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Domain Theoretic Models Of Polymorphism
, 1989
"... We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; th ..."
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Cited by 34 (2 self)
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We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; the universal types of the calculus are interpreted as the category of continuous sections of the fibration. As a major example a new model for the polymorphic calculus is presented. In it a type is interpreted as a Scott domain. In fact, understanding universal types of the polymorphic calculus as categories of continuous sections appears to be useful generally. For example, the technique also applies to the finitary projection model of Bruce and Longo, and a recent model of Girard. (Indeed the work here was inspired by Girard's and arose through trying to extend the construction of his model to Scott domains.) It is hoped that by pinpointing a key construction this paper will help towards...
Objects, Interference, and the Yoneda Embedding
, 1995
"... We present a new semantics for Algollike languages that combines methods from two prior lines of development: ffl the objectbased approach of [21,22], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functorcategory approach initiat ..."
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Cited by 16 (7 self)
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We present a new semantics for Algollike languages that combines methods from two prior lines of development: ffl the objectbased approach of [21,22], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functorcategory approach initiated by Reynolds [24], where the varying nature of the runtime stack is explained using functors from a category of store shapes to a category of cpos. The semantics
Universal Profinite Domains
 Information and Computation
, 1987
"... . We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite dom ..."
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Cited by 15 (1 self)
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. We introduce a bicartesian closed category of what we call profinite domains. Study of these domains is carried out through the use of an equivalent category of preorders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators. As a special instance of this construction, a universal domain for the category SFP is demonstrated. Necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations. A new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points. 1 Introduction. For our purposes a domain equation has the form X ¸ = F (X) where F is an operator on a class of semantic domains (typically, F is an endof...
A Convenient Category of Domains
 GDP FESTSCHRIFT ENTCS, TO APPEAR
"... We motivate and define a category of topological domains, whose objects are certain topological spaces, generalising the usual ωcontinuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also su ..."
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Cited by 13 (3 self)
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We motivate and define a category of topological domains, whose objects are certain topological spaces, generalising the usual ωcontinuous dcppos of domain theory. Our category supports all the standard constructions of domain theory, including the solution of recursive domain equations. It also supports the construction of free algebras for (in)equational theories, can be used as the basis for a theory of computability, and provides a model of parametric polymorphism.
An Operational Semantics for I/O in a Lazy Functional Language
 in Proc Functional Programming Languages and Computer Architecture
, 1993
"... I/O mechanisms are needed if functional languages are to be suitable for general purpose programming and several implementations exist. But little is known about semantic methods for specifying and proving properties of lazy functional programs engaged in I/O. As a step towards formal methods of rea ..."
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Cited by 9 (3 self)
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I/O mechanisms are needed if functional languages are to be suitable for general purpose programming and several implementations exist. But little is known about semantic methods for specifying and proving properties of lazy functional programs engaged in I/O. As a step towards formal methods of reasoning about realistic I/O we investigate three widely implemented mechanisms in the setting of teletype I/O: synchronisedstream (primitive in Haskell), continuationpassing (derived in Haskell) and Landinstream I/O (where programs map an input stream to an output stream of characters) . Using methods from Milner's CCS we give a labelled transition semantics for the three mechanisms. We adopt bisimulation equivalence as equality on programs engaged in I/O and give functions to map between the three kinds of I/O. The main result is the first formal proof of semantic equivalence of the three mechanisms, generalising an informal argument of the Haskell committee. 1 Introduction and motivation...
Retractions in Comparing Prolog Semantics
 IN PROC. COMPUTING SCIENCE IN THE NETHERLANDS, PART 1, P.M.G. APERS
, 1989
"... We present an operational model O and a continuation based denotational model D for a uniform variant of Prolog, including the cut operator. The two semantical definitions make use of higher order transformations F and Y, respectively. We prove O and D equivalent in a novel way by comparing yet anot ..."
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Cited by 2 (1 self)
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We present an operational model O and a continuation based denotational model D for a uniform variant of Prolog, including the cut operator. The two semantical definitions make use of higher order transformations F and Y, respectively. We prove O and D equivalent in a novel way by comparing yet another pair of higher order transformations F and Y , that yield F and Y, respectively, by application of a suitable abstraction operator.
Retractions in Comparing Prolog Semantics
, 1990
"... We present an operational model O and a continuation based denotational model D for a uniform variant of Prolog, including the cut operator. The two semantical definitions make use of higher order transformations F and Y, respectively. We prove O and D equivalent in a novel way by comparing yet anot ..."
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We present an operational model O and a continuation based denotational model D for a uniform variant of Prolog, including the cut operator. The two semantical definitions make use of higher order transformations F and Y, respectively. We prove O and D equivalent in a novel way by comparing yet another pair of higher order transformations F and Y , that yield F and Y, respectively, by application of a suitable abstraction operator. Section 1 Introduction In [BV] we presented both an operational and a denotational continuation based semantics for the core of Prolog, and we proved these two semantics equivalent. We used a two step approach, by first deriving these results for an intermediate language, obtained by stripping the logic programming aspects (substitutions, most general unifiers and all that) from Prolog. This resulted in the abstract language B in which only the control structure from Prolog remained, such as the backtrack mechanism and the cut operator. After having co...
Colimits in the category DCPO
"... : We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions we show how to construct a colimit for any functor F from a small category " into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate u ..."
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: We establish sufficient and necessary conditions for a natural sink to be a colimit in DCPO. Based on these conditions we show how to construct a colimit for any functor F from a small category " into the category DCPO. This demonstrates that the category DCPO is cocomplete. We also investigate under what conditions the colimit object is algebraic. 0 Introduction Colimits play an important role in modeling subtyping relations. Given a domain of type names D, it is common to interpret it with a functor F from the domain D into the category DCPO, where F assigns to each type name the corresponding dcpo of semantic values. A subtyping relation type 1 <type 2 in D is interpreted as a continuous function from F(type 1 ) into F(type 2 ). It is reasonable to require that if we have a (directed) set of type names Q st. type Q is the lub of Q in D, then the dcpo corresponding to type Q should be the colimit of all the dcpos corresponding to type names in Q. Existence of arbitrary colimits ...
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"... GRAEME FONBES, D.PHIL. Continuous d,irected complete partial orders (continuous dcpo's) are ordered algebraic structures which serve as mathematical models for the semantics of programming languages.. The class of continuous dcpo's is the closure of the class of algebraic dcpo's under images of Scot ..."
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GRAEME FONBES, D.PHIL. Continuous d,irected complete partial orders (continuous dcpo's) are ordered algebraic structures which serve as mathematical models for the semantics of programming languages.. The class of continuous dcpo's is the closure of the class of algebraic dcpo's under images of Scottcontinuous projections pz D+ D. The paradigm is lhe Cøntor functi,on p:C+ C, which is a Scottcontinuous projection on the Cantor set such that im(p) is isomorphic to the unit interval. A dcpo D is called projectíonsto,ble ifffor ali p € lD\Dl, i*(p) is algebraic. If all orderdense chains in /f(D) are degenerate, then an algebraic dcpo D is projectionstable. The converse is not true. If D has a bottom, then the converse is valid. The class of projectionstable dcpo's is closed under arbitrary products. Let D be a continuous Ldomain (profinite dcpo) with bottom. Then, lDl:Dl is a continuous Ldomain (profinite dcpo) with bottom itr [DSD] is a continuous dcpo iff D is projectionstable. Every dldomain is projectionstable. The dcpo (Proj(D), E) is a dldomain, if