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Subtyping Dependent Types
, 2000
"... The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system *P, which is an abstract versio ..."
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Cited by 69 (6 self)
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The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system *P, which is an abstract version of the type system of the Edinburgh Logical Framework LF. By using an equivalent formulation, we establish some important properties of the new system *P^, including subject reduction. Our analysis culminates in a complete and terminating algorithm which establishes the decidability of typechecking.
From Algebras and Coalgebras to Dialgebras
, 2001
"... This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras. ..."
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Cited by 11 (0 self)
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This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, and investigate the essential dierences between (co)algebras and arbitrary dialgebras.
A higherorder simulation relation for System F
 Proc. 3rd Intl. Conf. on Foundations of Software Science and Computation Structures. ETAPS 2000
, 2000
"... The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. Thi ..."
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Cited by 2 (2 self)
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The notion of data type specification refinement is discussed in a setting of System F and the logic for parametric polymorphism of Plotkin and Abadi. At first order, one gets a notion of specification refinement up to observational equivalence in the logic simply by using Luo's formalism. This paper generalises this notion to abstract data types whose signatures contain higherorder and polymorphic functions. At higher order, the tight connection in the logic between the existence of a simulation relation and observational equivalence ostensibly breaks down. We show that an alternative notion of simulation relation is suitable. This also gives a simulation relation in the logic that composes at higher order, thus giving a syntactic logical counterpart to recent advances on the semantic level.
Specification Refinement with System F, The HigherOrder Case
, 2000
"... . A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setti ..."
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Cited by 1 (1 self)
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. A typetheoretic counterpart to the notion of algebraic specification refinement is discussed for abstract data types with higherorder signatures. The typetheoretic setting consists of System F and the logic for parametric polymorphism of Plotkin and Abadi. For firstorder signatures, this setting immediately gives a natural notion of specification refinement up to observational equivalence via the notion of simulation relation. Moreover, a proof strategy for proving observational refinements formalised by Bidoit, Hennicker and Wirsing can be soundly imported into the type theory. In lifting these results to the higherorder case, we find it necessary firstly to develop an alternative simulation relation and secondly to extend the parametric PERmodel interpretation, both in such a way as to observe data type abstraction barriers more closely. 1 Introduction One framework in algebraic specification that has particular appeal and applicability is that of stepwise specification refi...
Abstraction Barriers and Refinement in the Polymorphic Lambda Calculus
, 2001
"... This thesis is written in LATEX2ε using the report class together with elements from the Edinburgh University csthesis class. The font is Computer Modern 12pt, but scaled down in the booklet format of this thesis. ..."
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Cited by 1 (1 self)
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This thesis is written in LATEX2ε using the report class together with elements from the Edinburgh University csthesis class. The font is Computer Modern 12pt, but scaled down in the booklet format of this thesis.
King’s Buildings Edinburgh EH9 3JZ, U. K.
, 2000
"... The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system P, which is an abstract version ..."
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The need for subtyping in typesystems with dependent types has been realized for some years. But it is hard to prove that systems combining the two features have fundamental properties such as subject reduction. Here we investigate a subtyping extension of the system P, which is an abstract version of the type system of the Edinburgh Logical Framework LF. By using an equivalent formulation, we establish some important properties of the new system P, including subject reduction. Our analysis culminates in a complete and terminating algorithm which establishes the decidability of typechecking.
Elaboration and Erasure in Type Theory
"... This thesis contributes to the construction of a convenient specification language on top of a type theoretic substrate. The subject arose in the context of the Typelab project that aimed at improving the machine assistance for the formal development of mathematics, software and hardware. Type theor ..."
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This thesis contributes to the construction of a convenient specification language on top of a type theoretic substrate. The subject arose in the context of the Typelab project that aimed at improving the machine assistance for the formal development of mathematics, software and hardware. Type theory was chosen as underlying theoretical framework, because it homogeneously comprises both the notion of computation and deduction. However, the price for its expressiveness is a verbose syntax. When I joined the Typelab group, my responsibility was to shape the external language of the Typelab system. Naturally, I first looked at related implementations. Most of them cope with the wordiness of type theory by allowing their users to omit on input redundant parts that can be inferred automatically through a process called elaboration. While the use of such a mechanism seems indispensable for serious verification tasks, I found the existing solutions unsatisfactory. Not only are the implemented algorithms seldom precisely documented and formally analyzed, they also lack strength. It is disappointing how much redundant information still has to be supplied on input. Furthermore, the ad hoc erasure algorithms, used to reduce
Formal Mathematical Documents
"... Subject headings: automated theorem proving / formal logic / ..."