This paper presents a new bisimulation theory for parametric polymorphism which enables straightforward coinductive proofs of program equivalences involving existential types. The theory is an instance of typed normal form bisimulation and demonstrates the power of this recent framework for modeling typed lambda calculi as labelled transition systems. We develop our theory for a continuation-passing style calculus, Jump-With-Argument, where normal form bisimulation takes a simple form. We equip the calculus with both existential and recursive types. An “ultimate pattern matching theorem ” enables us to define bisimilarity and we show it to be a congruence. We apply our theory to proving program equivalences, type isomorphisms and genericity. 1

We consider the following questions: What kind of logic has a natural semantics in multi-player (rather than 2-player) games? How can we express branching quantifiers, and other partial-information constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on Kahn-Plotkin concrete domains. Partial information constraints are represented as co-closure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and co-arities. This enables a fully compositional account of a wide

and recursive types

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Game Semantics was introduced in the early nineties in the construction of the first fully complete model of Classical Multiplicative Linear Logic, and in the construction model of PCF. By the time of the project proposal – some ten years on, Game Semantics had emerged as a powerful paradigm for giving accurate semantics to a variety of programming languages and logical systems. It had been used to construct fully abstract models for a wide spectrum of programming languages covering features such as recursive types and polymorphism, non-local control operators, block-allocated local variables, general references, probabilistic and non-deterministic constructs, etc. The aim of the project was to develop Game Semantics

We consider the following questions: What kind of logic has a natural semantics in multi-player (rather than 2-player) games? How can we express branching quantifiers, and other partial-information constructs, with a properly compositional syntax and semantics? We develop a logic in answer to these questions, with a formal semantics based on multiple concurrent strategies, formalized as closure operators on Kahn-Plotkin concrete domains. Partial information constraints are represented as co-closure operators. We address the syntactic issues by treating syntactic constituents, including quantifiers, as arrows in a category, with arities and co-arities. This enables a fully compositional account of a wide