48 3.1.1 Dependent Type Theory, 54 3.1.6 Coproduct and Natural Number, p.59 ,

60 3.2.1 Syntax and Operational Semantics of 60 3.2.2 Typing Rules, p.64 ,

66 3.3.1 Nominal Sets, p.67 ,

76 4.2.1 Definition of the Translation 77 4.2.2 Substitution as a propositional equality, p.92 ,

92 4.3.1 Defining new constructors in the Forcing Layer 92 4.3.2 Soundness and Consistency of the Forcing Layer, p.94 ,

103 4.6.1 Topos of trees 103 4.6.2 Higher-Order Abstract Syntax Forcing as a program transformation, p.105 ,

130 5.3.1 Denotation of variables 130 5.3.2 Denotation of ?-abstractions, p.137 ,

205 7.5.1 Model Checking as Presburger Arithmetic, 205 7.5.2 An Implementation using SMT-solvers . . . . . . . . . . . . . . 205 ,

one can imagine being able to prove any equivalence with it. However, inspecting its proof of completeness, we see that it relies on a notion of exhaustive LTS which is clearly not computable. However, it is in often possible to define worlds by inspecting terms, trying to find " smart " invariants on heaps. This opens the possibility to model-check the membership of two terms M 1 , M 2 of type ? to the logical relation E ? . This means that, providing a State-dependent representation independence, Having complete direct-style logical relations Proceedings of POPL'09, pp.16-18, 2009. ,

Nominal games and full abstraction for the nu-calculus, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004., pp.150-159, 2004. ,

DOI : 10.1109/LICS.2004.1319609

A fully abstract game semantics for general references, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226), pp.334-344, 1998. ,

DOI : 10.1109/LICS.1998.705669

Semantics of types for mutable state, p.39, 2004. ,

Step-indexed syntactic logical relations for recursive and quantified types. Programming Languages and Systems, pp.69-83, 2006. ,

Full abstraction for PCF Information and Computation Call-by-value games An indexed model of recursive types for foundational proof-carrying code, In Computer Science Logic ACM Transactions on Programming Languages and Systems (TOPLAS), vol.163, issue.14, pp.409-470, 1998. ,

Productive coprogramming with guarded recursion, Proceedings of the 18th ACM SIGPLAN international conference on Functional programming, pp.197-208, 2013. ,

A very modal model of a modern, major, general type system, Proceedings of the 34th Symposium on Principles of Programming Languages (POPL'07), pp.109-122, 2007. ,

URL : https://hal.archives-ouvertes.fr/hal-00150978

The Foundations of Mathematics Biorthogonality, step-indexing and compiler correctness Intensional type theory with guarded recursive types qua fixed points on universes, Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming, ICFP '09 Proceedings of the 28th Annual IEEE/ACM Symposium on Logic in Computer Science (LICS'13), pp.105-97, 1959. ,

First steps in synthetic guarded domain theory: step-indexing in the topos of trees Compiling functional types to relational specifications for low level imperative code, Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science (LICS'11) TLDI '09: Proceedings of the 4th international workshop on Types in language design and implementation, pp.55-64, 2009. ,

Set theory and the continuum hypothesis Theoretical aspects of object-oriented programming . chapter Coherence of Subsumption, Minimum Typing and Typechecking in F ?, pp.70-247, 1966. ,

Revisiting the categorical interpretation of dependent type theory, Theoretical Computer Science, vol.546, pp.2014-58 ,

DOI : 10.1016/j.tcs.2014.03.003

URL : https://hal.archives-ouvertes.fr/hal-01114033

Abstract machines for dialogue games. Panoramas et synthèses-Société mathématique de France, Jaber. A Note on Forcing and Type Theory. Fundamenta Informaticae, pp.231-275, 2009. ,

URL : https://hal.archives-ouvertes.fr/hal-00155295

A Computational Interpretation of Forcing in Type Theory, Epistemology versus Ontology, pp.203-213, 2012. ,

DOI : 10.1007/978-94-007-4435-6_10

Substitution up to isomorphism, Fundamenta Informaticae, vol.19, issue.58, pp.51-85, 1993. ,

Abstract böhm trees, Mathematical Structures in Computer Science, vol.8, issue.06, pp.559-591, 1998. ,

Logical step-indexed logical relations, Proceedings of LICS'09, p.43, 2009. ,

Higher-order abstract syntax in Coq, Typed Lambda Calculi and Applications, pp.124-138, 1995. ,

DOI : 10.1007/BFb0014049

URL : https://hal.archives-ouvertes.fr/inria-00074124

The impact of higher-order state and control effects on local relational reasoning, Proceeding of the 15th Conference on Functional programming, pp.143-156, 2010. ,

The impact of higher-order state and control effects on local relational reasoning, Journal of Functional Programming, vol.69, issue.4-5, pp.477-528 ,

DOI : 10.1145/1889997.1890002

A relational modal logic for higher-order stateful ADTs Continuity of gödel's system t definable functionals via effectful forcing Refinement types for ml, Proceedings of POPL'10 Proceedings of the ACM SIGPLAN 1991 Conference on Programming Language Design and Implementation, PLDI '91, pp.194119-141, 1991. ,

Abstract syntax and variable binding, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158), pp.193-104, 1999. ,

DOI : 10.1109/LICS.1999.782615

Game Semantics in the Nominal Model, Proceedings of ICALP'00 Murdoch Gabbay and Andrew Pitts. A new approach to abstract syntax involving binders Logic in Computer Science Proceedings. 14th Symposium on, pp.173-189, 1999. ,

DOI : 10.1016/j.entcs.2012.08.012

Types are weak ?-groupoid Geuvers and F. Wiedijk. A logical framework with explicit conversions, Proceedings of the London Mathematical Society, pp.370-394, 2008. ,

The marriage of bisimulations and kripke logical relations, POPL '12: Proceedings of the 39th ACM BIBLIOGRAPHY Symposium on Principles of Programming Languages, p.59 ,

A Fragment of ML Decidable by Visibly Pushdown Automata, Proceedings of the ICALP'11, pp.149-161 ,

DOI : 10.1007/978-3-540-31982-5_13

On full abstraction for PCF: I, II and III. Information and Computation, pp.195285-408, 2000. ,

Extensional concepts in intensional type theory, p.58, 1995. ,

On the interpretation of type theory in locally cartesian closed categories Syntax and semantics of dependent types Semantical analysis of higher-order abstract syntax, Computer Science Logic Semantics and Logics of Computation Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, pp.427-441, 1995. ,

The groupoid interpretation of type theory In Twenty-five years of constructive type theory Game-theoretic analysis of call-by-value computation, Tabareau. Krivine realizability for compiler correctness Workshop LOLA 2010, Syntax and Semantics of Low Level Languages, pp.83-111, 1995. ,

The journey of biorthogonal logical relations to the realm of assembly code Syntax and Semantics of Low Level Languages Extending Type Theory with Forcing Realizability algebras: a program to well order R A fully abstract trace semantics for general references, Proceedings of LICS'12 Proceedings of the ICALP'07, pp.37-95197, 2007. ,

A game semantics of names and pointers Game semantics for call-by-value polymorphism, Proceedings of ICALP'10, pp.151-169, 2008. ,

Formal verification of a realistic compiler One conservative extension of formal mathematic analysis with a scheme of dependent choice Typed normal form bisimulation, Computer Science Logic, pp.107-115, 1977. ,

Typed Normal Form Bisimulation for Parametric Polymorphism, 2008 23rd Annual IEEE Symposium on Logic in Computer Science, pp.341-352, 2008. ,

DOI : 10.1109/LICS.2008.26

Finitary pcf is not decidable Transition systems over games, Proceedings of LICS'14, pp.341-364, 2001. ,

Weak ?-categories from intensional type theory ,

Dependently typed functional programs and their proofs, College of Science and Engineering. School of Informatics, p.58, 2000. ,

Forcing as a program transformation, Proceedings of the 26th Symposium on Logic in Computer Science (LICS'11), pp.197-206, 2011. ,

An Intuitionistic Theory of Types: Predicative Part, Logic Colloquium, pp.73-118, 1973. ,

DOI : 10.1016/S0049-237X(08)71945-1

Sheaves in geometry and logic: A first introduction to topos theory, p.94, 1992. ,

Intuitionistic type theory, Bibliopolis Naples, vol.17, issue.49, p.51, 1984. ,

A type theory for productive coprogramming via guarded recursion, p.104 ,

Notions of computation and monads. Information and computation, pp.55-92, 1991. ,

Algorithmic Nominal Game Semantics, Proceedings of the 20th European Symposium on Programming, pp.419-463, 2011. ,

DOI : 10.1145/1013560.1013562

Game semantics for good general references Algorithmic games for full ground references, Proceedings of LICS'11 Proceedings of the ICALP'12, pp.75-84, 2011. ,

Full abstraction for reduced ml Annals of Pure and Applied Logic Functions with local state: regularity and undecidability A modality for recursion, Proceeding of the 15th Symposium on Logic in Computer Science (LICS'00), pp.192315-349, 2000. ,

Fixed-point logic with the approximation modality and its kripke completeness, Theoretical Aspects of Computer Software, pp.165-182 ,

Hoare type theory, polymorphism and separation Extensionality in the calculus of constructions, Proceedings of the 18th Conference on Theorem Proving in Higher Order Logics (TPHOLs'05) Typed Lambda Calculi and Applications, pp.5-6865, 1993. ,

Higher-order abstract syntax ACM. 104 [Pit00] A. Pitts. Parametric polymorphism and operational equivalence Nominal logic, a first order theory of names and binding. Information and computation, Proceedings of the ACM SIGPLAN 1988 Conference on Programming Language Design and Implementation, PLDI '88Pit13] A. Pitts. Nominal Sets: Names and Symmetry in Computer Science, pp.199-208321, 1988. ,

The temporal logic of programs, Foundations of Computer Science 18th Annual Symposium on Premonoidal categories and notions of computation . Mathematical structures in computer science, pp.46-57453, 1977. ,

Operational reasoning for functions with local state, Higher Order Operational Techniques in Semantics. CUP, pp.41-43, 1998. ,

Closed freyd-and kappa-categories, Proceedings of the 26th International Colloquium on Automata, Languages and Programming, pp.625-634, 1999. ,

Syntactic control of interference Types, abstraction and parametric polymorphism, Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages IFIP Congress, pp.39-46, 1978. ,

Separation logic: A logic for shared mutable data structures, Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science, pp.55-74, 2002. ,

Domains for denotational semantics, Automata, languages and programming, pp.577-610, 1982. ,

Univalence for inverse diagrams, oplax limits, and gluing, and homotopy canonicity. arXiv preprint arXiv:1203.3253, 2012 The univalence axiom for elegant reedy presheaves. arXiv preprint arXiv:1307 Environmental bisimulations for higher-order languages Toward A Mathematical Semantics for Computer Languages [Sta98] I. Stark. Names, equations, relations: Practical ways to reason about new A complete characterization of observational equivalence in polymorphic ?-calculus with general references Full abstraction for nominal general references, Pure type system conversion is always typable. Journal of Functional Programming ACM Transactions on Programming Languages and Systems (TOPLAS) Proceedings of the Symposium on Computers and Automata Computer Science Logic '09 Sheaf theory and the continuum hypothesis. LNM 274 Logic in Computer Science LICS 2007. 22nd Annual IEEE Symposium onTze11] N. Tzevelekos. Fresh-register automata Proceedings of POPL'11, pp.153-180, 1971. ,

Explicit convertibility proofs in pure type systems, Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice, LFMTP '13, pp.25-36, 2013. ,

DOI : 10.1145/2503887.2503890

A Constructive Model of Uniform Continuity, Typed Lambda Calculi and Applications LNCS 7941, pp.236-249, 2013. ,

DOI : 10.1007/978-3-642-38946-7_18

Finding and understanding bugs in c compilers, Proceedings of the 32Nd ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI '11, pp.283-294, 2011. ,