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18
A Variable Typed Logic of Effects
 Information and Computation
, 1993
"... In this paper we introduce a variable typed logic of effects inspired by the variable type systems of Feferman for purely functional languages. VTLoE (Variable Typed Logic of Effects) is introduced in two stages. The first stage is the firstorder theory of individuals built on assertions of equalit ..."
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Cited by 48 (12 self)
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In this paper we introduce a variable typed logic of effects inspired by the variable type systems of Feferman for purely functional languages. VTLoE (Variable Typed Logic of Effects) is introduced in two stages. The first stage is the firstorder theory of individuals built on assertions of equality (operational equivalence `a la Plotkin), and contextual assertions. The second stage extends the logic to include classes and class membership. The logic we present provides an expressive language for defining and studying properties of programs including program equivalences, in a uniform framework. The logic combines the features and benefits of equational calculi as well as program and specification logics. In addition to the usual firstorder formula constructions, we add contextual assertions. Contextual assertions generalize Hoare's triples in that they can be nested, used as assumptions, and their free variables may be quantified. They are similar in spirit to program modalities in ...
Categorical Models for Local Names
 LISP AND SYMBOLIC COMPUTATION
, 1996
"... This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. T ..."
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Cited by 39 (2 self)
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This paper describes the construction of categorical models for the nucalculus, a language that combines higherorder functions with dynamically created names. Names are created with local scope, they can be compared with each other and passed around through function application, but that is all. The intent behind this language is to examine one aspect of the imperative character of Standard ML: the use of local state by dynamic creation of references. The nucalculus is equivalent to a certain fragment of ML, omitting side effects, exceptions, datatypes and recursion. Even without all these features, the interaction of name creation with higherorder functions can be complex and subtle; it is particularly difficult to characterise the observable behaviour of expressions. Categorical monads, in the style of Moggi, are used to build denotational models for the nucalculus. An intermediate stage is the use of a computational metalanguage, which distinguishes in the type system between values and computations. The general requirements for a categorical model are presented, and two specific examples described in detail. These provide a sound denotational semantics for the nucalculus, and can be used to reason about observable equivalence in the language. In particular a model using logical relations is fully abstract for firstorder expressions.
References, Local Variables and Operational Reasoning
 In Seventh Annual Symposium on Logic in Computer Science
, 1992
"... this paper we regard the following as synonyms: references, program variables, pointers, locations, and unary cells) to a programming language complicates life. Adding them to the simply typed lambda calculus causes the failure of most of the nice mathematical properties and some of the more basic r ..."
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Cited by 30 (4 self)
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this paper we regard the following as synonyms: references, program variables, pointers, locations, and unary cells) to a programming language complicates life. Adding them to the simply typed lambda calculus causes the failure of most of the nice mathematical properties and some of the more basic rules (such as j). For example strong normalization fails since it is possible, for each provably nonempty function type, to construct a Y combinator for that type. References also interact unpleasantly with polymorphism [34, 35]. They are also troublesome from a denotational point of view as illustrated by the lack of fully abstract models. For example, in [22] Meyer and Sieber give a series of examples of programs that are operationally equivalent (according to the intended semantics of blockstructured Algollike programs) but which are not given equivalent denotations in traditional denotational semantics. They propose various modifications to the denotational semantics which solve some of these discrepancies, but not all. In [27, 26] a denotational semantics that overcomes some of these problems is presented. However variations on the seventh example remain problematic. Since numerous proof systems for Algol are sound for the denotational models in question, [8, 7, 32, 28, 16, 27, 26], these equivalences, if expressible, must be independent of these systems. The problem which motivated Meyer and Sieber's paper, [22], was to provide mathematical justification for the informal but convincing proofs of the operational equivalence of their examples. In this paper we approach the same problem, but from an operational rather than denotational perspective. This paper accomplishes two goals. Firstly, we present the firstorder part of a new logic for reasoning about programs....
The Formal Relationship Between Direct and ContinuationPassing Style Optimizing Compilers: A Synthesis of Two Paradigms
, 1994
"... Compilers for higherorder programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuationpassing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two co ..."
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Cited by 15 (0 self)
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Compilers for higherorder programming languages like Scheme, ML, and Lisp can be broadly characterized as either "direct compilers" or "continuationpassing style (CPS) compilers", depending on their main intermediate representation. Our central result is a precise correspondence between the two compilation strategies. Starting from
Reasoning about Functions with Effects
 See Gordon and Pitts
, 1997
"... ing and using (Lunif) we have that any two lambdas that are everywhere undefined are equivalent. The classic example of an everywhere undefined lambda is Bot 4 = x:app(x:app(x; x); x:app(x; x)) In f , another example of an everywhere undefined lambda is the "doforever" loop. Do 4 = f:Yv(Dox ..."
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Cited by 13 (1 self)
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ing and using (Lunif) we have that any two lambdas that are everywhere undefined are equivalent. The classic example of an everywhere undefined lambda is Bot 4 = x:app(x:app(x; x); x:app(x; x)) In f , another example of an everywhere undefined lambda is the "doforever" loop. Do 4 = f:Yv(Dox:Do(f(x)) By the recursive definition, for any lambda ' and value v Do(')(v) \Gamma!Ø Do(')('(v)) Reasoning about Functions with Effects 21 In f , either '(v) \Gamma!Ø v 0 for some v 0 or '(v) is undefined. In the latter case the computation is undefined since the redex is undefined. In the former case, the computation reduces to Do(')(v 0 ) and on we go. The argument for undefinedness of Bot relies only on the (app) rule and will be valid in any uniform semantics. In contrast the argument for undefinedness of Do(') relies on the (fred.isdef) property of f . Functional Streams We now illustrate the use of (Lunifsim) computation to reason about streams represented as functions ...
Logical reasoning for higherorder functions with local state
 In Foundations of Software Science and Computation Structure
"... ABSTRACT. We introduce an extension of Hoare logic for callbyvalue higherorder functions with MLlike local reference generation. Local references may be generated dynamically and exported outside their scope, may store higherorder functions and may be used to construct complex mutable data stru ..."
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Cited by 13 (4 self)
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ABSTRACT. We introduce an extension of Hoare logic for callbyvalue higherorder functions with MLlike local reference generation. Local references may be generated dynamically and exported outside their scope, may store higherorder functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higherorder datum and quantifiers over hidden references. We explore the logic’s descriptive and reasoning power with nontrivial programming examples combining higherorder procedures and dynamically generated local state. Axioms for reachability and local invariant play a central role for reasoning about the examples.
Reasoning about Explicit and Implicit Representations of State
 YALE UNIVERSITY
, 1993
"... The semantics of imperative languages are often expressed in terms of a storepassing translation and an algebra for reasoning about stores. We axiomatize the semantics of several typical imperative languages via equational axioms by "inverting" the storepassing translation as well as the algebra ..."
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Cited by 12 (4 self)
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The semantics of imperative languages are often expressed in terms of a storepassing translation and an algebra for reasoning about stores. We axiomatize the semantics of several typical imperative languages via equational axioms by "inverting" the storepassing translation as well as the algebraic axioms for reasoning about the store. The inversion process is simple and systematic and results in theories that are similar to equational theories for imperative languages that have been derived in more complicated ways, and is likely to be applicable to languages other than those presented here.
A Theory of Classes for a Functional Language with Effects
 In Proceedings of CSL92, volume 702 of Lecture Notes in Computer Science
, 1993
"... this paper we introduce a variable typed logic of effects (i.e. a logic of effects where classes can be defined and quantified over) inspired by the variable type systems of Feferman [3, 4] for purely functional languages. A similar extension incorporating nonlocal control operations was introduced ..."
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Cited by 7 (6 self)
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this paper we introduce a variable typed logic of effects (i.e. a logic of effects where classes can be defined and quantified over) inspired by the variable type systems of Feferman [3, 4] for purely functional languages. A similar extension incorporating nonlocal control operations was introduced in [27]. The logic we present provides an expressive language for defining specifications and constraints and for studying properties and program equivalences, in a uniform framework. Thus it has an advantage over a plethora of systems in the literature that aim to capture solitary aspects of computation. The theory also allows for the construction of inductively defined sets and derivation of the corresponding induction principles. Classes can be used to express, inter alia, the nonexpansiveness of terms [29]. Other effects can also be represented within the system. These include read/write effects and various forms of interference [24]. The first order fragment is described in [16] where it is used to resolve the denotationally problematic examples of [17]. In our language atoms, references and lambda abstractions are all first class values and as such are storable. This has several consequences. Firstly, mutation and variable binding are separate and so we avoid the problems that typically arise (e.g. in Hoare's and dynamic logic) from the conflation of program variables and logical variables. Secondly, the equality and sharing of references (aliasing) is easily expressed and reasoned about. Thirdly, the combination of mutable references and lambda abstractions allows us to study object based programming within our framework. Our atomic formulas express the (operational or observational) equivalence of programs `a la Plotkin [23]. Neither Hoare's logic nor Dynamic logi...
Names, Equations, Relations: Practical Ways to Reason about new
, 1996
"... The nucalculus of Pitts and Stark is a typed lambdacalculus, extended with state in the form of dynamicallygenerated names. These names can be created locally, passed around, and compared with one another. Through the interaction between names and functions, the language can capture notions of sc ..."
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Cited by 6 (0 self)
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The nucalculus of Pitts and Stark is a typed lambdacalculus, extended with state in the form of dynamicallygenerated names. These names can be created locally, passed around, and compared with one another. Through the interaction between names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nucalculus has connections to other kinds of local declaration, and to the mobile processes of the calculus. This