## Temporal Logic in Coq (1998)

Citations: | 1 - 0 self |

### BibTeX

@TECHREPORT{Paiva98temporallogic,

author = {Nuno Paiva and Supervised Am'ilcar Sernadas and Carlos Caleiro},

title = {Temporal Logic in Coq},

institution = {},

year = {1998}

}

### OpenURL

### Abstract

The aim of this work is to implement temporal logic in the Coq proof assistant system. This implementation uses the logical language of Coq as meta-language for temporal logic representation. The work starts with a crash introduction to Coq devoted to introduce the Coq system. The implementation of linear temporal logic and two branching temporal logics is discussed. In both linear and branching temporal logic soundness verification of proposed axiomatizations is made. Some application examples are shown. 1 Acknowledgments To Prof. Am'ilcar Sernadas, whitout whom this work would not have been possible, for his ideas and guidance. To Carlos for his guidance, constant help, presence and friendship. To Jaime and Paulo for their suggestions. To Sara and Alexandra for their good humor, support and fellowship. To all section 84. This work was partially supported by the PRAXIS XXI Program and FCT, as well as by PRAXIS XXI Projects 2/2.1/MAT/262/94 SitCalc, PCEX/P/MAT/46/96 ACL plus 2/2.1/TI...

### Citations

1108 | Temporal and Modal Logic
- Emerson
- 1990
(Show Context)
Citation Context ...ystem. The implementation uses the logical language of Coq as meta-language for temporal logic representation. Temporal logic is designed to reason about how truth values of assertions vary with time =-=[Eme90]-=-. It is useful, among other applications, to specify and verify correctness of computer programs, especially appropriate for reasoning about nonterminating or continuously operating concurrent program... |

304 | Introduction to Mathematical Logic - Mendelson - 1987 |

200 |
Logics of Time and Computation
- Goldblatt
- 1987
(Show Context)
Citation Context ...ation of PLTL It is now possible to use this implementation of the semantics of propositional linear temporal logic to prove the soundness of the axiomatization. The axiomatization used is taken from =-=[Gol92]-=-, and includes the axioms: Fx1: ((:(X a)) , (X (:a))) Fx2: ((X (a ) b)) , ((X a) ) (X b))) Fx3: ((G(a ) b)) ) ((G a) ) (G b))) Fx4: ((G(a ) (X a))) ) (a ) (G a))) Fx5: ((G a) ) (as(G a))) Fx6: ((a U b... |

15 |
Circuits as Streams in Coq: Verification of a Sequential Multiplier
- Paulin-Mohring
- 1995
(Show Context)
Citation Context ... is made by creating the Und inductive type with an unique element und, and then making the disjoint sum of this type with the previous ones, using TSum (refer to Apendix A and similar command Sum in =-=[PM95]-=-). Inductive Und : Type := und : Und. Definition Label plus Und : Type := (Tsum L Und). Definition Forest plus Und : Type := (Tsum Forest Und). Definition Tree plus Und : Type := (Tsum Tree Und). It i... |

13 | Branching Time and Partial Order in Temporal Logics, Time and Logic: A Computational Approach
- Penczek
- 1995
(Show Context)
Citation Context ...) is a formula. The basic abbreviations are: ffl (8G a) j abv (:(9F (:a))), 31 ffl (8F a) j abv (:(9G (:a))), ffl (8X a) j abv (:(9X (:a))). The set of UB formulae is equivalent to the one defined in =-=[Pen95]. The temporal operators have -=-intuitive meanings linked to linear temporal logic: (9G a) "there is a path where (G a)", (9F a) "there is a path where (F a)" and (9X a) "there is a path where (X a)". T... |

7 | Coquand's calculus of constructions: A mathematical foundation for a proof development system - Seldin - 1992 |

2 | Course notes in typed lambda calculus - Coquand - 1997 |

1 | The Coq Proof Assistant: A Tutorial. INRIA Rocquencourt - Huet, Kahn, et al. - 1996 |

1 |
The Coq Proof Assistant: The Standard Library
- Rocquencourt
- 1996
(Show Context)
Citation Context ...ent purposes. The following are just the equivalent for TStream to the basic definitions of streams provided by the library of Coq Stream.v and introduced in chapter 10 of [PM96]. Refer to [PM96] and =-=[INR96]-=- for further explanations. Section Type Streams. Section Type Streams. Variable L : Type. CoInductive Type TStream := TScons : L!TStream!TStream. Definition TShead := [s:TStream] Cases s of (TScons a ... |

1 |
The Coq Proof Assistant
- Paulin-Mohring
- 1996
(Show Context)
Citation Context ...t is a reserved word of Coq. The same happens with and and or. The constructors must satisfy a well-foundedness condition called the positivity conditionswhich is better explained in Section 6.5.3 of =-=[PM96]-=-. Roughly, this means that the basis of induction must be well defined. In the present it corresponds to the constructor id. The Coq system provides three destructors for Pform named Pform ind, Pform ... |

1 |
Introduc~ao `a teoria da computac~ao
- Sernadas
- 1993
(Show Context)
Citation Context ...ndix. 5 Chapter 2 A Crash introduction to Coq In this chapter a short presentation of the specification language Gallina and the proof system of Coq is given. Propositional Logic (PL) as described in =-=[Ser93]-=- is the chosen example. The representations of both its syntax and semantics are used to help describe both the specification language (used as a meta-language for the representation of PL) and the pr... |

1 | Folhas de Elementos L'ogicos da Programac~ao I, Secc~ao de Ciencia da Computac~ao - Sernadas, Sernadas, et al. - 1993 |