Results 1  10
of
110
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
Abstract

Cited by 406 (43 self)
 Add to MetaCart
In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
The slam calculus: programming with secrecy and integrity
 In POPL ’98: Proceedings of the 25th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 1998
"... The SLam calculus is a typed λcalculus that maintains security information as well as type information. The type system propagates security information for each object in four forms: the object’s creators and readers, and the object’s indirect creators and readers (i.e., those agents who, through f ..."
Abstract

Cited by 279 (1 self)
 Add to MetaCart
The SLam calculus is a typed λcalculus that maintains security information as well as type information. The type system propagates security information for each object in four forms: the object’s creators and readers, and the object’s indirect creators and readers (i.e., those agents who, through flowofcontrol or the actions of other agents, can influence or be influenced by the content of the object). We prove that the type system prevents security violations and give some examples of its power. 1
An Indexed Model of Recursive Types for Foundational ProofCarrying Code
 ACM Transactions on Programming Languages and Systems
, 2000
"... The proofs of "traditional" proof carrying code (PCC) are typespecialized in the sense that they require axioms about a specific type system. In contrast, the proofs of foundational PCC explicitly define all required types and explicitly prove all the required properties of those types as ..."
Abstract

Cited by 155 (13 self)
 Add to MetaCart
The proofs of "traditional" proof carrying code (PCC) are typespecialized in the sense that they require axioms about a specific type system. In contrast, the proofs of foundational PCC explicitly define all required types and explicitly prove all the required properties of those types assuming only a fixed foundation of mathematics such as higherorder logic. Foundational PCC is both more flexible and more secure than typespecialized PCC.
Games and Full Abstraction for the Lazy lambdacalculus
 In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typ ..."
Abstract

Cited by 149 (9 self)
 Add to MetaCart
ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typefree functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E . This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the first purely semantic construction of a fully abstract model for a reflexivelytyped sequential language. 1 Introduction Full Abstraction is a key concept in programming language semantics [9, 12, 23, 26]. The ingredients are as follows. We are given a language L, with an `observational preorder'  on terms in L such that P  Q means that every observable property of P is also satisfied by Q; and a denotational model MJ\DeltaK. The model M is then said to be f...
Simple Relational Correctness Proofs for Static Analyses and Program Transformations
, 2004
"... We show how some classical static analyses for imperative programs, and the optimizing transformations which they enable, may be expressed and proved correct using elementary logical and denotational techniques. The key ingredients are an interpretation of program properties as relations, rather tha ..."
Abstract

Cited by 104 (9 self)
 Add to MetaCart
(Show Context)
We show how some classical static analyses for imperative programs, and the optimizing transformations which they enable, may be expressed and proved correct using elementary logical and denotational techniques. The key ingredients are an interpretation of program properties as relations, rather than predicates, and a realization that although many program analyses are traditionally formulated in very intensional terms, the associated transformations are actually enabled by more liberal extensional properties.
Structural Induction and Coinduction in a Fibrational Setting
 Information and Computation
, 1997
"... . We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for in ..."
Abstract

Cited by 89 (16 self)
 Add to MetaCart
. We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle for terminal coalgebras is admissible. After giving an alternative formulation of induction in terms of binary relations, we combine both principles and obtain a mixed induction/coinduction principle which allows us to reason about minimal solutions X = oe(X) where X may occur both positively and negatively in the type constructor oe. We further strengthen these logical principles to deal with contexts and prove that such strengthening is valid when the (abstract) logic we consider is contextually/functionally complete. All the main results follow from a basic result about adjunc...
StepIndexed Syntactic Logical Relations for Recursive and Quantified Types
 of Lecture Notes in Computer Science
, 2006
"... We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a #calculus with recursive types and impredicative universal and existential types. Our development builds on the stepindexed PER model of recursive types ..."
Abstract

Cited by 86 (11 self)
 Add to MetaCart
(Show Context)
We present a sound and complete proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a #calculus with recursive types and impredicative universal and existential types. Our development builds on the stepindexed PER model of recursive types presented by Appel and McAllester. We have discovered that a direct proof of transitivity of that model does not go through, leaving the "PER" status of the model in question. We show how to extend the AppelMcAllester model to obtain a logical relation that we can prove is transitive, as well as sound and complete with respect to contextual equivalence. We then augment this model to support relational reasoning in the presence of quantified types.
Parametric Polymorphism and Operational Equivalence
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
"... Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where ..."
Abstract

Cited by 83 (2 self)
 Add to MetaCart
Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard–Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite (‘lazy’) data types. An approach to Reynolds' notion of relational parametricity is developed that works directly on the syntax of a programming language, using a novel closure operator to relate operational behaviour to parametricity properties of types. Working with an extension of Plotkin's PCF with ∀types, lazy lists and existential types, we show by example how the resulting logical relation can be used to prove properties of polymorphic types up to operational equivalence.
Coinductive Axiomatization of Recursive Type Equality and Subtyping
, 1998
"... e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The mai ..."
Abstract

Cited by 78 (2 self)
 Add to MetaCart
e present new sound and complete axiomatizations of type equality and subtype inequality for a firstorder type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle), which has the form A; P ` P A ` P (Fix) where P is either a type equality = 0 or type containment 0 and the proof of the premise must be contractive in a formal sense. In particular, a proof of A; P ` P using the assumption axiom is not contractive. The fixpoint rule embodies a finitary coinduction principle and thus allows us to capture a coinductive relation in the fundamentally inductive framework of inference systems. The new axiomatizations are more concise than previous axiomatizations, particularly so for type containment since no separate axiomatization of type equality is required, as in A...