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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 arities. T ..."
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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.
A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF c ..."
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Cited by 217 (44 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
An Overview of the FLINT/ML Compiler
 In Proc. 1997 ACM SIGPLAN Workshop on Types in Compilation
, 1997
"... The FLINT project at Yale aims to build a stateoftheart systems environment for modern typesafe languages. One important component of the FLINT system is a highperformance typedirected compiler for SML'97 (extended with higherorder modules). The FLINT/ML compiler provides several new capabilit ..."
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Cited by 90 (17 self)
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The FLINT project at Yale aims to build a stateoftheart systems environment for modern typesafe languages. One important component of the FLINT system is a highperformance typedirected compiler for SML'97 (extended with higherorder modules). The FLINT/ML compiler provides several new capabilities that are not available in other typebased compilers: ffl typedirected compilation is carried over across the higherorder module boundaries; ffl recursive and mutable data objects can use unboxed representations without incurring expensive runtime cost on heavily polymorphic code; ffl parameterized modules (functors) can be selectively specialized, just as normal polymorphic functions; ffl new type representations are used to reduce the cost of type manipulation thus the compilation time. This paper gives an overview of these novel aspects, and a preliminary report on the current status of the implementation. 1 Introduction The FLINT project at Yale aims to build a stateofthear...
Logical Support for Modularisation
 LOGICAL ENVIRONMENTS
, 1993
"... Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of ..."
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Cited by 85 (28 self)
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Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of modules. Our results show some new connections among: (1) the preservation of various kinds of conservative extension under pushouts; (2) various distributive laws for information hiding over sums; and (3) (Craig style) interpolation properties. In addition, we study differences between syntactic and semantic formulations of conservative extension properties, and of distributive laws. A model theoretic property that we call exactness plays an important role in some results. This paper explores the interplay between syntax and semantics, and thus lies in the tradition of abstract model theory. We represent logical systems as institutions. An important technical foundation is a new ...
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
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Cited by 73 (25 self)
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The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
Implementing Tactics and Tacticals in a HigherOrder Logic Programming Language
 Journal of Automated Reasoning
, 1993
"... We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement tactic style theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped terms ..."
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Cited by 66 (11 self)
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We argue that a logic programming language with a higherorder intuitionistic logic as its foundation can be used both to naturally specify and implement tactic style theorem provers. The language extends traditional logic programming languages by replacing firstorder terms with simplytyped terms, replacing firstorder unification with higherorder unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of inference systems can be naturally specified in this language. The higherorder features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many inference systems. Tactics and tacticals, which provide a framework for highlevel control over search for proofs, can be directly and naturally implemented in the extended language. This framework serves as a starting point for implementing theorem provers an...
Implementing Typed Intermediate Languages
, 1998
"... Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, u ..."
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Cited by 61 (16 self)
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Recent advances in compiler technology have demonstrated the benefits of using strongly typed intermediate languages to compile richly typed source languages (e.g., ML). A typepreserving compiler can use types to guide advanced optimizations and to help generate provably secure mobile code. Types, unfortunately, are very hard to represent and manipulate efficiently; a naive implementation can easily add exponential overhead to the compilation and execution of a program. This paper describes our experience with implementing the FLINT typed intermediate language in the SML/NJ production compiler. We observe that a typepreserving compiler will not scale to handle large types unless all of its typepreserving stages preserve the asymptotic time and space usage in representing and manipulating types. We present a series of novel techniques for achieving this property and give empirical evidence of their effectiveness.
Metatheory and Reflection in Theorem Proving: A Survey and Critique
, 1995
"... One way to ensure correctness of the inference performed by computer theorem provers is to force all proofs to be done step by step in a simple, more or less traditional, deductive system. Using techniques pioneered in Edinburgh LCF, this can be made palatable. However, some believe such an appro ..."
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Cited by 53 (2 self)
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One way to ensure correctness of the inference performed by computer theorem provers is to force all proofs to be done step by step in a simple, more or less traditional, deductive system. Using techniques pioneered in Edinburgh LCF, this can be made palatable. However, some believe such an approach will never be efficient enough for large, complex proofs. One alternative, commonly called reflection, is to analyze proofs using a second layer of logic, a metalogic, and so justify abbreviating or simplifying proofs, making the kinds of shortcuts humans often do or appealing to specialized decision algorithms. In this paper we contrast the fullyexpansive LCF approach with the use of reflection. We put forward arguments to suggest that the inadequacy of the LCF approach has not been adequately demonstrated, and neither has the practical utility of reflection (notwithstanding its undoubted intellectual interest). The LCF system with which we are most concerned is the HOL proof ...
Verification of NonFunctional Programs using Interpretations in Type Theory
"... We study the problem of certifying programs combining imperative and functional features within the general framework of type theory. Type theory constitutes a powerful specification language, which is naturally suited for the proof of purely functional programs. To deal with imperative programs, we ..."
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Cited by 52 (4 self)
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We study the problem of certifying programs combining imperative and functional features within the general framework of type theory. Type theory constitutes a powerful specification language, which is naturally suited for the proof of purely functional programs. To deal with imperative programs, we propose a logical interpretation of an annotated program as a partial proof of its specification. The construction of the corresponding partial proof term is based on a static analysis of the effects of the program, and on the use of monads. The usual notion of monads is refined in order to account for the notion of effect. The missing subterms in the partial proof term are seen as proof obligations, whose actual proofs are left to the user. We show that the validity of those proof obligations implies the total correctness of the program. We also establish a result of partial completeness. This work has been implemented in the Coq proof assistant. It appears as a tactic taking an ann...