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Objects and classes in Algollike languages
 Information and Computation
, 2002
"... Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and ..."
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Cited by 22 (5 self)
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Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and classes. An important idea that comes to light is that classes are abstract data types, whose theory corresponds to that of existential types. Equational and Hoarelike reasoning methods, and relational parametricity provide powerful formal tools for reasoning about Algollike objectoriented programs. 1
Recursive Polymorphic Types and Parametricity in an Operational Framework
, 2005
"... We construct a realizability model of recursive polymorphic types, starting from an untyped language of terms and contexts. An orthogonality relation e # indicates when a term e and a context # may be safely combined in the language. Types are interpreted as sets of terms closed by biorthogonalit ..."
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Cited by 22 (1 self)
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We construct a realizability model of recursive polymorphic types, starting from an untyped language of terms and contexts. An orthogonality relation e # indicates when a term e and a context # may be safely combined in the language. Types are interpreted as sets of terms closed by biorthogonality. Our main result states that recursive types are approximated by converging sequences of interval types. Our proof is based on a "typedirected" approximation technique, which departs from the "languagedirected" approximation technique developed by MacQueen, Plotkin and Sethi in the ideal model. We thus keep the language elementary (a callbyname #calculus) and unstratified (no typecase, no reduction labels). We also include a short account of parametricity, based on an orthogonality relation between quadruples of terms and contexts.
Parametricity as a Notion of Uniformity in Reflexive Graphs
, 2002
"... data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information. ..."
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Cited by 11 (3 self)
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data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information.
When Parametricity implies Naturality (Notes)
"... .79> R ? ? S A 0 f 0  B 0 The terminology is motivated by the fact that edges R and S determine a relation [R ! S] ` hom(A;B) \Theta hom(A 0 ; B 0 ). We assume that all our reflexive graphs are relational. A reflexive graph is symmetric if it is equipped with a family of bijections (\Gamma) ` A;A 0 ..."
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.79> R ? ? S A 0 f 0  B 0 The terminology is motivated by the fact that edges R and S determine a relation [R ! S] ` hom(A;B) \Theta hom(A 0 ; B 0 ). We assume that all our reflexive graphs are relational. A reflexive graph is symmetric if it is equipped with a family of bijections (\Gamma) ` A;A 0 : edge(A; A 0 ) ¸ = edge(A 0 ; A) such that 1. (I A ) ` = I A , and 2. the left hand diagram is a parametricity square iff the right hand diagram is a parametricity square: A f  B 6 6 R ? ? S A 0 f 0 