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Cayenne  a Language With Dependent Types
 IN INTERNATIONAL CONFERENCE ON FUNCTIONAL PROGRAMMING
, 1998
"... Cayenne is a Haskelllike language. The main difference between Haskell and Cayenne is that Cayenne has dependent types, i.e., the result type of a function may depend on the argument value, and types of record components (which can be types or values) may depend on other components. Cayenne also co ..."
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Cited by 216 (0 self)
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Cayenne is a Haskelllike language. The main difference between Haskell and Cayenne is that Cayenne has dependent types, i.e., the result type of a function may depend on the argument value, and types of record components (which can be types or values) may depend on other components. Cayenne also combines the syntactic categories for value expressions and type expressions; thus reducing the number of language concepts. Having dependent types and combined type and value expressions makes the language very powerful. It is powerful enough that a special module concept is unnecessary; ordinary records suffice. It is also powerful enough to encode predicate logic at the type level, allowing types to be used as specifications of programs. However, this power comes at a cost: type checking of Cayenne is undecidable. While this may appear to be a steep price to pay, it seems to work well in practice.
Higherorder abstract syntax in Coq
, 1995
"... The terms of the simplytyped λcalculus can be used to express the higherorder abstract syntax of objects such as logical formulas, proofs, and programs. Support for the manipulation of such objects is provided in several programming languages (e.g. λProlog, Elf). Such languages also provide embed ..."
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Cited by 41 (1 self)
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The terms of the simplytyped λcalculus can be used to express the higherorder abstract syntax of objects such as logical formulas, proofs, and programs. Support for the manipulation of such objects is provided in several programming languages (e.g. λProlog, Elf). Such languages also provide embedded implication, a tool which is widely used for expressing hypothetical judgments in natural deduction. In this paper, we show how a restricted form of secondorder syntax and embedded implication can be used together with induction in the Coq Proof Development system. We specify typing rules and evaluation for a simple functional language containing only function abstraction and application, and we fully formalize a proof of type soundness in the system. One difficulty we encountered is that expressing the higherorder syntax of an objectlanguage as an inductive type in Coq generates a class of terms that contains more than just those that directly represent objects in the language. We ove...
The Conservation Theorem revisited
, 1993
"... This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result ..."
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Cited by 32 (0 self)
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This paper describes a method of proving strong normalization based on an extension of the conservation theorem. We introduce a structural notion of reduction that we call fi S , and we prove that any term that has a fi I fi Snormal form is strongly finormalizable. We show how to use this result to prove the strong normalization of different typed calculi.
A Modal Lambda Calculus with Iteration and Case Constructs
 TYPES FOR PROOFS AND PROGRAMS: INTERNATIONAL WORKSHOP, TYPES ’98, KLOSTER IRSEE
, 1997
"... An extension of the simplytyped lambdacalculus allowing iteration and case reasoning over terms defined by means of higher order abstract syntax has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operato ..."
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Cited by 8 (1 self)
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An extension of the simplytyped lambdacalculus allowing iteration and case reasoning over terms defined by means of higher order abstract syntax has recently been introduced by Joëlle Despeyroux, Frank Pfenning and Carsten Schürmann. This thorny mixing is achieved thanks to the help of the operator ` ' of modal logic IS4. Here we give a new presentation of their system, with reduction rules, instead of evaluation judgments, that compute the canonical forms of terms. Our presentation is based on a modal lambdacalculus that is better from the user's point of view, is more concise and we do not impose a particular strategy of reduction during the computation. Our system enjoys the decidability of typability, soundness of typed reduction with respect to typing rules, the ChurchRosser and strong normalization properties. Finally it is a conservative extension of the simplytyped lambdacalculus.
Encoding Natural Semantics in Coq
 In Proc. AMAST, LNCS 936
, 1995
"... . We address here the problem of automatically translating the Natural Semantics of programming languages to Coq, in order to prove formally general properties of languages. Natural Semantics [18] is a formalism for specifying semantics of programming languages inspired by Plotkin's Structural Opera ..."
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Cited by 7 (0 self)
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. We address here the problem of automatically translating the Natural Semantics of programming languages to Coq, in order to prove formally general properties of languages. Natural Semantics [18] is a formalism for specifying semantics of programming languages inspired by Plotkin's Structural Operational Semantics [22]. The Coq proof development system [12], based on the Calculus of Constructions extended with inductive types (CCind), provides mechanized support including tactics for building goaldirected proofs. Our representation of a language in Coq is inAEuenced by the encoding of logics used by Church [6] and in the Edinburgh Logical Framework (ELF) [15, 3]. 1 Introduction The motivation for our work is the need for an environment to help develop proofs in Natural Semantics. The interactive programming environment generator Centaur [17] allows us to compile a Natural Semantics speciøcation of a given language into executable code (typecheckers, evaluators, compilers, program t...
Tool Support for Logics of Programs
 Mathematical Methods in Program Development: Summer School Marktoberdorf 1996, NATO ASI Series F
, 1996
"... Proof tools must be well designed if they... ..."
Program Development in Constructive Type Theory
 Theoretical Computer Science
, 1992
"... We present the program development concept in a logical framework including constructive type theory and then show how to use such theories to derive programs from proofs of formal specifications. We are interested in two important facts that are the mechanization of the proof construction and the p ..."
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Cited by 4 (2 self)
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We present the program development concept in a logical framework including constructive type theory and then show how to use such theories to derive programs from proofs of formal specifications. We are interested in two important facts that are the mechanization of the proof construction and the possibility to express in the theory significiant concepts for programming (like inductively deøned types and general recursion). We give here a survey on some results and problems appearing in logical frameworks devoted to the programming with proofs approach.
Weak Transitivity in Coercive Subtyping
 TYPES FOR PROOFS AND PROGRAMS, VOLUME 2646 OF LNCS
, 2001
"... Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtyping is that of coherence which essentially says that coercions between any two types must be unique. Another important task for coercive subtyping is ..."
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Cited by 4 (4 self)
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Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtyping is that of coherence which essentially says that coercions between any two types must be unique. Another important task for coercive subtyping is to prove the admissibility or elimination of transitivity and substitution. In this paper, we propose and study the notion of Weak Transitivity, consider suitable subtyping rules for certain parameterised inductive types and prove its coherence and the admissibility of substitution and weak transitivity in the coercive subtyping framework.
A Machineassisted Proof that Well Typed Expressions Cannot Go Wrong
, 1998
"... This paper deals with the application of constructive type theory to the theory of programming languages. The main aim of this work is to investigate constructive formalisations of the mathematics of programs. Here, we consider a small typed functional language and prove some properties about it, ar ..."
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Cited by 3 (0 self)
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This paper deals with the application of constructive type theory to the theory of programming languages. The main aim of this work is to investigate constructive formalisations of the mathematics of programs. Here, we consider a small typed functional language and prove some properties about it, arriving at the property that establishes that well typed expressions cannot go wrong. First, we give the definitions and proofs in an informal style, and then we present and explain the formalisation of these definitions and proofs. For the formalisation, we use the proof editor ALF and its pattern matching facility.