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Coalgebras for Binary Methods: Properties of Bisimulations and Invariants

Hendrik Tews (2010)

RAIRO - Theoretical Informatics and Applications

Coalgebras for endofunctors 𝒞 → 𝒞 can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors 𝒞 o p × 𝒞 → 𝒞 . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many...

Coproducts of ideal monads

Neil Ghani, Tarmo Uustalu (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...

Coproducts of Ideal Monads

Neil Ghani, Tarmo Uustalu (2010)

RAIRO - Theoretical Informatics and Applications

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly  [Bull.  Austral. Math. Soc.22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell.2309 (2002)...

Declarative and procedural semantics of fuzzy similarity based unification

Peter Vojtáš (2000)

Kybernetika

In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming extended...

Definition of Flat Poset and Existence Theorems for Recursive Call

Kazuhisa Ishida, Yasunari Shidama, Adam Grabowski (2014)

Formalized Mathematics

This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...

Denotational aspects of untyped normalization by evaluation

Andrzej Filinski, Henning Korsholm Rohde (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the standard normalization-by-evaluation construction for the simply-typed λ β η -calculus has a natural counterpart for the untyped λ β -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...

Denotational aspects of untyped normalization by evaluation

Andrzej Filinski, Henning Korsholm Rohde (2010)

RAIRO - Theoretical Informatics and Applications

We show that the standard normalization-by-evaluation construction for the simply-typed λβη-calculus has a natural counterpart for the untyped λβ-calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal...

Denotational semantics of languages with fuzzy data.

Daniel Sánchez Alvarez, Antonio F. Gómez Skarmeta (2000)

Mathware and Soft Computing

The denotational semantics of a programming language which manages fuzzy data is presented. The introduction of blocks poses problems regarding transmission, both for the degree at which the work is carried out and for triangular operations necessary for the evaluation of the degrees of the fuzzy data. We propose some solutions. The possibility of defining linguistic variables is provided.

Domain mu-calculus

Guo-Qiang Zhang (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The basic framework of domain μ -calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the μ -calculus without function space or powerdomain constructions, and studies some open problems related to this μ -calculus such as decidability and expressive power. A class of language equations is introduced for encoding μ -formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain μ -calculus....

Domain mu-calculus

Guo-Qiang Zhang (2010)

RAIRO - Theoretical Informatics and Applications

The basic framework of domain μ-calculus was formulated in [39] more than ten years ago. This paper provides an improved formulation of a fragment of the μ-calculus without function space or powerdomain constructions, and studies some open problems related to this μ-calculus such as decidability and expressive power. A class of language equations is introduced for encoding μ-formulas in order to derive results related to decidability and expressive power of non-trivial fragments of the domain...

Dynamic overloading with copy semantics in object-oriented languages: a formal account

Lorenzo Bettini, Sara Capecchi, Betti Venneri (2009)

RAIRO - Theoretical Informatics and Applications

Mainstream object-oriented languages often fail to provide complete powerful features altogether, such as, multiple inheritance, dynamic overloading and copy semantics of inheritance. In this paper we present a core object-oriented imperative language that integrates all these features in a formal framework. We define a static type system and a translation of the language into the meta-language λ_object,, in order to account for semantic issues and prove type safety of our proposal.

Encoding FIX in Object Calculi

Roy L. Crole (2010)

RAIRO - Theoretical Informatics and Applications

We show that the FIX type theory introduced by Crole and Pitts [3] can be encoded in variants of Abadi and Cardelli's object calculi. More precisely, we show that the FIX type theory presented with judgements of both equality and operational reduction can be translated into object calculi, and the translation proved sound. The translations we give can be seen as using object calculi as a metalanguge within which FIX can be represented; an analogy can be drawn with Martin Löf's Theory of Arities...

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and...

Enumerated type semantics for the calculus of looping sequences

Livio Bioglio (2011)

RAIRO - Theoretical Informatics and Applications

The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure...

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