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....value is used to initialize the class s private field. The parent value is used as an argument to the superclass generator. 9.3 Reduction Rules The operational semantics for our calculus extends that of Reference ML [WF94] Reduction rules are given in Fig.9. 2, where R are reduction contexts [CF91, FH92, MT89]. Expression Gen is defined below. Relation is the reflexive, transitive, contextual closure of , with respect to contexts C, as defined (in a standard way) in Appendix H.1. Reduction contexts are necessary to provide a minimal relative linear order among the creation, dereferencing and ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. of ICALP'89, volume 372 of LNCS, pages 574--588. SpringerVerlag, 1989.

....calculus is designed to make memory operations explicit, it does not necessarily provide for local state. This is a non trivial addition with respect to an equational theory. Mason and Talcott de ne a context lemma particularly tailored towards state operations. This is known as CIU equivalence [31 33, 47]. Pitts [40] and Pitts and Stark [42] use logical relations and an unwinding theorem to prove equivalences in state based languages. In this paper, we do not pursue these alternative methods since bisimilarity seems to work well for state less polymorphic calculi [16, 39] As far as we know, the ....

Ian Mason and Carolyn Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 1989.

....calculus is designed to make memory operations explicit, it does not necessarily provide for local state. This is a non trivial addition with respect to an equational theory. Mason and Talcott define a context lemma particularly tailored towards state operations. This is known as CIUequivalence [29 31, 45]. Pitts [37] and Pitts and Stark [39] use logical relations and an unwinding theorem to prove equivalences in state based languages. In this paper, we do not pursue these alternative methods since bisimilarity seems to work well for state less polymorphic calculi [17, 36] As far as we know, the ....

Ian Mason and Carolyn Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. Sixteenth International EATCS Colloquium on Automata, Languages and Programming, volume 372 of Lecture Notes in Computer Science, pages 574--588. Springer-Verlag, 1989.

....calculus is designed to make memory operations explicit, it does not necessarily provide for local state. This is a non trivial addition with respect to an equational theory. Mason and Talcott de ne a context lemma particularly tailored towards state operations. This is known as CIUequivalence [29 31, 45]. Pitts [37] and Pitts and Stark [39] use logical relations and an unwinding theorem to prove equivalences in state based languages. In this paper, we do not pursue these alternative methods since bisimilarity seems to work well for state less polymorphic calculi [17, 36] As far as we know, the ....

Ian Mason and Carolyn Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. Sixteenth International EATCS Colloquium on Automata, Languages and Programming, volume 372 of Lecture Notes in Computer Science, pages 574-588. Springer-Verlag, 1989.

....make memory operations explicit, it does not necessarily provide for local state. This is a non trivial addition with respect to an operational theory. For example, Mason and Talcott de ne some sort of context lemma particularly tailored towards state operations. This is known as CIU equivalence [25 27, 40]. Pitts [33] and Pitts and Stark [35] use logical relations to specify equivalences for state based languages. In this paper, we do not pursue these alternative methods since bisimilarity seems to work well for state less polymorphic calculi [16, 32] As far as we know, the only other work which ....

Ian Mason and Carolyn Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. Sixteenth International EATCS Colloquium on Automata, Languages and Programming, volume 372 of Lecture Notes in Computer Science, pages 574-588. Springer-Verlag, 1989.

....w.r.t. an operational equivalence, was first considered in [Plo75] for call by value and call by name operational equivalence. This approach was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84] and sideeffects (see [FFKD86, MT89]) The calculi based only on operational considerations, like the v calculus, are sound and complete w.r.t. the operational semantics, i.e. a program M has a value according to the operational semantics iff it is provably equivalent to a value (not necessarily the same) in the calculus, but they ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In 16th Colloquium on Automata, Languages and Programming. EATCS, 1989.

....classvalhGen ; m j ] M; p ] Pi (mixin) if [m j ] M = mk ] ae M; and [p ] ae [m j ] M;Gen is defined below Fig. 2. Reduction Rules The operational semantics for our calculus extends that of Reference ML [45] Reduction rules are given in Fig.2, where R are reduction contexts [22, 24, 37]. Expression Gen is defined below. Relation is the reflexive, transitive, contextual closure of , with respect to contexts C, as defined (in a standard way) in appendix A. Reduction contexts are necessary to provide a minimal relative linear order among the creation, dereferencing and ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. ICALP '89, pages 574--588. LNCS 372, Springer-Verlag, 1989.

....is used to initialize the class s private field. The superinit value is used as an argument to the superclass generator. 4 Operational Semantics The operational semantics for our calculus extends that of Reference ML [WF94] Reduction rules are given in Fig.2, where R are reduction contexts [CF91, FH92, MT89]. Expression Gen is defined below. Relation 6 is the reflexive, transitive, contextual closure of , with respect to contexts C, as defined (in a standard way) in appendix A. Reduction contexts are necessary to provide a minimal relative linear order among the creation, dereferencing and ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In ICALP '89, LNCS 372, 574-588. Springer-Verlag, 1989.

....and could be implemented with reasonable efficiency on MIMD, SIMD, and MIMD SIMD machines. Carolyn Talcott Dr. Talcott has substantial expertise in formal reasoning and in developing semantics and methods for reasoning about higher order programs with effects, both sequential and concurrent. In [103, 104, 105] a language, mk , based on the call by value lambda calculus extended by reference primitives a la ML was studied: methods for defining operational semantics and for proving program equivalence were developed and a complete axiomatization of equivalence in the zero order fragment of mk was ....

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, volume 372 of Lecture Notes in Computer Science, pages 574--588. Springer-Verlag, 1989.

....w.r.t. an operational equivalence, was rst considered in [Plo75] for call by value and call by name operational equivalence. This approach was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84] and sidee ects (see [FFKD86, MT89]) The calculi based only on operational considerations, like the v calculus, are sound and complete w.r.t. the operational semantics, i.e. a program M has a value according to the operational semantics i it is provably equivalent to a value (not necessarily the same) in the calculus, but they ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In 16th Colloquium on Automata, Languages and Programming. EATCS, 1989.

....semantics i it is provably equivalent to a value (not necessarily the same) in the calculus, but they are too weak for proving equivalences of programs. Previous work on axiom systems for proving equivalence of programs with side e ects has shown the importance of the let constructor (see [Mas88, MT89a, MT89b]) In the framework of the computational lambda calculus the importance of let becomes even more apparent. The denotational approach may suggest important principles, e.g. x point induction (see [Sco69, GMW79] that can be found only after developing a semantics based on mathematical structures ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In 16th Colloquium on Automata, Languages and Programming. EATCS, 1989.

...., two properties which are the operational analogues the least fixed point and continuity properties of domains, and a fixed point induction principle. 32 To prove the congruence of , is proved substitutive, which follows directly from the substitutivity of 0 . The proof here is adapted from [MT91] Lemma 6.9 0 is substitutive, i.e. if a 0 b then c[a] 0 c[b] Proof. To show c[a] 0 c[b] which by definition means r[ c[a] # implies r[ c[b] #, we generalize this statement to allow a=b to occur elsewhere in r; this will be notated by r[ Gamma] using hole = for the reduction ....

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. to appear in Functional Programming, 1991.

....fragments of our language. In particular we present results that essentially characterize the difference between operational equivalence and strong isomorphism in the presence of higher order objects. In the x7 we discuss additional related work. An abbreviated version of this paper appears as [20] We conclude this section with a summary of notational conventions. A glossary of notations can be found in the appendix. We use the usual notation for set membership and function application. Let Y; Y 0 ; Y 1 be sets. Y n is the set of sequences of elements of Y of length n. Y is the set of ....

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, volume 372 of Lecture Notes in Computer Science, pages 574--588. Springer-Verlag, 1989.

....e 0 ; e n . A unary cell is the analog of an ML reference. We define operations mk , get , set to represent the constructor, access, and update operations on unary cells. An operational semantics based on memory structures and a purely syntactic operational semantics for E are given in [11, 13]. We give a very brief outline of the syntactic semantics here, as it provides a natural basis for reasoning about program equivalence. Details may be found in [11, 13] Computation is a process of stepwise reduction of an expression to a canonical form. In order to define the reduction rules we ....

....unary cells. An operational semantics based on memory structures and a purely syntactic operational semantics for E are given in [11, 13] We give a very brief outline of the syntactic semantics here, as it provides a natural basis for reasoning about program equivalence. Details may be found in [11, 13]. Computation is a process of stepwise reduction of an expression to a canonical form. In order to define the reduction rules we introduce the notions of memory context, reduction context, and redex. Memory contexts describe memory states and are contexts, Gamma, of the form: letfz 1 : ....

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, 1989.

....program equivalence. Many examples of proving program equivalence can be found in Mason and Talcott [16, 14, 15, 18, 21, 20] Felleisen [7] and Felleisen and Hieb [9] develop a calculus for reasoning about programs with memory, function abstractions and control abstractions. Mason and Talcott [17, 19] develop the theory of operational 3 equivalence for programs with memory and function abstractions. More complete surveys of reasoning about programs with memory can be found in Mason [14, 13, 15] and Felleisen [7, 8] The remainder of this paper is organized as follows. In x2. we define our ....

....and hence that Sigma Gamma 0 ; M 0 0 [ u 0 ] Gamma 0 ; M 0 [ u 0 ] Consequently we can remove y from Dom(M 0 ) Repeating this we can transform M 0 and M 1 into the same modification. Hence Sigma e 0 e 1 . 4 7. Relating notions of equivalence and fragments In Mason and Talcott [17, 19] we presented a study of operational equivalence and strong isomorphism in the presence of function abstractions and mutable binary cells. The first order language presented in this paper can be thought of as a fragment of the higher order language. Since both operational equivalence and strong ....

[Article contains additional citation context not shown here]

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, volume 372 of Lecture Notes in Computer Science. Springer-Verlag, 1989.

....have based their work on the V calculus of Plotkin[15] instead of the pure calculus. It is inherent in their goal of reasoning about Scheme that their theories are not a conservative extension with respect to operational equivalence of either the classical calculus or of V . Mason and Talcott [11, 12] have also developed equational calculi with motivations similar to those of Felleisen et al. and with comparable results. Our work was influenced in part by the Imperative Lambda Calculus (ILC) of Swarup, Reddy and Ireland [18] Like var , ILC assumes call by name and models assignment by ....

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Automata, Languages, and Programming: 16th International Colloquium, Lecture Notes in Computer Science 372, pages 574--588. Springer-Verlag, 1989.

....if they cannot be distinguished by any program context. Operational equivalence enjoys many nice properties such as being a congruence relation on expressions. It subsumes the lambda v calculus [26] and the lambda c calculus [22] The theory of operational equivalence for mk is presented in [17, 18]. In [10] we began the development of the full logic of VTLoE, including general properties of contextual assertions and valid forms of class comprehension. In this setting induction principles for reasoning about programs can derived using minimal and maximal fixed points of class operators. ....

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, volume 372 of Lecture Notes in Computer Science, pages 574--588. Springer-Verlag, 1989.

No context found.

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. ICALP '89, pages 574--588. LNCS 372, Springer-Verlag, 1989.

No context found.

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. ICALP '89, pages 574--588. LNCS 372, Springer-Verlag, 1989.

No context found.

I. Mason and C. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proc. ICALP '89, pages 574--588. LNCS 372, Springer-Verlag, 1989.

No context found.

I. A. Mason and C. L. Talcott. Programming, transforming, and proving with function abstractions and memories. In Proceedings of the 16th EATCS Colloquium on Automata, Languages, and Programming, Stresa, volume 372 of Lecture Notes in Computer Science, pages 574--588. Springer-Verlag, 1989.

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