I. Stark, Names and Higher-Order Functions, Ph.D. thesis, University of Cambridge, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....validated. While remarkable progress has been made in understanding local variables (cf. the collection [15] none of this theory is directly applicable to heap variables because the shape of the heap storage dynamically varies. A number of attacks have been made on the problem: Stark s thesis [25, 24], which deals with dynamic allocation but not pointers, and Ghica s and Levy s theses [4, 5, 7, 8] which address the general semantic structure but not data representation reasoning. The recent paper of Banerjee and Naumann [2] is the rst to address data representation correctness with heap ....

Stark, I. Names and higher-order functions. Technical Report 363, University of Cambridge Computer Laboratory, April 1995.

....show that two programs p and q are operationally equivalent, it is sufficient to show that their graphical denotations [ p] and [ q] are equivalent, using the equational theory for flow graphs. An example of such a language, its operational semantics, and sound categorical models is given in [Sta94]. The language considered, the n calculus, is a typed lambda calculus with an operation for dynamically creating names. The language is extended to obtain a typed lambda calculus with operations for creating, reading, and updating integer reference cells, i.e. a fragment of the programming ....

....which creates the new names s , and returns the value a. The second example is the full subcategory of Set of pullback preserving functors, presented in a topological way as continuous G sets, i.e. sets with a group action of a topological group. A similar programme is carried out in [Sta94] for the language Reduced ML, a typed lambda calculus with integer references. An operational semantics is defined as a big step evaluation relation taking a pair (s; p) of an initial state s and a program p to a pair (s ; v) of the final state s after evaluating p, and a result value v; ....

Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994.

....follow the lead of Volpano and Smith in using simple standard semantic notions to the extent possible. Second, although it is easy to see how to maintain the bijection in a small step semantics, it is not as simple in a 3 compositional semantics. Some other possibilities for relating heaps are in [29, 30], though we have not pursued these ideas. Our approach depends on the allocator satisfying a mild parametricity condition which is also needed for the abstraction theorem of [3] The condition says that the choice of a fresh location for an object of class C depends only on currently allocated C ....

I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994. http://www.dcs.ed.ac.uk/home/stark/publications/thesis.html.

....ACI jeunes chercheurs S ecurit e informatique, protocoles cryptographiques et d etection d intrusions and the ACI Cryptologie PSI Robuste . Logical relations are a powerful technique to prove properties of typed lambda calculi such like the nu calculus and the cryptographic lambda calculus. In [11, 12], Pitts and Stark de ne an operational logical relation to establish the observational equivalence between nu calculus expressions. They also prove that this logical relation is complete for rst order types. But the operational logical relation is a quite syntactic one and it is de ned based on ....

....in a categorical style. We also show that, this logical relation is equivalent to Pitts and Stark s operational logical relation up to rstorder types. As preliminaries, Section 2 gives a brief review of the nu calculus and the operational logical relation, more details of which can be found in [11, 12, 14]. Section 3 introduces a categorical model Set Set Set for the nu calculus [12, 13] to provide a basis for our Kripke logical relation. We give in Section 4 the de nition of the Kripke logical relation, while before that, we derive another one from Goubault Larrecq, Lasota and Nowak s de ....

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Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994.

....(5) Finally it would be very interesting to nd out if the observationalequivalence of (low orders of) Reduced ML is decidable. Reduced ML is a call by value PCF augmented by statically scoped, dynamically allocated, mutable state, with equality test for references as studied in [30] see also [36]) Our preferred approach is by Algorithmic Game Semantics, but to our knowledge, the prior (for this approach) problem of the existence of a fully abstract game semantics for Reduced ML is still open. Acknowledgements The author is grateful to Samson Abramsky and Dan Ghica for helpful ....

I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge Computing Laboratory, 1995.

....6= j, where i; j is the secret data, p is the program carrying secret data and f is the attacker. 2 CHAPTER 1. INTRODUCTION The proof technique used by Sumii and Pierce is logical relation. The nu calculus is a small language designed to study dynamically generated names in programming languages [5, 6]. It is also an extension of the simply typed lambda calculus with a ground type for names and a primitive of dynamical name generation. It is easy to see that the nu calculus is a syntactical subset of the cryptographic lambda calculus when we regard the type for names and the type for keys as a ....

....on it and show that, with some renaming strategy, the improved Kripke logical relation is equivalent to the operational logical relation. The Nu Calculus The nu calculus is a small language designed to show the interaction between dynamically generated names and higher order functions [5, 6]. We give its syntax and describe an operational semantics in a big step evaluation style. We go on to de ne a notion of contextual equivalence for expressions of the language and present some examples of expressions that are equivalent or inequivalent. The nu calculus is a typed call by value ....

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I. D. B. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994.

....that the size of the store, as well as its contents, may change over time. To specify how the state is allowed to change at any point in the program, they use functor categories indexed by possible worlds or store shapes. We note, however, that these models do not handle general references. Stark [22] (building on work done with Pitts on possible world models of the nu calculus [19] describes a denotational semantics for Reduced ML that includes integer references. Recently, Levy [10] has described a possible world model for general references. There are interesting correspondences between ....

Ian D. B. Stark. Names and Higher-Order Functions.Ph.D. dissertation, University of Cambridge, Cambridge, England, December 1994.

....developed by Reynolds and Oles [27, 21, 22] make use of functor categories indexed by possible worlds or store shapes to specify how the size of the store, as well as its contents, may change at any point in the program. We note, however, that these models do not handle general references. Stark [30] (building on work done with Pitts on possible world models of the nu calculus [26] describes a denotational semantics for Reduced ML that includes integer references. 12 Future work All practical languages provide some means for managing memory, but the model that we have described does not ....

I. D. B. Stark. Names and Higher-Order Functions.Ph.D. dissertation, University of Cambridge, Cambridge, England, December 1994.

....notably by O Hearn and Tennent [21] The idea is essentially to take a traditional global state model and parameterize it with respect to store shapes, to account for the allocation and later deallocation of local variables. Stark has also used functor categories to model ML style references [31], and similar ideas have led to denotational models of the calculus [10, 32] The second, perhaps computationally more compelling, method has been termed Object based semantics by Reddy [26] In this view, commands, procedures and variables are seen as objects or processes which interact with ....

I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, December 1994. 39

....notably by O Hearn and Tennent [24] The idea is essentially to take a traditional global state model and parameterize it with respect to store shapes, to account for the allocation and later deallocation of local variables. Stark has also used functor categories to model ML style references [35], and similar ideas have led to denotational models of the calculus [10, 36] The second, perhaps computationally more compelling, method has been termed Object based semantics by Reddy [30] In this view, commands, procedures and variables are seen as objects or processes which interact with ....

I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, Dec 1994.

....community. Non interference reasoning in protocol verification can be found in [9, 24, 26] among others. Since the cryptographic # calculus has a key generation primitive, we must be able to reason about generative names. We adopted Pitts and Stark s work on # calculus with name generation [25] in formulating both the semantics in Section 4 and the logical relation in Section 6.1. Encryption is similar to type abstraction in that both restrict access to secrets (the former dynamically obfuscates their values, while the latter statically hide their types) To define the logical relation ....

Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994. Available at http://www.dcs.ed.ac.uk/home/stark/publications/thesis.html.

....the correctness of these transformations by using a denotational semantics. However, giving a good denotational semantics of MIL lite is surprisingly tricky, not really because of the multiple computational types, but because of the presence of dynamically allocated references. Stark s thesis [Sta94] examines equivalence in a very minimal language with dynamically generated names in considerable detail and does give a functor category semantics for a language with higher order functions and integer references. But MIL lite is rather more complex than Stark s language, requiring a functor ....

I. D. B. Stark. Names and Higher Order Functions. PhD thesis, Computer Laboratory, University of Cambridge, 1994.

....of the above examples (compared with analogous examples in other formalisms) as a good sign 6. Relation to presheaf models One origin of the work presented here lies in the calculus , a calculus of higher order functions and dynamically created names introduced by the second author and Stark [32, 36] (see also [17] In [37] Stark studies a model of the calculus based on one of Moggi s dynamic allocation monads [29] in the presheaf category Set I , where I is the category of finite ordinals and injective functions between them. Crucial ingredients of the dynamic allocation monad used ....

I. D. B. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1995.

....the correctness of these transformations by using a denotational semantics. However, giving a good denotational semantics of MIL lite is surprisingly tricky, not really because of the multiple computational types, but because of the presence of dynamically allocated references. Stark s thesis [Sta94] examines equivalence in a very minimal language with dynamically generated names in considerable detail and does give a functor category semantics for a language with higher order functions and integer references. But MIL lite is rather more complex than Stark s language, requiring a functor ....

I. D. B. Stark. Names and Higher Order Functions. PhD thesis, Computer Laboratory, University of Cambridge, 1994. 71

....kind of functional extensionality fails, due to the complicated interactions possible between call by value function application and locally declared state in expressions of function type, permitting leakage of private names out of the textual scope of local declarations. See Pitts and Stark [15, 23] for examples. By contrast, Algol like languages, by virtue of having call by name function application and having local variable declarations restricted to commands, do satisfy (1) This is part of the Algol Operational Extensionality Theorem which we shall prove (Theorem 2.5) It is a ....

I. D. B. Stark. Names and higher-order functions. Technical Report 363, Cambridge Univ. Computer Laboratory, Apr. 1995.

....as dynamic allocation. Here, it is possible for access to a variable allocated in a block to be passed outside that block, so a variable, once allocated, must be seen as persisting forever. A detailed analysis of the behaviour of languages with this feature has been undertaken by Pitts and Stark [20, 13, 12] using both operational and denotational techniques, but until now, no fully abstract model was known. A fully abstract games model has already been given for Idealized Algol using the category I [3] We now show that the category Fam(I) is fully abstract for a language with dynamically allocated ....

I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, Dec 1994.

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I. D. B. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, December 1994.

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I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, December 1994.

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I. Stark, Names and Higher-Order Functions, Ph.D. thesis, University of Cambridge, 1994.

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Stark, I., "Names and Higher-Order Function," Ph.D. thesis, University of Cambridge, Cambridge Computer Laboratory (1994).

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I. Stark, "Names and Higher-Order Function," Ph.D. thesis, University of Cambridge, Cambridge Computer Laboratory (1994).

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Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994. http://www.dcs.ed.ac.uk/home/stark/publications/thesis. html.

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Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994. Available at http://www.dcs.ed.ac.uk/home/stark /publications/thesis.html.

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Ian D. B. Stark. Names and Higher-Order Functions. Ph. D. dissertation, University of Cambridge, Cambridge, England, December 1994.

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Ian Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, 1994. Available at http://www.dcs.ed.ac.uk/home/stark/publications/thesis.html.

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