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65
Statedependent representation independence
 In Proceedings of the 36th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2009
"... Mitchell’s notion of representation independence is a particularly useful application of Reynolds ’ relational parametricity — two different implementations of an abstract data type can be shown contextually equivalent so long as there exists a relation between their type representations that is pre ..."
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Cited by 87 (24 self)
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Mitchell’s notion of representation independence is a particularly useful application of Reynolds ’ relational parametricity — two different implementations of an abstract data type can be shown contextually equivalent so long as there exists a relation between their type representations that is preserved by their operations. There have been a number of methods proposed for proving representation independence in various pure extensions of System F (where data abstraction is achieved through existential typing), as well as in Algol or Javalike languages (where data abstraction is achieved through the use of local mutable state). However, none of these approaches addresses the interaction of existential type abstraction and local state. In particular, none allows one to prove representation independence results for generative ADTs — i.e., ADTs that both maintain some local state and define abstract types whose internal
Relational parametricity and separation logic
 In 10th FOSSACS, LNCS 4423
, 2007
"... Abstract. Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types. Our interpretation is based on Reynolds’s relation ..."
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Cited by 33 (14 self)
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Abstract. Separation logic is a recent extension of Hoare logic for reasoning about programs with references to shared mutable data structures. In this paper, we provide a new interpretation of the logic for a programming language with higher types. Our interpretation is based on Reynolds’s relational parametricity, and it provides a formal connection between separation logic and data abstraction.
Imperative selfadjusting computation
 In POPL ’08: Proceedings of the 35th annual ACM SIGPLANSIGACT symposium on Principles of programming languages
, 2008
"... Recent work on selfadjusting computation showed how to systematically write programs that respond efficiently to incremental changes in their inputs. The idea is to represent changeable data using modifiable references, i.e., a special data structure that keeps track of dependencies between read an ..."
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Cited by 33 (16 self)
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Recent work on selfadjusting computation showed how to systematically write programs that respond efficiently to incremental changes in their inputs. The idea is to represent changeable data using modifiable references, i.e., a special data structure that keeps track of dependencies between read and writeoperations, and to let computations construct traces that later, after changes have occurred, can drive a change propagation algorithm. The approach has been shown to be effective for a variety of algorithmic problems, including some for which adhoc solutions had previously remained elusive. All previous work on selfadjusting computation, however, relied on a purely functional programming model. In this paper, we show that it is possible to remove this limitation and support modifiable references that can be written multiple times. We formalize this using a language AIL for which we define evaluation and changepropagation semantics. AIL closely resembles a traditional higherorder imperative programming language. For AIL we state and prove consistency, i.e., the property that although the semantics is inherently nondeterministic, different evaluation paths will still give observationally equivalent results. In the imperative setting where pointer graphs in the store can form cycles, our previous proof techniques do not apply. Instead, we make use of a novel form of a stepindexed logical relation that handles modifiable references. We show that AIL can be realized efficiently by describing implementation strategies whose overhead is provably constanttime per primitive. When the number of reads and writes per modifiable is bounded by a constant, we can show that change propagation becomes as efficient as it was in the pure case. The general case incurs a slowdown that is logarithmic in the maximum number of such operations. We use DFS and related algorithms on graphs as our running examples and prove that they respond to insertions and deletions of edges efficiently. 1.
Stepindexed Kripke models over recursive worlds
 In Proc. of POPL
, 2011
"... Over the last decade, there has been extensive research on modelling challenging features in programming languages and program logics, such as higherorder store and storable resource invariants. A recent line of work has identified a common solution to some of these challenges: Kripke models over w ..."
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Cited by 31 (13 self)
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Over the last decade, there has been extensive research on modelling challenging features in programming languages and program logics, such as higherorder store and storable resource invariants. A recent line of work has identified a common solution to some of these challenges: Kripke models over worlds that are recursively defined in a category of metric spaces. In this paper, we broaden the scope of this technique from the original domaintheoretic setting to an elementary, operational one based on step indexing. The resulting method is widely applicable and leads to simple, succinct models of complicated language features, as we demonstrate in our semantics of Charguéraud and Pottier’s typeandcapability system for an MLlike higherorder language. Moreover, the method provides a highlevel understanding of the essence of recent approaches based on step indexing. 1.
Relational reasoning for recursive types and references
 ASIAN SYMPOSIUM ON PROGRAMMING LANGUAGES AND SYSTEMS (APLAS)
, 2006
"... We present a local relational reasoning method for reasoning about contextual equivalence of expressions in a λcalculus with recursive types and general references. Our development builds on the work of Benton and Leperchey, who devised a nominal semantics and a local relational reasoning method fo ..."
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Cited by 30 (7 self)
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We present a local relational reasoning method for reasoning about contextual equivalence of expressions in a λcalculus with recursive types and general references. Our development builds on the work of Benton and Leperchey, who devised a nominal semantics and a local relational reasoning method for a language with simple types and simple references. Their method uses a parameterized logical relation. Here we extend their approach to recursive types and general references. For the extension, we build upon Pitts ’ and Shinwell’s work on relational reasoning about recursive types (but no references) in nominal semantics. The extension is nontrivial because of general references (higherorder store) and makes use of some new ideas for proving the existence of the parameterized logical relation and for the choice of parameters.
A typed, compositional logic for a stackbased abstract machine
 In Proc. 3rd Asian Symposium on Programming Languages and Systems (APLAS), volume 3780 of Lecture Notes in Computer Science
, 2005
"... Abstract. We define a compositional program logic in the style of Floyd and Hoare for a simple, typed, stackbased abstract machine with unstructured control flow, global variables and mutually recursive procedure calls. Notable features of the logic include a careful treatment of auxiliary variable ..."
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Cited by 24 (7 self)
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Abstract. We define a compositional program logic in the style of Floyd and Hoare for a simple, typed, stackbased abstract machine with unstructured control flow, global variables and mutually recursive procedure calls. Notable features of the logic include a careful treatment of auxiliary variables and quantification and the use of substructural typing to permit local, modular reasoning about program fragments. Semantic soundness is established using an interpretation of types and assertions defined by orthogonality with respect to sets of contexts. 1
Realizability semantics of parametric polymorphism, general references, and recursive types
, 2010
"... Abstract. We present a realizability model for a callbyvalue, higherorder programming language with parametric polymorphism, general firstclass references, and recursive types. The main novelty is a relational interpretation of open types (as needed for parametricity reasoning) that include gener ..."
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Cited by 23 (14 self)
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Abstract. We present a realizability model for a callbyvalue, higherorder programming language with parametric polymorphism, general firstclass references, and recursive types. The main novelty is a relational interpretation of open types (as needed for parametricity reasoning) that include general reference types. The interpretation uses a new approach to modeling references. The universe of semantic types consists of worldindexed families of logical relations over a universal predomain. In order to model general reference types, worlds are finite maps from locations to semantic types: this introduces a circularity between semantic types and worlds that precludes a direct definition of either. Our solution is to solve a recursive equation in an appropriate category of metric spaces. In effect, types are interpreted using a Kripke logical relation over a recursively defined set of worlds. We illustrate how the model can be used to prove simple equivalences between different implementations of imperative abstract data types. 1
A Relational Modal Logic for HigherOrder Stateful ADTs
"... The method of logical relations is a classic technique for proving the equivalence of higherorder programs that implement the same observable behavior but employ different internal data representations. Although it was originally studied for pure, strongly normalizing languages like System F, it ha ..."
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Cited by 22 (12 self)
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The method of logical relations is a classic technique for proving the equivalence of higherorder programs that implement the same observable behavior but employ different internal data representations. Although it was originally studied for pure, strongly normalizing languages like System F, it has been extended over the past two decades to reason about increasingly realistic languages. In particular, Appel and McAllester’s idea of stepindexing has been used recently to develop syntactic Kripke logical relations for MLlike languages that mix functional and imperative forms of data abstraction. However, while stepindexed models are powerful tools, reasoning with them directly is quite painful, as one is forced to engage in tedious stepindex arithmetic to derive even simple results. In this paper, we propose a logic LADR for equational reasoning about higherorder programs in the presence of existential type abstraction, general recursive types, and higherorder mutable state. LADR exhibits a novel synthesis of features from PlotkinAbadi logic, GödelLöb logic, S4 modal logic, and relational separation logic. Our model of LADR is based on Ahmed, Dreyer, and Rossberg’s stateoftheart stepindexed Kripke logical relation, which was designed to facilitate proofs of representation independence for “statedependent ” ADTs. LADR enables one to express such proofs at a much higher level, without counting steps or reasoning about the subtle, stepstratified construction of possible worlds.
Abstracting Allocation: The New new Thing
 In Computer Science Logic
, 2006
"... Abstract. We introduce a FloydHoarestyle framework for specification and verification of machine code programs, based on relational parametricity (rather than unary predicates) and using both stepindexing and a novel form of separation structure. This yields compositional, descriptive and extensi ..."
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Cited by 20 (6 self)
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Abstract. We introduce a FloydHoarestyle framework for specification and verification of machine code programs, based on relational parametricity (rather than unary predicates) and using both stepindexing and a novel form of separation structure. This yields compositional, descriptive and extensional reasoning principles for many features of lowlevel sequential computation: independence, ownership transfer, unstructured control flow, firstclass code pointers and address arithmetic. We demonstrate how to specify and verify the implementation of a simple memory manager and, independently, its clients in this style. The work has been fully machinechecked within the Coq proof assistant. 1