as a formalization of intuitionistic higher-order logic and includes operators for monotone induction and coinduction and simple realizers for them.

## References

SHOWING 1-10 OF 19 REFERENCES

### TWO EXTENSIONS OF SYSTEM F WITH ( CO ) ITERATION AND PRIMITIVE ( CO ) RECURSION PRINCIPLES

- Mathematics, Computer Science
- 2008

Two extensions of the second order polymorphic lambda calculus, system F, with monotone (co)inductive types supporting ( co)iteration, primitive (Co)recursion and inversion principles as primitives are presented, with expressiveness shown by means of several programming examples.

### Least and greatest fixed points in intuitionistic natural deduction

- MathematicsTheor. Comput. Sci.
- 2002

### Least and Greatest Fixed Points in Linear Logic

- MathematicsTOCL
- 2012

This work designs a focused proof system that proves complete with respect to the initial system, and establishes weak normalization for it, and shows how these foundations can be applied to intuitionistic logic.

### Natural deduction for intuitionistic least and greatest fixedpoint logics : with an application to program construction

- Computer Science
- 1998

It is argued that all eight systems can be interpreted as terminating and deterministic systems of typed functional programming with primitive formers of inductive and coinductive types and employed an media for program construction from judgements-as-specifications.

### Data Types, Infinity and Equality in System AF2

- Computer Science, MathematicsCSL
- 1993

Since the pure λ-calculus is used to represent data types, it is proved uniqueness of the representation of data up to Bohm tree equivalence.

### Reasoning about functional programs and complexity classes associated with type disciplines

- Mathematics, Computer Science24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
- 1983

This work presents a method of reasoning directly about functional programs in Second-Order Logic, based on the use of explicit second-order definitions for inductively defined data-types, which implies that, for functions defined over inductivelydefined types, the property of being proved everywhere-defined in Second -Order Logic is equivalent to theproperty of being representable in the Second- order Lambda Calculus.

### On the Representation of Data in Lambda-Calculus

- Computer Science, MathematicsCSL
- 1989

The results in this paper state a fundamental duality between the iterative and recursive representation of data in lambda-calculus.

### Automatizing Termination Proofs of Recursively Defined Functions

- Computer ScienceTheor. Comput. Sci.
- 1994