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Domain Theory in Logical Form
 Annals of Pure and Applied Logic
, 1991
"... The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and system ..."
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Cited by 228 (10 self)
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The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: • Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for denotational semantics. • The theory of concurrency and systems behaviour developed by Milner, Hennessy et al. based on operational semantics. • Logics of programs. Stone duality provides a junction between semantics (spaces of points = denotations of computational processes) and logics (lattices of properties of processes). Moreover, the underlying logic is geometric, which can be computationally interpreted as the logic of observable properties—i.e. properties which can be determined to hold of a process on the basis of a finite amount of information about its execution. These ideas lead to the following programme:
Design of the Programming Language Forsythe
, 1996
"... This is a description of the programming language Forsythe, which is a descendant of Algol 60 intended to be as uniform and general as possible, while retaining the basic character of its progenitor. This document supercedes Report CMUCS88159, "Preliminary Design of the Programming Language Fo ..."
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Cited by 109 (0 self)
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This is a description of the programming language Forsythe, which is a descendant of Algol 60 intended to be as uniform and general as possible, while retaining the basic character of its progenitor. This document supercedes Report CMUCS88159, "Preliminary Design of the Programming Language Forsythe" [1]. c fl1996 John C. Reynolds Research suuported by National Science Foundation Grant CCR9409997. Keywords: Forsythe, Algollike languages, Algol 60, intersection types 1. Introduction In retrospect, it is clear that Algol 60 [2, 3] was an heroic and surprisingly successful attempt to design a programming language from first principles. Its creation gave a formidable impetus to the development and use of theory in language design and implementation, which has borne rich fruit in the intervening thirtysix years. Most of this work has led to languages that are quite different than Algol 60, but there has been a continuing thread of concern with languages that retain the essentia...
Complete restrictions of the intersection type discipline
 Theoretical Computer Science
, 1992
"... In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its m ..."
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Cited by 103 (40 self)
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In this paper the intersection type discipline as defined in [Barendregt et al. ’83] is studied. We will present two different and independent complete restrictions of the intersection type discipline. The first restricted system, the strict type assignment system, is presented in section two. Its major feature is the absence of the derivation rule (≤) and it is based on a set of strict types. We will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in [Barendregt et al. ’83]. We will show that the strict type assignment system is the nucleus of the full system, i.e. for every derivation in the intersection type discipline there is a derivation in which (≤) is used only at the very end. Finally we will prove that strict type assignment is complete for inference semantics. The second restricted system is presented in section three. Its major feature is the absence of the type ω. We will show that this system gives rise to a filter λImodel and that type assignment without ω is complete for the λIcalculus. Finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable.
Programming with Intersection Types and Bounded Polymorphism
, 1991
"... representing the official policies, either expressed or implied, of the U.S. Government. ..."
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representing the official policies, either expressed or implied, of the U.S. Government.
Intersection Type Assignment Systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
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Cited by 61 (33 self)
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This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
The Relevance of Semantic Subtyping
 In IEEE Symposium on Logic in Computer Science (LICS
, 2002
"... We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, ..."
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Cited by 52 (9 self)
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We compare Meyer and Routley's minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that  for the functional core of the system  such notion of subtyping, which is defined in purely settheoretical terms, coincides with the relevant entailment of the logic B+ . 1
SetTheoretical and Other Elementary Models of the lambdacalculus
 Theoretical Computer Science
, 1993
"... Part 1 of this paper is the previously unpublished 1972 memorandum [43], with editorial changes and some minor corrections. Part 2 presents what happened next, together with some further development of the material. The first part begins with an elementary settheoretical model of the ficalculus. F ..."
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Cited by 40 (0 self)
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Part 1 of this paper is the previously unpublished 1972 memorandum [43], with editorial changes and some minor corrections. Part 2 presents what happened next, together with some further development of the material. The first part begins with an elementary settheoretical model of the ficalculus. Functions are modeled in a similar way to that normally employed in set theory, by their graphs; difficulties are caused in this enterprise by the axiom of foundation. Next, based on that model, a model of the fijcalculus is constructed by means of a natural deduction method. Finally, a theorem is proved giving some general properties of those nontrivial models of the fijcalculus which are continuous complete lattices. The second part begins with a brief discussion of models of the calculus in set theories with antifoundation axioms. Next the model of the fi calculus of Part 1 and also the closely relatedbut different!models of Scott [53, 54] and of Engeler [21, 22] are reviewed....
Intersection Types and Bounded Polymorphism
, 1996
"... this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism ..."
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Cited by 36 (0 self)
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this paper (Compagnoni, Intersection Types and Bounded Polymorphism 3 1994; Compagnoni, 1995) has been used in a typetheoretic model of objectoriented multiple inheritance (Compagnoni & Pierce, 1996). Related calculi combining restricted forms of intersection types with higherorder polymorphism and dependent types have been studied by Pfenning (Pfenning, 1993). Following a more detailed discussion of the pure systems of intersections and bounded quantification (Section 2), we describe, in Section 3, a typed calculus called F ("Fmeet ") integrating the features of both. Section 4 gives some examples illustrating this system's expressive power. Section 5 presents the main results of the paper: a prooftheoretic analysis of F 's subtyping and typechecking relations leading to algorithms for checking subtyping and for synthesizing minimal types for terms. Section 6 discusses semantic aspects of the calculus, obtaining a simple soundness proof for the typing rules by interpreting types as partial equivalence relations; however, another prooftheoretic result, the nonexistence of least upper bounds for arbitrary pairs of types, implies that typed models may be more difficult to construct. Section 7 offers concluding remarks. 2. Background
Graph lambda theories
 Journal of Logic and Computation
, 2004
"... Lambda theories are equational extensions of the untyped lambda calculus that are closed under derivation. The set of lambda theories is naturally equipped with a structure of complete lattice, where the meet of a family of lambda theories is their intersection, and the join is the least lambda theo ..."
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Cited by 19 (11 self)
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Lambda theories are equational extensions of the untyped lambda calculus that are closed under derivation. The set of lambda theories is naturally equipped with a structure of complete lattice, where the meet of a family of lambda theories is their intersection, and the join is the least lambda theory containing their union. In this paper we study the structure of the lattice of lambda theories by universal algebraic methods. We show that nontrivial quasiidentities in the language of lattices hold in the lattice of lambda theories, while every nontrivial lattice identity fails in the lattice of lambda theories if the language of lambda calculus is enriched by a suitable finite number of constants. We also show that there exists a sublattice of the lattice of lambda theories which satisfies: (i) a restricted form of distributivity, called meet semidistributivity; and (ii) a nontrivial identity in the language of lattices enriched by the relative product of binary relations.