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141
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 696 (39 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
Type systems
 The Computer Science and Engineering Handbook
, 1997
"... This paper presents an overview of the programming language Modula3, and a more detailed description of its type system. 1 ..."
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Cited by 202 (1 self)
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This paper presents an overview of the programming language Modula3, and a more detailed description of its type system. 1
Operations on records
 Mathematical Structures in Computer Science
, 1991
"... We define a simple collection of operations for creating and manipulating record structures, where records are intended as finite associations of values to labels. A secondorder type system over these operations supports both subtyping and polymorphism. We provide typechecking algorithms and limite ..."
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Cited by 142 (13 self)
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We define a simple collection of operations for creating and manipulating record structures, where records are intended as finite associations of values to labels. A secondorder type system over these operations supports both subtyping and polymorphism. We provide typechecking algorithms and limited semantic models. Our approach unifies and extends previous notions of records, bounded quantification, record extension, and parametrization by rowvariables. The general aim is to provide foundations for concepts found in objectoriented languages, within a framework based on typed lambdacalculus.
Type Inference with Polymorphic Recursion
 Transactions on Programming Languages and Systems
, 1991
"... The DamasMilner Calculus is the typed Acalculus underlying the type system for ML and several other strongly typed polymorphic functional languages such as Mirandal and Haskell. Mycroft has extended its problematic monomorphic typing rule for recursive definitions with a polymorphic typing rule. H ..."
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Cited by 136 (0 self)
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The DamasMilner Calculus is the typed Acalculus underlying the type system for ML and several other strongly typed polymorphic functional languages such as Mirandal and Haskell. Mycroft has extended its problematic monomorphic typing rule for recursive definitions with a polymorphic typing rule. He proved the resulting type system, which we call the MilnerMycroft Calculus, sound with respect to Milner’s semantics, and showed that it preserves the principal typing property of the DamasMilner Calculus. The extension is of practical significance in typed logic programming languages and, more generally, in any language with (mutually) recursive definitions. In this paper we show that the type inference problem for the MilnerMycroft Calculus is logspace equivalent to semiunification, the problem of solving subsumption inequations between firstorder terms. This result has been proved independently by Kfoury et al. In connection with the recently established undecidability of semiunification this implies that typability in the MilnerMycroft Calculus is undecidable. We present some reasons why type inference with polymorphic recursion appears to be practical despite its undecidability. This also sheds some light on the observed practicality of ML
DTD Inference for Views of XML Data
, 1999
"... We study the inference of Data Type Definitions (DTDs) for views of XML data, using an abstraction that focuses on document content structure. The views are defined by a query language that produces a list of documents selected from one or more input sources. The selection conditions involve vertica ..."
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Cited by 119 (12 self)
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We study the inference of Data Type Definitions (DTDs) for views of XML data, using an abstraction that focuses on document content structure. The views are defined by a query language that produces a list of documents selected from one or more input sources. The selection conditions involve vertical and horizontal navigation, thus querying explicitly the order present in input documents. We point several strong limitations in the descriptive ability of current DTDs and the need for extending them with (i) a subtyping mechanism and (ii) a more powerful specification mechanism than regular languages, such as contextfree languages. With these extensions, we show that one can always infer tight DTDs, that precisely characterize a selection view on sources satisfying given DTDs. We also show important special cases where one can infer a tight DTD without requiring extension (ii). Finally we consider related problems such as verifying conformance of a view definition with a predefined DTD....
A Paradigmatic ObjectOriented Programming Language: Design, Static Typing and Semantics
 Journal of Functional Programming
, 1993
"... In order to illuminate the fundamental concepts involved in objectoriented programming languages, we describe the design of TOOPL, a paradigmatic, staticallytyped, functional, objectoriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and in ..."
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Cited by 117 (9 self)
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In order to illuminate the fundamental concepts involved in objectoriented programming languages, we describe the design of TOOPL, a paradigmatic, staticallytyped, functional, objectoriented programming language which supports classes, objects, methods, hidden instance variables, subtypes, and inheritance. It has proven to be quite difficult to design such a language which has a secure type system. A particular problem with statically type checking objectoriented languages is designing typechecking rules which ensure that methods provided in a superclass will continue to be type correct when inherited in a subclass. The typechecking rules for TOOPL have this feature, enabling library suppliers to provide only the interfaces of classes with actual executable code, while still allowing users to safely create subclasses. In order to achieve greater expressibility while retaining typesafety, we choose to separate the inheritance and subtyping hierarchy in the language. The design of...
An Interactionbased Language and its Typing System
 In PARLE’94, volume 817 of LNCS
, 1994
"... We present a small language L and its typing system based on the idea of interaction, one of the important notions in parallel and distributed computing. L is based on, apart from such constructs as parallel composition and process creation, three pairs of communication primitives which use the noti ..."
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Cited by 109 (17 self)
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We present a small language L and its typing system based on the idea of interaction, one of the important notions in parallel and distributed computing. L is based on, apart from such constructs as parallel composition and process creation, three pairs of communication primitives which use the notion of a session, a semantically atomic chain of communication actions which can interleave with other such chains freely, for highlevel abstraction of interactionbased computing. Three primitives enable programmers to elegantly describe complex interactions among processes with a rigorous type discipline similar to ML [4]. The language is given formal operational semantics and a type inference system, regarding which we prove that if a program is welltyped in the typing system, it never causes runtime error due to type inconsistent communication patterns, offering a new foundation for type discipline in parallel programming languages. 1 Introduction The idea of interaction, that is, rec...
Abstract Models of Memory Management
, 1995
"... Most specifications of garbage collectors concentrate on the lowlevel algorithmic details of how to find and preserve accessible objects. Often, they focus on bitlevel manipulations such as "scanning stack frames," "marking objects," "tagging data," etc. While these d ..."
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Cited by 90 (16 self)
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Most specifications of garbage collectors concentrate on the lowlevel algorithmic details of how to find and preserve accessible objects. Often, they focus on bitlevel manipulations such as "scanning stack frames," "marking objects," "tagging data," etc. While these details are important in some contexts, they often obscure the more fundamental aspects of memory management: what objects are garbage and why? We develop a series of calculi that are just lowlevel enough that we can express allocation and garbage collection, yet are sufficiently abstract that we may formally prove the correctness of various memory management strategies. By making the heap of a program syntactically apparent, we can specify memory actions as rewriting rules that allocate values on the heap and automatically dereference pointers to such objects when needed. This formulation permits the specification of garbage collection as a relation that removes portions of the heap without affecting the outcome of the evaluation. Our highlevel approach allows us to specify in a compact manner a wide variety of memory management techniques, including standard tracebased garbage collection (i.e., the family of copying and mark/sweep collection algorithms), generational collection, and typebased, tagfree collection. Furthermore, since the definition of garbage is based on the semantics of the underlying language instead of the conservative approximation of inaccessibility, we are able to specify and prove the idea that type inference can be used to collect some objects that are accessible but never used.
Types for Dyadic Interaction
, 1993
"... We formulate a typed formalism for concurrency where types denote freely composable structure of dyadic interaction in the symmetric scheme. The resulting calculus is a typed reconstruction of name passing process calculi. Systems with both the explicit and implicit typing disciplines, where types f ..."
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Cited by 86 (10 self)
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We formulate a typed formalism for concurrency where types denote freely composable structure of dyadic interaction in the symmetric scheme. The resulting calculus is a typed reconstruction of name passing process calculi. Systems with both the explicit and implicit typing disciplines, where types form a simple hierarchy of types, are presented, which are proved to be in accordance with each other. A typed variant of bisimilarity is formulated and it is shown that typed fiequality has a clean embedding in the bisimilarity. Name reference structure induced by the simple hierarchy of types is studied, which fully characterises the typable terms in the set of untyped terms. It turns out that the name reference structure results in the deadlockfree property for a subset of terms with a certain regular structure, showing behavioural significance of the simple type discipline. 1 Introduction This is a preliminary study of types for concurrency. Types here denote freely composable structur...