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23
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 26 (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.
Reducibility and ⊤⊤lifting for computation types
 In Proc. 7th International Conference on Typed Lambda Calculi and Applications (TLCA), volume 3461 of Lecture Notes in Computer Science
, 2005
"... Abstract. We propose ⊤⊤lifting as a technique for extending operational predicates to Moggi’s monadic computation types, independent of the choice of monad. We demonstrate the method with an application to GirardTait reducibility, using this to prove strong normalisation for the computational meta ..."
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Cited by 19 (3 self)
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Abstract. We propose ⊤⊤lifting as a technique for extending operational predicates to Moggi’s monadic computation types, independent of the choice of monad. We demonstrate the method with an application to GirardTait reducibility, using this to prove strong normalisation for the computational metalanguage λml. The particular challenge with reducibility is to apply this semantic notion at computation types when the exact meaning of “computation ” (stateful, sideeffecting, nondeterministic, etc.) is left unspecified. Our solution is to define reducibility for continuations and use that to support the jump from value types to computation types. The method appears robust: we apply it to show strong normalisation for the computational metalanguage extended with sums, and with exceptions. Based on these results, as well as previous work with local state, we suggest that this “leapfrog ” approach offers a general method for raising concepts defined at value types up to observable properties of computations. 1
Relational Parametricity for Computational Effects
"... According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricit ..."
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Cited by 5 (1 self)
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According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Real programs, however, exhibit computational effects. In this paper, we develop a framework for extending the notion of relational parametricity to languages with effects.
A Semantic Formulation of ⊤⊤lifting and Logical Predicates for Computational Metalanguage
 In Proc. CSL 2005. LNCS 3634
, 2005
"... Abstract. A semantic formulation of Lindley and Stark’s ⊤⊤lifting is given. We first illustrate our semantic formulation of the ⊤⊤lifting in Set with several examples, and apply it to the logical predicates for Moggi’s computational metalanguage. We then abstract the semantic ⊤⊤lifting as the lif ..."
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Cited by 4 (1 self)
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Abstract. A semantic formulation of Lindley and Stark’s ⊤⊤lifting is given. We first illustrate our semantic formulation of the ⊤⊤lifting in Set with several examples, and apply it to the logical predicates for Moggi’s computational metalanguage. We then abstract the semantic ⊤⊤lifting as the lifting of strong monads across bifibrations with lifted symmetric monoidal closed structures. 1
On the geometry of intuitionistic S4 proofs
 Homology, Homotopy and Applications
, 2003
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Functional Concepts in C++
"... We describe a parsertranslator program that translates typed λterms into C++ classes so as to integrate functional concepts. We prove the correctness of the translation of λterms into C++ with respect to a denotational semantics using Kripkestyle logical relations. We introduce a general techniq ..."
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Cited by 2 (0 self)
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We describe a parsertranslator program that translates typed λterms into C++ classes so as to integrate functional concepts. We prove the correctness of the translation of λterms into C++ with respect to a denotational semantics using Kripkestyle logical relations. We introduce a general technique for introducing lazy evaluation into C++, and illustrate it by carrying out in C++ the example of computing the Fibonacci numbers efficiently using infinite streams and lazy evaluation. Finally, we show how merge higherorder λterms with imperative C++ code. 1
Relating computational effects by ⊤⊤lifting, in
 of Lecture Notes in Computer Science
"... We consider the problem of establishing a relationship between two interpretations of base type terms of a λccalculus extended with algebraic operations. We show that the given relationship holds if it satisfies a set of natural conditions. We apply this result to 1) comparing two monadic semantics ..."
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We consider the problem of establishing a relationship between two interpretations of base type terms of a λccalculus extended with algebraic operations. We show that the given relationship holds if it satisfies a set of natural conditions. We apply this result to 1) comparing two monadic semantics related by a strong monad morphism, and 2) comparing two monadic semantics of fresh name creation: Stark’s new name creation monad [32], and the global counter monad. We also consider the same problem, relating semantics of computational effects, in the presence of recursive functions. We apply this additional by extending the previous monad morphism comparison result to the recursive case.
Complete Lax Logical Relations for Cryptographic LambdaCalculi
 In Proceedings of CSL’2004, volume 3210 of LNCS
, 2004
"... Security properties are profitably expressed using notions of contextual equivalence, and logical relations are a powerful proof technique to establish contextual equivalence in typed lambda calculi, see e.g. Sumii and Pierce's logical relation for a cryptographic lambdacalculus. We clarify Su ..."
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Security properties are profitably expressed using notions of contextual equivalence, and logical relations are a powerful proof technique to establish contextual equivalence in typed lambda calculi, see e.g. Sumii and Pierce's logical relation for a cryptographic lambdacalculus. We clarify Sumii and Pierce's approach, showing that the right tool is prelogical relations, or lax logical relations in general: relations should be lax at encryption types, notably. To explore the difficult aspect of fresh name creation, we use Moggi's monadic lambdacalculus with constants for cryptographic primitives, and Stark's name creation monad. We define logical relations which are lax at encryption and function types but strict (nonlax) at various other types, and show that they are sound and complete for contextual equivalence at all types.
Probabilistic applicative bisimulation for callbyvalue lambda calculi (long version). Available at http://arxiv.org
, 2013
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Preorders on Monads and Coalgebraic Simulations
 In Proc. FoSSaCS 2013, LNCS 7794, pp.145–160
, 2013
"... Abstract. We study the construction of preorders on Setmonads by the semantic ⊤⊤lifting. We show the universal property of this construction, and characterise the class of preorders on a monad as a limit of a Cardopchain. We apply these theoretical results to identifying preorders on some concret ..."
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Abstract. We study the construction of preorders on Setmonads by the semantic ⊤⊤lifting. We show the universal property of this construction, and characterise the class of preorders on a monad as a limit of a Cardopchain. We apply these theoretical results to identifying preorders on some concrete monads, including the powerset monad, maybe monad, and their composite monad. We also relate the construction of preorders and coalgebraic formulation of simulations. 1