## Themes in Final Semantics (1998)

Venue: | Dipartimento di Informatica, Università di |

Citations: | 6 - 2 self |

### BibTeX

@TECHREPORT{Lenisa98themesin,

author = {Marina Lenisa},

title = {Themes in Final Semantics},

institution = {Dipartimento di Informatica, Università di},

year = {1998}

}

### OpenURL

### Abstract

C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e

### Citations

1163 |
The Lambda Calculus Its Syntax and Semantics
- Barendregt
- 1984
(Show Context)
Citation Context ...s\ThetasV alh satisfying the following rules, for n * 0: xM1 : : : Mn +h xM1 : : : Mn M +h N *x:M +h *x:N M [N=x]M1 : : : Mn +h P (*x:M)N M1 : : : Mn +h P fi-reduction is correct w.r.t. ssh (see e.g. =-=[Bar84]-=-). !n strategy. The normalizing strategy !n` \Lambdas\Thetas\Lambdasreduces the leftmost firedex. V aln is the set of *-terms in normal form. The evaluation +n is the least binary relation over \Lambd... |

1057 | A calculus of mobile processes - Milner, Parrow, et al. - 1992 |

711 | A framework for defining logics
- Harper, Honsel, et al.
- 1987
(Show Context)
Citation Context ...-calculus, we have found it convenient to give first a higher order presentation of it, using as metalanguage a logical framework based on typed *-calculus, such as the Edinburgh Logical Framework LF =-=[HHP93]-=-. This LF presentation provides useful insights into the nature of the various binding operators of the ss-calculus thus allowing to focus on the uses of free and bound names. Capitalizing on this, on... |

693 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...mulation. When specializing the Principle 2.1.5 to maximal fixpoints of relations, the object x which appears in the premise of the Coinduction Principle 2.1.5 is called \Phi -bisimulation, following =-=[Par81]-=-. It is interesting to point out that, in the context of non-wellfounded set theory, the same notion was independently called conservative relation by Forti and Honsell ([FH83]), and contraction by Hi... |

327 | Calculi for synchrony and asynchrony - Milner - 1983 |

314 | Subtyping recursive types - Amadio, Cardelli - 1993 |

307 | The linear time – branching time spectrum I
- Glabbeek
- 2001
(Show Context)
Citation Context ...3. Final Semantics for LP A: Linear-like Equivalences 67 Remark 5.2.21 (Simulation-like Equivalences) In order to give final semantics to simulation-like equivalences (see e.g. van Glabbeek spectrum, =-=[Gla90]-=-), we need a refined notion of categorical F -bisimulation, i.e. that of ordered categorical bisimulation in a order enriched categorical setting (see [RT93, Fio96]). We shall not develop this. 5.3 Fi... |

220 |
A filter lambda model and the completeness of type assignment
- Barendregt, Coppo, et al.
- 1983
(Show Context)
Citation Context ...natory *-algebra, and we state the Soundness Theorem 7.6.48 for combinatory oe-algebras. w.r.t. the type theory Toe, and the Completeness Theorem 7.6.49, which generalizes the Completeness Theorem of =-=[BCD83]-=-. Up to a first approximation, our main result states that, if the model Doe is a combinatory oe-algebra and A is a combinatory oe-algebra with an adequate Toe type interpretation for which the Soundn... |

211 | Non-well-founded Sets - Aczel - 1988 |

199 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ..., these languages cannot be captured by any of the general formats introduced in the literature, in particular they are not instances of the tyf t=tyxt format with global state operator introduced in =-=[GV92]-=-. We extend the final semantics paradigm to imperative concurrent languages, providing two alternative final descriptions, to which correspond different, logically independent coinduction principles. ... |

164 | A final coalgebra theorem - Aczel, Mendler - 1989 |

148 |
Intuitionistic Type Theory. Bibliopolis
- Martin-Löf
- 1984
(Show Context)
Citation Context ...r Order Logic, where the theory of maximal fixed points can be explicitly formalized; - the various systems of Intuitionistic Type Theories such as Constable's NUPRL, based on Martin-L"of Type Theory =-=[Mar84]-=-, where one can introduce special expressions and proof rules for dealing with infinite objects [MPC86]. An extremely interesting technique for dealing with coinductive types in Intuitionistic Type Th... |

137 | Full abstraction in the lazy lambda calculus
- Abramsky, Ong
- 1993
(Show Context)
Citation Context ... functors F and G, respectively. The functors F and G induce two conceptually independent coinduction principles. The first turns out to be the one corresponding to applicative bisimulation (see e.g. =-=[AO93]-=-), and the latter appears to be a new coinduction principle, which exploits the alternation of 8 and 9 quantifiers. A large part of Chapter 7 is devoted to the investigation of the general conditions ... |

137 |
Terminal coalgebras in well-founded set theory, Theoret
- Barr
- 1993
(Show Context)
Citation Context ...ne should also try to avoid "sweeping under the rug" many details for the sake of categorical elegance. Hence, contrary to the position advocated by Barr, such "exotica as nonwellfounded set theory" (=-=[Bar93]-=-), is welcome in Final Semantics, in that it allows to avoid using elaborate indirect encodings or cumbersome quotients. Using hypersets one operates, once and for all, a unique quotient operation at ... |

126 |
A complete inference system for a class of regular behaviours
- Milner
- 1984
(Show Context)
Citation Context ...rphic subobjects. To put it differently, we axiomatize the equivalence induced by the final semantics. Alternative axiomatizations of the notion of strong bisimulation have been proposed by Milner in =-=[Mil84]-=-. Our work is probably related to [Coq94]. It is inspired by [BH97], where a coinductive axiomatization of the type (in)equality for a simple first order language of regular recursive types is provide... |

125 | Bisimilarity as a theory of functional programming - Gordon - 1995 |

108 | Functional Programming and Input/Output - Gordon - 1994 |

75 | Codifying guarded definitions with recursion schemes - Giménez - 1994 |

66 | Coinductive axiomatization of recursive type equality and subtyping
- Brandt, Henglein
- 1998
(Show Context)
Citation Context ...ce induced by the final semantics. Alternative axiomatizations of the notion of strong bisimulation have been proposed by Milner in [Mil84]. Our work is probably related to [Coq94]. It is inspired by =-=[BH97]-=-, where a coinductive axiomatization of the type (in)equality for a simple first order language of regular recursive types is provided. The types considered in [BH97] are terms for denoting regular bi... |

59 |
Vicious Circles. On the Mathematics of Non-Wellfounded Phenomena
- Barwise, Moss
- 1996
(Show Context)
Citation Context ...st of related work, presenting approaches alternative to the ones we have explored, which would be extremely interesting to compare to ours. The classification is done by topic: ffl Barwise and Moss (=-=[BM96]-=-) presented an approach to circular objects based on hypersets, developing some sort of "category-free" final semantics; ffl Pitts ([Pit96a]), and Hermida and Jacobs ([HJ95]) presented categorical acc... |

56 | Bisimulation can't be traced: preliminary report
- Bloom, Istrail, et al.
- 1988
(Show Context)
Citation Context ...anguages, in a uniform way. In particular, in Section 5.1, we present the syntax of a generic process algebra language, and we recall the strong operational semantics of it, expressed in GSOS format (=-=[BIM88]-=-). In Sections 5.2 and 5.3, we provide a general definition of branching-like bisimulations, which we call B-bisimulations, and a general definition of linear-like bisimulations, i.e. L-bisimulations.... |

54 |
Set Theory with Free Construction Principles , Ann
- Forti, Honsell
- 1983
(Show Context)
Citation Context ...gs. This thesis can be viewed also as an investigation in the applicability of hypersets, i.e. non-wellfounded sets belonging to a universe satisfying the antifoundation axiom X1 of Forti and Honsell =-=[FH83]-=- (Aczel's AF A of [Acz88]). In this sense, the work in this thesis goes in the line of ([Bar91, BM96]). Particularly interesting in this respect are the connections that we draw with metric semantics ... |

52 | Inductive and coinductive types with iteration and recursion - Geuvers - 1992 |

44 | Mechanizing coinduction and corecursion in higher-order logic
- Paulson
- 1997
(Show Context)
Citation Context ...ch make use of partial elements, see e.g. [Plo85]; - the various framework theories such as Talcott's IOCC [Tal90], based on Feferman's theory of operations and classes [Fef90], or Paulson's Isabelle =-=[Pau93]-=-, based on Higher Order Logic, where the theory of maximal fixed points can be explicitly formalized; - the various systems of Intuitionistic Type Theories such as Constable's NUPRL, based on Martin-L... |

37 | A coinduction principle for recursive data types based on bisimulation - Fiore - 1996 |

37 | From Operational Semantics to Domain Theory - Mason, Smith, et al. - 1996 |

36 | Dynamic congruence vs. progressing bisimulation for CCS
- Montanari, Sassone
- 1992
(Show Context)
Citation Context ...e equivalences are special instances of B-equivalences, e.g. the strong bisimulation, the branching bisimulation of [GW89], Milner's weak bisimulation and weak congruence, the dynamic bisimulation of =-=[MS92]-=-. Particular instances of L-equivalences are: the partial trace equivalence, the completed trace equivalence, the failure equivalence, etc.. We give final semantics descriptions for the B-equivalence ... |

28 |
An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus
- Honsell, Rocca
- 1992
(Show Context)
Citation Context ...ruence which is a *-equivalence. ffl A *-theory is the restriction of a *-congruence to \Lambda 0(C). The following proposition gives a useful characterization of *-pre-congruences and *-congruences (=-=[HR92]-=-): Proposition 7.1.2 ffl Any *-pre-congruence ^oe` \Lambda (C) \Thetas\Lambda (C) is induced by a suitable set of oe-valuable terms Voe ` \Lambda ffi(C)2, in the following sense: M ^oe N () 8C[ ]: (C[... |

27 | Control Flow Semantics. Foundations of Computing Series - Bakker, Vink - 1996 |

26 |
Type Theories, Normal Forms and D1-Lambda-Models. Information and Computation 72
- COPPO, DEZANI-CIANCAGLINI, et al.
- 1987
(Show Context)
Citation Context ...7.4.10 (Computational Adequacy of Dh) M +h () 9\Gammas9OE 6=h !: \Gammas`h M : OE : 7.4.5 A Computationally Adequate Model for ssn A computationally adequate model for ssn is the model Dn, studied in =-=[CDZ87]-=-. The model Dn is the inverse limit solution of the equation D ' [D ! D] in the category CP O, with domain Dn0 = f?; 0; 1g, with 0 `Dn 1, and projection jn1;0 : Dn1 ! Dn0 defined by: jn1;0(?) =?, jn1;... |

23 |
Polymorphic typed lambda-calculi in a type-free axiomatic framework
- Feferman
- 1990
(Show Context)
Citation Context ...ons based on Domain theory, which make use of partial elements, see e.g. [Plo85]; - the various framework theories such as Talcott's IOCC [Tal90], based on Feferman's theory of operations and classes =-=[Fef90]-=-, or Paulson's Isabelle [Pau93], based on Higher Order Logic, where the theory of maximal fixed points can be explicitly formalized; - the various systems of Intuitionistic Type Theories such as Const... |

22 | Computational adequacy via “mixed” inductive definitions - Pitts - 1994 |

20 | Coalgebra semantics for hidden algebra: parameterized objects and inheritance - Cı̂rstea - 1998 |

18 |
Ronchi Della Rocca S., “Operational, Denotational and Logical Description: a case study
- Egidi, Honsell
- 1992
(Show Context)
Citation Context ...case for initial models. In [Len97], we generalize Pitts' method also to non-initial models, using a different technique for proving the induction-coinduction principle. This technique is inspired by =-=[EHR92]-=-, where a related method is presented for proving that the applicative equivalence corresponding to the observational equivalence ssv induced by the lazy by-value strategy (see Section 7.3) is a congr... |

17 | A complete calculus for equational deduction in coalgebraic specification - Corradini - 1998 |

15 | Final semantics for a higher order concurrent language
- Lenisa
- 1996
(Show Context)
Citation Context ...the language Lco2 with second order communication. These languages are introduced and studied from the metric perspective in [BB93, BB9?]. Lpas2 is studied from the set-theoretic final perspective in =-=[Len96]-=-. We discuss the a priori approach for showing the compositionality of the final semantics for Lpas2 and Lco2, by defining semantical operators corresponding to the syntactical operators of the langua... |

12 | Co-Inductive Types in Coq : An Experiment with the Alternating Bit Protocol. Submitted for the proceedings of the BRA Workshop on Types for Proofs and Programs. Also available by ftp at ftp.ens-lyon.fr/pub/users/LIP/ABP.ps.Z
- Gim'enez
- 1995
(Show Context)
Citation Context ...tionistic Type Theories was introduced by Coquand in his seminal paper, [Coq94]. This technique, originally developed for predicative systems, was later extended by Gim'enez to impredicative systems, =-=[Gim95]-=-. In a sense, one can say that Coquand defines a system which can make sense of infinitely regressive proofs, by means of the guarded induction principle. This approach is particularly appealing, beca... |

11 | A sound metalogical semantics for input/output effects - Crole, Gordon - 1995 |

11 |
Innite objects in type theory
- Mendler, Panangaden, et al.
- 1986
(Show Context)
Citation Context ...tems of Intuitionistic Type Theories such as Constable's NUPRL, based on Martin-L"of Type Theory [Mar84], where one can introduce special expressions and proof rules for dealing with infinite objects =-=[MPC86]-=-. An extremely interesting technique for dealing with coinductive types in Intuitionistic Type Theories was introduced by Coquand in his seminal paper, [Coq94]. This technique, originally developed fo... |

11 | A note on logical relations between semantics and syntax
- Pitts
- 1997
(Show Context)
Citation Context ...3. Logical Relations method based on a mixed induction-coinduction principle. This semantical method is presented in [Len97]. It is the generalization of the technique originally introduced by Pitts (=-=[Pit96]-=-) for observational equivalences which have a suitable computationally adequate initial model, like ssl and ssv. In [Len97], this method is applied to all the strategies of Section 7.3. The method in ... |

10 | Algebraically complete categories, in: Category Theory - Freyd - 1990 |

10 |
Final semantics for untyped lambda-calculus
- Honsell, Lenisa
- 1995
(Show Context)
Citation Context ... functional languages, and its denotational semantics is usually expressed via contravariant functors in categories of complete partial orders (see [Wad76, CDZ87, HR92, EHR92, AO93, HL9?]). Following =-=[HL95]-=-, in Chapter 7, we present two alternative (uniform) final descriptions of *-theories, corresponding to the functors F and G, respectively. The functors F and G induce two conceptually independent coi... |

9 | Topological Models in Comparative Semantics - Breugel - 1994 |

9 |
Semantic Techniques for Deriving Coinductive Characterizations of Observational Equivalences for -calculi
- Lenisa
(Show Context)
Citation Context ...for the case of the observational equivalences which arise from lazy strategies. Pitts' technique is based on Plotkin's minimal invariance property of the model, as is the case for initial models. In =-=[Len97]-=-, we generalize Pitts' method also to non-initial models, using a different technique for proving the induction-coinduction principle. This technique is inspired by [EHR92], where a related method is ... |

7 | Topological Models for Higher Order Control Flow
- Bakker, Breugel
- 1993
(Show Context)
Citation Context ...fining semantical operators corresponding to the syntactical operators of the languages. Then we work out in detail the comparison between our final semantics and the metric denotational semantics of =-=[BB93]-=-. This section expands [Len96]. We prove that the equivalences induced by the two semantics coincide. This can be viewed as a sort of full abstraction of the metric semantics w.r.t. the syntactical fi... |

7 | Semantical analysis of perpetual strategies in -calculus. Theoret - Honsell, Lenisa - 1999 |

7 | An extensional partial combinatory algebra based on λ-terms - Perez - 1991 |

5 |
Comparative Metric Semantics for Programming Languages
- Breugel
- 1998
(Show Context)
Citation Context ...ntroduced a categorical definition of bisimulation based on open maps; ffl there exist the traditional domain-based approaches to coinductive types based on partial orders ([Plo85]) or metric spaces (=-=[Bre97a]-=-). But theres173 exist also new frameworks for reasoning on infinite objects, such as hyperuniverses ([FH96, FHL94, FHL95]), which try to combine metric spaces and hypersets; ffl there exists at lest ... |

5 |
Branching Time and Abstraction
- Glabbeek, Weijland
- 1996
(Show Context)
Citation Context ...linear equivalence, which we call L-equivalence. As we will show, many branching-like equivalences are special instances of B-equivalences, e.g. the strong bisimulation, the branching bisimulation of =-=[GW89]-=-, Milner's weak bisimulation and weak congruence, the dynamic bisimulation of [MS92]. Particular instances of L-equivalences are: the partial trace equivalence, the completed trace equivalence, the fa... |

5 | and Classes, co-algebraically, Object-Orientation with Parallelism and Book Persistence, B.Freitag et - Objects - 1996 |