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NonDeterministic Extensions of Untyped λcalculus
 INFO. AND COMP
, 1995
"... The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in ..."
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The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in presence of functional application and abstraction. We identify non determinism in the setting of λcalculus with the absence of the ChurchRosser property plus the inconsistency of the equational theory obtained by the symmetric closure of the reduction relation. We argue in favour of a distinction between non determinism and parallelism, due to the conjunctive nature of the former in contrast to the disjunctive character of the latter. This is the basis of our analysis of the operational and denotational semantics of non deterministiccalculus, which is the classical calculus plus a choice operator, and of our election of bounded indeterminacy as the semantical counterpart of conjunctive non determinism. This leads to operational semantics based on...
Proof Methods for Structured Corecursive Programs
, 1999
"... Corecursive programs produce values of greatest fixpoint types, in contrast to recursive programs, which consume values of least fixpoint types. There are a number of widely used methods for proving properties of corecursive programs, including fixpoint induction, the take lemma, and coinduction. Ho ..."
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Cited by 12 (3 self)
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Corecursive programs produce values of greatest fixpoint types, in contrast to recursive programs, which consume values of least fixpoint types. There are a number of widely used methods for proving properties of corecursive programs, including fixpoint induction, the take lemma, and coinduction. However, these methods are all rather lowlevel, in the sense that they do not exploit the common structure that is often present in corecursive definitions. We argue for a more structured approach to proving properties of corecursive programs. In particular, we show that by writing corecursive programs using an operator called unfold that encapsulates a common pattern of corecursive de nition, we can then use highlevel algebraic properties of this operator to conduct proofs in a purely calculational style that avoids the use of either induction or coinduction.
From coalgebraic to monoidal traces
 Coalgebraic Methods in Computer Science (CMCS 2010), volume 264 of Elect. Notes in Theor. Comp. Sci
, 2010
"... The main result of this paper shows how coalgebraic traces, in suitable Kleisli categories, give rise to traced monoidal structure in those Kleisli categories, with finite coproducts as monoidal structure. At the heart of the matter lie partially additive monads inducing partially additive structure ..."
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Cited by 8 (2 self)
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The main result of this paper shows how coalgebraic traces, in suitable Kleisli categories, give rise to traced monoidal structure in those Kleisli categories, with finite coproducts as monoidal structure. At the heart of the matter lie partially additive monads inducing partially additive structure in their Kleisli categories. By applying the standard “Int ” construction one obtains compact closed categories for “bidirectional monadic computation”. 1
An extension theorem with an application to formal tree series
 BRICS Report Series
, 2002
"... series ..."
Approximation in quantaleenriched categories
 DIRK HOFMANN AND PAWE L WASZKIEWICZ
, 2010
"... ar ..."
CSP, Partial Automata, and Coalgebras
, 1999
"... Based on the theory of coalgebras the paper builds a bridge between CSP and automata theory. We show that the concepts of processes in [4] coincide with the concepts of states for special, namely, final partial automata. Moreover, we show how the deterministic and nondeterministic operations in [4] ..."
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Cited by 3 (0 self)
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Based on the theory of coalgebras the paper builds a bridge between CSP and automata theory. We show that the concepts of processes in [4] coincide with the concepts of states for special, namely, final partial automata. Moreover, we show how the deterministic and nondeterministic operations in [4] can be interpreted in a compatible way by constructions on the semantical level of automata. Especially, we are able to interpret each finite process expression as representing a finite partial automaton with a designated initial state. In such a way we provide a new method for solving recursive process equations which is based on the concept of final automata. That is, there is no need to impose a cpo structure on the set of processes to describe the solutions of recursive process equations. 1 Introduction For people usually working on model theory or semantics of formal specifications it becomes often very hard to approach the area of process calculi and process algebras. There are proces...
Difunctorial Semantics of Object Calculus
 WOOD 2004 PRELIMINARY VERSION
, 2004
"... In this paper we give a denotational model for Abadi and Cardelli’s first order object calculus FOb1+×µ (without subtyping) in the category pCpo. The key novelty of our model is its extensive use of recursively defined types, supporting selfapplication, to model objects. At a technical level, this ..."
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In this paper we give a denotational model for Abadi and Cardelli’s first order object calculus FOb1+×µ (without subtyping) in the category pCpo. The key novelty of our model is its extensive use of recursively defined types, supporting selfapplication, to model objects. At a technical level, this entails using some sophisticated techniques such as Freyd’s algebraic compactness to guarantee the existence of the denotations of the object types. The last sections of the paper demonstrates that the canonical recursion operator inherent in our semantics is potentially useful in objectoriented programming. This is witnessed by giving a straightforward translation of algebraic datatypes into so called wrapper classes.
Coalgebraic Representation Theory of Fractals (Extended Abstract)
"... We develop a representation theory in which a point of a fractal specified by metric means (by a variant of an iterated function system, IFS) is represented by a suitable equivalence class of infinite streams of symbols. The framework is categorical: symbolic representatives carry a final coalgebra; ..."
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We develop a representation theory in which a point of a fractal specified by metric means (by a variant of an iterated function system, IFS) is represented by a suitable equivalence class of infinite streams of symbols. The framework is categorical: symbolic representatives carry a final coalgebra; an IFSlike metric specification of a fractal is an algebra for the same functor. Relating the two there canonically arises a representation map, much like in America and Rutten’s use of metric enrichment in denotational semantics. A distinctive feature of our framework is that the canonical representation map is bijective. In the technical development, gluing of shapes in a fractal specification is a major challenge. On the metric side we introduce the notion of injective IFS to be used in place of conventional IFSs. On the symbolic side we employ Leinster’s presheaf framework that uniformly addresses necessary identification of streams—such as.0111... =.1000... in the binary expansion of real numbers. Our leading example is the unit interval I = [0, 1].
ISBN: 9789090228273
, 1978
"... The work in this thesis has been carried out under the auspices of the research school ..."
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The work in this thesis has been carried out under the auspices of the research school