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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 26 (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.
Semantic Types: A Fresh Look at the Ideal Model for Types
, 2004
"... We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact tha ..."
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Cited by 25 (2 self)
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We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact that the identity is the limit of a sequence of projection terms. This establishes a connection with the work of Pitts on relational properties of domains. This also suggests that ideals are better understood as closed sets of terms defined by orthogonality with respect to a set of contexts.
Reversible structures
"... Abstract. Reversible structures are computational units that may progress forward and backward and are primarily inspired by dna circuits. We demonstrate a standardization theorem that bears a quadratic algorithm for reachability when units have unique id. We also discuss the encoding of a reversibl ..."
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Cited by 7 (1 self)
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Abstract. Reversible structures are computational units that may progress forward and backward and are primarily inspired by dna circuits. We demonstrate a standardization theorem that bears a quadratic algorithm for reachability when units have unique id. We also discuss the encoding of a reversible concurrent calculus into reversible structures. 1
Reversibility in Massive Concurrent Systems
"... We introduce reversible structures, an algebra for massive concurrent systems, where terms retain bits of causal dependencies that allow one to reverse computation histories. We then study the implementation of (weak coherent) reversible structures in threedomains dna strands, which is the natural ..."
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We introduce reversible structures, an algebra for massive concurrent systems, where terms retain bits of causal dependencies that allow one to reverse computation histories. We then study the implementation of (weak coherent) reversible structures in threedomains dna strands, which is the natural model that has inspired reversible structures. We finally provide schemas for modeling significant synchronization patterns of process algebra into reversible structures and discuss the encoding of asynchronous Reversible CCS.
Simplified Reducibility Proofs of ChurchRosser for β and βηreduction
"... Reducibility has been used to prove a number of properties in the λcalculus and is well known to offer on one hand very general proofs which can be applied to a number of instantiations, and on the other hand, to be quite mysterious and inflexible. It has, amongst other things, been used along with ..."
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Reducibility has been used to prove a number of properties in the λcalculus and is well known to offer on one hand very general proofs which can be applied to a number of instantiations, and on the other hand, to be quite mysterious and inflexible. It has, amongst other things, been used along with the so called method of parallel reductions to prove the ChurchRosser property. In this paper, we concentrate on using the methods of reducibility and of parallel reductions for proving ChurchRosser for both β and βηreduction. Our contributions are two fold: We give a simple proof of CR for βreduction which unlike the common proofs in the literature, avoids any type machinery and is solely carried out in a completely untyped setting. We give a new proof of CR for βηreduction which is a generalisation of our simple proof for βreduction. Keywords:
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"... Recursive polymorphic types and parametricity in an operational framework We construct a realizability model of recursive polymorphic types, starting from an untyped language of terms and contexts. An orthogonality relation e ⊥ π indicates when a term e and a context π may be safely combined in the ..."
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Recursive polymorphic types and parametricity in an operational framework We construct a realizability model of recursive polymorphic types, starting from an untyped language of terms and contexts. An orthogonality relation e ⊥ π indicates when a term e and a context π 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 λcalculus) 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. 1