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Semicontinuous sized types and termination
 In Zoltán Ésik, editor, Computer Science Logic, 20th International Workshop, CSL 2006, 15th Annual Conference of the EACSL
"... Abstract. Some typebased approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is onl ..."
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Abstract. Some typebased approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is only sound if the type of the recursive function is admissible, i.e., depends on the size index in a certain way. To explore the space of admissible functions in the presence of higherkinded data types and impredicative polymorphism, a semantics is developed where sized types are interpreted as functions from ordinals into sets of strongly normalizing terms. It is shown that upper semicontinuity of such functions is a sufficient semantic criterion for admissibility. To provide a syntactical criterion, a calculus for semicontinuous functions is developed. 1.
Strong normalization and equi(co)inductive types
 Proc. of the 8th Int. Conf. on Typed Lambda Calculi and Applications, TLCA 2007, volume 4583 of Lect. Notes in Comput. Sci. SpringerVerlag (2007), 8–22
"... Abstract. A type system for the lambdacalculus enriched with recursive and corecursive functions over equiinductive andcoinductive types is presented in which all welltyped programs are strongly normalizing. The choice of equiinductive types, instead of the more common isoinductive types, in ue ..."
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Cited by 3 (1 self)
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Abstract. A type system for the lambdacalculus enriched with recursive and corecursive functions over equiinductive andcoinductive types is presented in which all welltyped programs are strongly normalizing. The choice of equiinductive types, instead of the more common isoinductive types, in uences both reduction rules and the strong normalization proof. By embedding iso into equitypes, the latter ones are recognized as more fundamental. A model based on orthogonality is constructed where a semantical type corresponds to a set of observations, and soundness of the type system is proven. 1
Verification of the Redecoration Algorithm for Triangular Matrices
, 2007
"... Abstract. Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. R ..."
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Cited by 2 (1 self)
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Abstract. Triangular matrices with a dedicated type for the diagonal elements can be profitably represented by a nested datatype, i. e., a heterogeneous family of inductive datatypes. These families are fully supported since the version 8.1 of the Coq theorem proving environment, released in 2007. Redecoration of triangular matrices has a succinct implementation in this representation, thus giving the challenge of proving it correct. This has been achieved within Coq, using also induction with measures. An axiomatic approach allowed a verification in the Isabelle theorem prover, giving insights about the differences of both systems. 1
HASCASL: Integrated HigherOrder Specification and Program Development
"... We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that serves both as a widespectrum language for the rigorous specification and development of software, in particular but not exclusively in modern functional programming languages, and as an exp ..."
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We lay out the design of HasCasl, a higher order extension of the algebraic specification language Casl that serves both as a widespectrum language for the rigorous specification and development of software, in particular but not exclusively in modern functional programming languages, and as an expressive standard language for higherorder logic. Distinctive features of HasCasl include partial higher order functions, higher order subtyping, shallow polymorphism, and an extensive typeclass mechanism. Moreover, HasCasl provides dedicated specification support for monadbased functionalimperative programming with generic side effects, including a monadbased generic Hoare logic.
System Fi A HigherOrder Polymorphic λCalculus with Erasable TermIndices
"... Abstract. We introduce a foundational lambda calculus, System Fi, for studying programming languages with termindexed datatypes – higherkinded datatypes whose indices range over data such as natural numbers or lists. System Fi is an extension of System Fω that introduces the minimal features needed ..."
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Abstract. We introduce a foundational lambda calculus, System Fi, for studying programming languages with termindexed datatypes – higherkinded datatypes whose indices range over data such as natural numbers or lists. System Fi is an extension of System Fω that introduces the minimal features needed to support termindexing. We show that System Fi provides a theory for analysing programs with termindexed types and also argue that it constitutes a basis for the design of logicallysound lightweight dependent programming languages. We establish erasure properties of Fitypes that capture the idea that termindices are discardable in that they are irrelevant for computation. Index erasure projects typing in System Fi to typing in System Fω. So,SystemFi inherits strong normalization and logical consistency from System Fω.
Polarized Subtyping for Sized Types
, 2006
"... We present an algorithm for deciding polarized higherorder subtyping without bounded quantification. Constructors are identified not only modulo β, but also η. We give a direct proof of completeness, without constructing a model or establishing a strong normalization theorem. Inductive and coinduct ..."
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We present an algorithm for deciding polarized higherorder subtyping without bounded quantification. Constructors are identified not only modulo β, but also η. We give a direct proof of completeness, without constructing a model or establishing a strong normalization theorem. Inductive and coinductive types are enriched with a notion of size and the subtyping calculus is extended to account for the arising inclusions between the sized types. 1.