#### DMCA

## Coinduction in Coq (2005)

### Cached

### Download Links

- [www.cs.chalmers.se]
- [cel.archives-ouvertes.fr]
- DBLP

### Other Repositories/Bibliography

Venue: | Lecture Notes of TYPES Summer School 2005, Sweden, Volume II |

Citations: | 4 - 0 self |

### Citations

699 |
Interactive Theorem Proving and Program Development. Coq’Art: The Calculus of Inductive Constructions
- Bertot, Castéran
- 2004
(Show Context)
Citation Context ...es of execution, and temporal logic [5, 8]. The guarded by constructors structure of co-recursive functions is adapted to representing finite state automata. A few concrete examples are also given in =-=[4]-=-. Co-inductive types are especially well suited to model and reason about lazy functional programs that compute on infinite lists. However, the constraints of having co-recursive calls guarded by cons... |

255 |
Non-well-founded sets,
- Aczel
- 1988
(Show Context)
Citation Context ...ssibility to have co-inductive types in theorem proving tools was studied by Coquand [7], Paulson [19], Leclerc and Paulin-Mohring [16], and Gimenez [13]. Most of these authors were inspired by Aczel =-=[1]-=-. The paper [2] provides a short presentation of terms and (possibly infinite) trees, mainly in set-theoretic terms; it also explains recursion and co-recursion. In this document, we only consider the... |

83 |
Codifying guarded definitions with recursive schemes.
- Gimenez
- 1994
(Show Context)
Citation Context ...ection of what happens with inductive types. The possibility to have co-inductive types in theorem proving tools was studied by Coquand [7], Paulson [19], Leclerc and Paulin-Mohring [16], and Gimenez =-=[13]-=-. Most of these authors were inspired by Aczel [1]. The paper [2] provides a short presentation of terms and (possibly infinite) trees, mainly in set-theoretic terms; it also explains recursion and co... |

52 |
A fixedpoint approach to implementing (Co) inductive definitions.
- Paulson
- 1994
(Show Context)
Citation Context ...s that are not so simple to derive from a mere reflection of what happens with inductive types. The possibility to have co-inductive types in theorem proving tools was studied by Coquand [7], Paulson =-=[19]-=-, Leclerc and Paulin-Mohring [16], and Gimenez [13]. Most of these authors were inspired by Aczel [1]. The paper [2] provides a short presentation of terms and (possibly infinite) trees, mainly in set... |

27 | Fileters on coinductive streams, an application to eratosthenes’ sieve
- Bertot
(Show Context)
Citation Context ...ng co-recursive calls guarded by constructors imposes that one scrutinizes the structure of recursive functions to understand whether they really can be encoded in the language. One approach, used in =-=[3]-=- is to show that co-inductive objects also satisfy some inductive properties, which make it possible to define functions that have a recursive part, with usual structural recursive calls with respect ... |

19 |
An application of co-inductive types in Coq: Verification of the alternating bit protocol
- Giménez
- 1996
(Show Context)
Citation Context ...d it checks whether illegal uses of the co-recursive tactic have already been performed. 4 Applications Co-inductive types can be used to reason about hardware descriptions [9] concurrent programming =-=[14]-=-, finite state automata and infinite traces of execution, and temporal logic [5, 8]. The guarded by constructors structure of co-recursive functions is adapted to representing finite state automata. A... |

17 |
An axiomatization of linear temporal logic in the calculus of inductive constructions
- Coupet-Grimal
(Show Context)
Citation Context ...formed. 4 Applications Co-inductive types can be used to reason about hardware descriptions [9] concurrent programming [14], finite state automata and infinite traces of execution, and temporal logic =-=[5, 8]-=-. The guarded by constructors structure of co-recursive functions is adapted to representing finite state automata. A few concrete examples are also given in [4]. Co-inductive types are especially wel... |

14 |
Programming with streams in Coq — a case study: the sieve of Eratosthenes
- Leclerc, Paulin-Mohring
- 1993
(Show Context)
Citation Context ...e from a mere reflection of what happens with inductive types. The possibility to have co-inductive types in theorem proving tools was studied by Coquand [7], Paulson [19], Leclerc and Paulin-Mohring =-=[16]-=-, and Gimenez [13]. Most of these authors were inspired by Aczel [1]. The paper [2] provides a short presentation of terms and (possibly infinite) trees, mainly in set-theoretic terms; it also explain... |

9 |
Gianantonio. A Co-Inductive Approach to Real Numbers. Types for Proofs and Programs
- Ciaffaglione, Di
- 2000
(Show Context)
Citation Context ...troduction to exact real arithmetics The work presented in this section is my own, but it is greatly inspired by reading the lecture notes [10] and the thesis [17] and derived papers [18, 15], and by =-=[6]-=-. These papers 6sshould be consulted for further references about exact real arithmetics, lazy computation, and co-inductive types. We are going to represent real numbers between 0 and 1 (included) as... |

7 |
Innite objects in type theory, in: Types for Proofs and
- Coquand
- 1993
(Show Context)
Citation Context ...nductive types that are not so simple to derive from a mere reflection of what happens with inductive types. The possibility to have co-inductive types in theorem proving tools was studied by Coquand =-=[7]-=-, Paulson [19], Leclerc and Paulin-Mohring [16], and Gimenez [13]. Most of these authors were inspired by Aczel [1]. The paper [2] provides a short presentation of terms and (possibly infinite) trees,... |

7 |
Formalising Exact Arithmetic: Representations, Algorithms and Proofs
- Niqui
- 2004
(Show Context)
Citation Context ...rded co-recursive parts. 5 An example: introduction to exact real arithmetics The work presented in this section is my own, but it is greatly inspired by reading the lecture notes [10] and the thesis =-=[17]-=- and derived papers [18, 15], and by [6]. These papers 6sshould be consulted for further references about exact real arithmetics, lazy computation, and co-inductive types. We are going to represent re... |

6 |
Reasoning about parametrized automata
- Castéran, Rouillard
- 2000
(Show Context)
Citation Context ...formed. 4 Applications Co-inductive types can be used to reason about hardware descriptions [9] concurrent programming [14], finite state automata and infinite traces of execution, and temporal logic =-=[5, 8]-=-. The guarded by constructors structure of co-recursive functions is adapted to representing finite state automata. A few concrete examples are also given in [4]. Co-inductive types are especially wel... |

3 | Formalising exact arithmetic in type theory
- Niqui
- 2005
(Show Context)
Citation Context ... 5 An example: introduction to exact real arithmetics The work presented in this section is my own, but it is greatly inspired by reading the lecture notes [10] and the thesis [17] and derived papers =-=[18, 15]-=-, and by [6]. These papers 6sshould be consulted for further references about exact real arithmetics, lazy computation, and co-inductive types. We are going to represent real numbers between 0 and 1 (... |

2 |
Algebras and Coalgebras. Algebraic and Coalgebraic
- Bertot
- 2002
(Show Context)
Citation Context ...ve co-inductive types in theorem proving tools was studied by Coquand [7], Paulson [19], Leclerc and Paulin-Mohring [16], and Gimenez [13]. Most of these authors were inspired by Aczel [1]. The paper =-=[2]-=- provides a short presentation of terms and (possibly infinite) trees, mainly in set-theoretic terms; it also explains recursion and co-recursion. In this document, we only consider the use of co-indu... |

2 |
Computing with Real Numbers. Applied semantics
- Edalat, Heckmann
- 2002
(Show Context)
Citation Context ... properties, and guarded co-recursive parts. 5 An example: introduction to exact real arithmetics The work presented in this section is my own, but it is greatly inspired by reading the lecture notes =-=[10]-=- and the thesis [17] and derived papers [18, 15], and by [6]. These papers 6sshould be consulted for further references about exact real arithmetics, lazy computation, and co-inductive types. We are g... |

2 |
Admissible digit sets
- Hughes, Niqui
- 2006
(Show Context)
Citation Context ... 5 An example: introduction to exact real arithmetics The work presented in this section is my own, but it is greatly inspired by reading the lecture notes [10] and the thesis [17] and derived papers =-=[18, 15]-=-, and by [6]. These papers 6sshould be consulted for further references about exact real arithmetics, lazy computation, and co-inductive types. We are going to represent real numbers between 0 and 1 (... |