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413
Singleton types here Singleton types there Singleton Types Everywhere
, 2009
"... Singleton types are often considered a poor man’s substitute for dependent types. But their generalization in the form of GADTs has found quite a following. The main advantage of singleton types and GADTs is to preserve the so-called phase distinction, which seems to be so important to make use of t ..."
Abstract
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Cited by 10 (0 self)
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Singleton types are often considered a poor man’s substitute for dependent types. But their generalization in the form of GADTs has found quite a following. The main advantage of singleton types and GADTs is to preserve the so-called phase distinction, which seems to be so important to make use
Subtyping with Singleton Types
- In Eighth International Workshop on Computer Science Logic
, 1995
"... . We give syntax and a PER-model semantics for a typed -calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtyping ..."
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Cited by 49 (4 self)
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. We give syntax and a PER-model semantics for a typed -calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent
Subtyping with Singleton Types
- In Eighth International Workshop on Computer Science Logic
, 1995
"... We give syntax and a PER-model semantics for a typed h-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtypi ..."
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We give syntax and a PER-model semantics for a typed h-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of subtyping with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent
Extensional equivalence and singleton types
- ACM Transactions on Computational Logic
"... We study the λΠΣS ≤ calculus, which contains singleton types S(M) classifying terms of base type provably equivalent to the term M. The system includes dependent types for pairs and functions (Σ and Π) and a subtyping relation induced by regarding singletons as subtypes of the base type. The decidab ..."
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Cited by 33 (4 self)
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We study the λΠΣS ≤ calculus, which contains singleton types S(M) classifying terms of base type provably equivalent to the term M. The system includes dependent types for pairs and functions (Σ and Π) and a subtyping relation induced by regarding singletons as subtypes of the base type
Strong Normalization with Singleton Types
, 2002
"... This paper presents a new lambda-calculus with singleton types, called . The main novelty of is the introduction of a new reduction, the -reduction, replacing any variable declared of singleton type by its value, and the denition of equality as the syntactic equality of -normal forms. The ..."
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Cited by 6 (0 self)
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This paper presents a new lambda-calculus with singleton types, called . The main novelty of is the introduction of a new reduction, the -reduction, replacing any variable declared of singleton type by its value, and the denition of equality as the syntactic equality of -normal forms
Strong Normalization with Singleton Types Abstract
"... This paper presents a new lambda-calculus with singleton types, called λ βδ The main novelty of λ βδ ≤{} is the introduction of a new reduction, the δ-reduction, replacing any variable declared of singleton type by its value, and the definition of equality as the syntactic equality of βδ-normal form ..."
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This paper presents a new lambda-calculus with singleton types, called λ βδ The main novelty of λ βδ ≤{} is the introduction of a new reduction, the δ-reduction, replacing any variable declared of singleton type by its value, and the definition of equality as the syntactic equality of βδ
FUZZY INFERENCE MODELING BASED ON FUZZY SINGLETON-TYPE REASONING
, 2006
"... Abstract. In this paper, the idea of the neuro-fuzzy learning algorithm has been extended, by which the tuning parameters in the fuzzy rules can be learned without changing the fuzzy rule table form used in usual fuzzy applications. A new neuro-fuzzy learning algorithm in the case of the fuzzy singl ..."
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singleton-type reasoning method has been proposed. Due to the flexibility of the fuzzy singleton-type reasoning method, the extended method is more reasonable and suitable for constructing an optimum fuzzy system model than the conventional neuro-fuzzy learning algorithm. Moreover, the efficiency
A syntactic account of singleton types via hereditary substitution
- 4th Int. Wksh. on Logical Frameworks and Meta-languages: Theory and Practice (LFMTP 2009
, 2009
"... We give a syntactic proof of decidability and consistency of equivalence for the singleton type calculus, which lies at the foundation of modern module systems such as that of ML. Unlike existing proofs, which work by constructing a model, our syntactic proof makes few demands on the un-derlying pro ..."
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Cited by 6 (3 self)
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We give a syntactic proof of decidability and consistency of equivalence for the singleton type calculus, which lies at the foundation of modern module systems such as that of ML. Unlike existing proofs, which work by constructing a model, our syntactic proof makes few demands on the un
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