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Probabilistic coherence spaces are fully abstract for probabilistic PCF
It is proved that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive, the first result of full abstraction for a semantics of probabilistic PCF. Expand
A semantic measure of the execution time in linear logic
A semantic account of the execution time (i.e. the number of cut elimination steps leading to the normal form) of an untyped MELL net and proves that a net is head-normalizable if and only if its exhaustive interpretation (a suitable restriction of its interpretation) is not empty. Expand
Applying quantitative semantics to higher-order quantum computing
This paper proposes a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic. Expand
Full Abstraction for Probabilistic PCF
A probabilistic version of PCF, a well-known simply typed universal functional language, is presented and an adequacy and an equational full abstraction theorem are proved showing that equality in the model coincides with a natural notion of observational equivalence. Expand
Weighted Relational Models of Typed Lambda-Calculi
The generalization of the category Rel of sets and relations to an arbitrary continuous semiring R is considered, producing a cpo-enriched category which is a semantics of LL, and its (co)Kleisli category is an adequate model of an extension of PCF, parametrized by R. Expand
Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotationalExpand
Parallel Reduction in Resource Lambda-Calculus
This work defines parallel reduction in resource calculus and applies the technique by Tait and Martin-Lof to achieve confluence, and slightly generalizes a technique by Takahashi to obtain a standardization result. Expand
The conservation theorem for differential nets
The conservation theorem for differential nets – the graph-theoretical syntax of the differential extension of Linear Logic (Ehrhard and Regnier's DiLL) is proved, which turns the quest for strong normalisation into one for non-erasing weak normalisation (WN), and indeed this result is used to prove SN of simply typed DiLL. Expand
The Computational Meaning of Probabilistic Coherence Spaces
This paper proves that a denotational semantics interpreting programs by power series with non negative real coefficients is adequate for a probabilistic extension of the untyped $\lambda$-calculus: the probability that a term reduces to ahead normal form is equal to its denotation computed on a suitable set of values. Expand
Strong normalization property for second order linear logic
The paper contains the first complete proof of strong normalization (SN) for full second order linear logic (LL) by showing how standardization for sps allows to prove SN of LL, using as usual Girard's reducibility candidates. Expand