Behavioural Equivalence and Indistinguishability in Higher-Order Typed Languages
نویسنده
چکیده
We extend the study of the relationship between behavioural equivalence and the indistinguishability relation[4, 7] to the simply typed lambda calculus, where higher-order types are available. The relationship between these two notions is established in terms of factorisability[4]. The main technical tool of this study is pre-logical relations[8], which give a precise characterisation of behavioural equivalence. We then consider a higher-order logic to reason about models of the simply typed lambda calculus, and relate the resulting standard satisfaction relation to behavioural satisfaction.
منابع مشابه
On Equivalences, Metrics, and Polynomial Time (Long Version)
Interactive behaviors are ubiquitous in modern cryptography, but are also present in λcalculi, in the form of higher-order constructions. Traditionally, however, typed λ-calculi simply do not fit well into cryptography, being both deterministic and too powerful as for the complexity of functions they can express. We study interaction in a λ-calculus for probabilistic polynomial time computable ...
متن کاملTowards a Coinductive Characterization of Computational Indistinguishability
Computational indistinguishability (CI in the following) is one of the most central concepts in modern cryptography, and many other definitions (e.g. pseudorandomness, security of cryptographic schemes) can be formulated in terms of CI. We present the results of a study directed towards giving a direct and precise characterization of computational indistinguishability in an higher-order functio...
متن کاملOn behavioural abstraction and behavioural satisfaction in higher-order logic?
The behavioural semantics of specifications with higher-order logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of first-order logic by Bidoit et al, is further generalized to this case....
متن کاملOn Behavioral Abstraction and Behavioural Satisfaction in Higher-Order Logic
The behavioural semantics of speciications with higher-order logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of rst-order logic by Bidoit et al, is further generalized to this case. Th...
متن کاملCharacteristic Bisimulations for Higher-Order Session Processes
Characterising contextual equivalence is a long-standing issue for higher-order (process) languages. In the setting of a higher-order π-calculus with sessions, we develop characteristic bisimilarity, a typed bisimilarity which fully characterises contextual equivalence. To our knowledge, ours is the first characterisation of its kind. Using simple values inhabiting (session) types, our approach...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002