Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of their issues: ideally, first class continuations should exert zero overhead for programs that do not use them. Our goal and non goal: We formalize implementation strategies for first class continuations. We do not formalize first class continuations per se (cf. e.g. Felleisen s PhD thesis [12] or Duba, Harper, and MacQueen s formal account of call cc in ML [10] Our work: We consider abstract machines for continuation passing style (CPS) programs, focusing on the implementation of continuations. As a stepping stone, we formalize the folklore theorem that one register is enough to ....

Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

....a means of enforcing levels of abstraction [40] and as such is primarily concerned with the static structure and properties of programs. Matters of control are elegantly addressed using the method of continuations. The semantics of control operations may be concisely expressed using continuations [9, 36, 38, 42, 43]. Important control constructs such as co routines [21] and user level threads [5, 37] can be defined using primitives for reifying continuations. Conversion into continuationpassing style (CPS) is a useful compilation technique for higher order functional languages [3, 2, 23, 41] ....

....call by name strategy, but only a restricted language enjoys this property when interpreted under the ML like call by value strategy. The focus of our study is on the typing properties of CPS conversion of F# control, following the seminal work of Plotkin [36] extended by Felleisen, et al. [10, 9]) and Meyer and Wand [27] extended by Griffin [16] and Duba, et al. 8, 18] First, we isolate several continuation passing style sub languages of F# . The standard CPS language is the largest sub language of F# on which the by value and by name variants of the standard strategies coincide, ....

Matthias Felleisen. The Calculi of #v-CS Conversion: A Syntactic Theory of Control and State in Imperative HigherOrder Programming Languages. PhD thesis, Indiana University, Bloomington, IN, 1987.

....strings, and memory operations (assignment, reference, and dereference) here. In reality, we work on the complete core language of Standard ML. 2. 2 Operational semantics We de ne the semantics of expressions with a structural operational semantics [Plo81] using Felleisen s evaluation contexts [Fel87] In doing so, we need to extend the expressions to contain a set of values v and raised exceptions p that represent terminated computations: v : 1 unit j v exception value with argument v p : v raised exception The evaluation context C is de ned by C : hole j con C j ....

Matthias Felleisen. The Calculi of -v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

....The isomorphism has evolved with the invention of numerous typed calculi and corresponding natural deduction logics see [4, 28] Until the the late 1980 s, the Curry Howard isomorphism was concerned exclusively with constructive logics. At that time GriOEn [31] discovered that Felleisen s [22, 24] control operator C could be meaningfully added to the simply typed calculus by typing C with the double negation rule. The reduction rules for C are related to well known reductions on classical proofs [53, 62, 67] Moreover, GriOEn discovered that well known double negation embeddings of ....

M. Felleisen. The Calculi of v-CS Conversion: A Syntactic theory of Control and State in Imperative Higher Order programming Languages. PhD thesis, Indiana University, 1987.

....T. Gri#n [4] Because of our restricted reduction, we only have to define the law of reduction of c when it is in head position. This is: ctt 1 . t n # t.#x xt 1 . t n (x is a new # variable) This is a particular case of the rule of reduction for control operators given by M. Felleisen [1]. 1 These rules will be called rules of head c reduction. They are global rules, i.e. they apply only to the whole term. These rules are particularly interesting because of the following claim: the second order # calculus with head c reduction is a good model for imperative programming ....

....when c is in head position. Indeed, ordinary head reduction will stop only when c is in head position. The rule of reduction is: ctt 1 . t n # t.#x xt 1 . t n , where x is a new variable. Remark. This rule is a particular case of a general law of reduction for control operators, given in [1], which is: E[ct x] # t.#x E. But this general rule gives rise to problems with preservation of types under reduction, unless types are restricted to propositional calculus. Remark. An instruction like exit(P) of C programming language, which carries out the program P at the top level (by ....

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M. Felleisen. The Calculi of # v -CS conversion: a syntactic theory of control and state in imperative higher order programming. Ph. D. dissertation, Indiana University, 1987.

....E is called the continuation (or control context) of N at this point in the evaluation sequence. The notation of evaluation contexts allows, as we shall see below, a concise specification of the operational semantics of operators that manipulate continuations (indeed, this was its intended use [3, 2, 4, 1]) The programming language Scheme [16] contains call cc, a control construct that provides programs with direct access to a procedural abstraction representing the current continuation (the current control context) Felleisen et al. [3, 2, 4, 1] have presented an extension to ISWIM called ....

.... continuations (indeed, this was its intended use [3, 2, 4, 1] The programming language Scheme [16] contains call cc, a control construct that provides programs with direct access to a procedural abstraction representing the current continuation (the current control context) Felleisen et al. [3, 2, 4, 1] have presented an extension to ISWIM called Idealized Scheme 3 , or IS, which incorporates two constructs that manipulate control contexts. IS expressions are defined by extending the grammar of ISWIM as follows: N : Delta Delta Delta A(N ) j C(N ) The operators A and C are called, ....

M. Felleisen. The calculi of v -CS conversion: a syntactic theory of control and state in imperative higher-order programming languages. PhD thesis, Indiana University, 1987. Technical Report No. 226.

....raise expression, then the current handler function x:e 1 handles it: the v is bound to x in e 1 . Otherwise, the value of the handle expression is the value of e 0 . We define the formal semantics of DS terms with a structural operational semantics [Plo81] using Felleisen s evaluation contexts [Fel87] In doing so, we need to extend the expressions to contain a set of raised values t that are thrown from raise expressions: e : Delta Delta Delta j t. An evaluation context C is defined by the following grammar: C : j C e j (x: r) C j handle C x: e j raise C This context defines a ....

Matthias Felleisen. The Calculi of -v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

....as intuitionistic proofs with the axiom #X(X # X) give # terms with the constant c inside. Now, for such # terms, we extend the weak head reduction strategy with the following rule of reduction: ctt 1 . t n # (t)#x xt 1 . t n . This is a particular case of a rule given by Felleisen [1] for control operators. Indeed, this new instruction c allows to introduce in # terms, mechanisms of escape which are much used in real programming languages, particularly in order to handle errors. Examples of such instructions are Call cc in SCHEME, and setjmp, longjmp in the C language. The ....

M. Felleisen. The Calculi of # v -CS conversion: a syntactic theory of control and state in imperative higher order programming. Ph. D. dissertation, Indiana University, 1987.

....strings, and memory operations (assignment, reference, and dereference) here. In reality, we work on the complete core language of Standard ML. 2. 2 Operational semantics We define the semantics of expressions with a structural operational semantics [Plo81] using Felleisen s evaluation contexts [Fel87] In doing so, we need to extend the expressions to contain a set of values v and raised exceptions p that represent terminated computations: v : 1 unit j x: e function j fix f x: e recursive function j Delta v exception value with argument v p : Delta v raised exception The ....

Matthias Felleisen. The Calculi of -v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

....11] However, Martin Lof made earlier use of this approach is his highly influential constructive type theory [40, 41] Plotkin s study of two operational semantics for the untyped calculus [55] is fundamental to the field. It was subsequently extended by Felleisen, et al. in a number of papers [16, 19, 17, 18]. The definition of Standard ML constitutes an extensive experiment in programming language specification based on operational semantics [46, 45] The method of logical relations is fundamental to the study of the typed calculus, as emphasized by Friedman [23] Statman [64] and Plotkin [57] ....

Matthias Felleisen. The Calculi of v -CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, Bloomington, IN, 1987.

....for all n A Y : A 1 : o o A sub1 : o o A if0 : o o o o A is const : o o) o A error 1 : o A error 2 : o Figure 7.1 SPCF: Syntax 7.1.1 Operational Semantics Figure 7.2 presents the operational semantics. This presentation follows the style used in [Fel87] First, we present a scheme of rewriting rules. These rewriting rules transform one phrase into another. Later, we use these rewriting rules to provide an evaluation of the programs. According to the rewriting rules in Figure 7.2, the meaning of phrases in SPCF is the usual one, i.e. numerals ....

M. Felleisen. The Calculi of Lambda-v-CS-Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

.... These systems are two sorted theories of operations and classes initially developed for the formalization of constructive mathematics [12, 13] and later applied to the study of purely functional languages [14, 15] VTLoE builds upon recent advances in the semantics of languages with effects [16, 19, 28, 32, 33] and goes well beyond traditional programming logics, such as Hoare s logic [7] and Dynamic logic [22] by treating a richer language and expressing more properties. It is close in spirit to Specification Logic [49] and to Evaluation Logic [44] The underlying programming language of VTLoE, mk , ....

M. Felleisen. The Calculi of Lambda-v-cs Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

....and equivalence are congruence relations on expressions and hence closed under substitution and abstraction. Mason and Talcott in [39, 17, 18, 40] study operational approximation and equivalence for subsets of a language with function and control abstractions and objects with memory. Felleisen [8] defines reduction calculi extending the call by value lambda calculus to languages with control and assignment abstractions. These calculi are simplified and extended by Felleisen and Hieb in [9] Talcott, Mason, and Felleisen all apply their theories to expressing and proving properties of ....

....the language is extended to treat additional language constructs. However, simple reduction calculi are not adequate to prove many basic equivalences in languages with effects. For example, Felleisen found it is necessary to extend his reduction calculus by meta principles (cf. the safety rule [8], thm 5.27, p.149] Operational equivalence is, by definition, sensitive to the set of language constructs and basic data available. Using operational approximation we can express and prove properties such as non termination, computation induction and existence of least fixed points which cannot ....

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M. Felleisen. The Calculi of Lambda-v-cs Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

....a brief overview of both the object logic, VTLoE, and Isabelle. 1. 1 An Introduction to VTLoE VTLoE is a logic for reasoning about imperative functional programs, inspired by the variable type systems of Feferman [5, 6] VTLoE builds upon recent advances in the semantics of languages with effects [7, 9, 15, 18, 19] and goes well beyond traditional programming logics, such as Hoare s logic [2] and Dynamic logic [10] by treating a richer programming language and more expressive logical language. It is close in spirit to Specification Logic [29] and to Evaluation Logic [27] Proceedings of CATS 96 (Computing: ....

M. Felleisen. The Calculi of Lambda-v-cs Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. Ph.D. thesis, Indiana University, 1987.

....or the application of a primitive operation to a sequence of value expressions) Reduction contexts identify the subexpression of an expression that is to be evaluated next. They correspond to the left first, call by value reduction strategy of Plotkin [23] and were first introduced in [5]. R= ffflg app(R;E) app(V; R) Fm n 1 (V m ; R;E n ) R ranges over R. The crucial fact to note is that an arbitrary expression is either a value expression, or decomposes uniquely into a redex placed in a reduction context. We represent the state of memory using memory contexts. A memory ....

M. Felleisen. The Calculi of Lambda-v-cs Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

....studied the question informally in [Gri90] but found that the desired derived reduction rules did not generally hold. Both Griffin s and Murthy s work draw on the fundamental work of Felleisen and his co workers on calculi with control operators, which is conducted in an untyped setting e.g. [Fel87b]. Felleisen devised a control calculus, an extension of the calculus, and carried out what could aptly be called Plotkin s program (see [Plo75] for the study of the relation between calculi and programming languages (see also [Fel87b] Originally, the rules of the control calculus were split ....

.... operators, which is conducted in an untyped setting e.g. Fel87b] Felleisen devised a control calculus, an extension of the calculus, and carried out what could aptly be called Plotkin s program (see [Plo75] for the study of the relation between calculi and programming languages (see also [Fel87b]. Originally, the rules of the control calculus were split into so called reduction rules and computation rules. The former are completely compatible (applicable in any context) whereas the latter are restricted to the top level of a program, i.e. applicable in the empty context only. However, ....

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Matthias Felleisen, The Calculi of v -CS Conversion : A Syntactic Theory of Control and State in Imperative Higher Order Programming Languages. Ph.D. Thesis, Indiana University, 1987.

....abstractions and control abstractions. Mason and Talcott [9] give an alternative approach to treating programs with memory and function abstractions and develop the theory of operational equivalence for this case. More complete surveys of reasoning about programs with memory can be found in [5, 6, 7, 2, 3]. The remainder of this paper is organized as follows. We first define our language and its operational semantics. We then present the axioms and rules of the formal system. Following that we define memory models and semantic consequence and prove the soundness theorem. Finally we outline the ....

....contents of a cell and not the cell itself. However the loss of the beta rule poses a serious problem for reasoning about programs. This approach also violates the principle of separating the mechanism for binding from that of allocation of memory [12] Following the Scheme tradition, Felleisen [2] takes the Lisp approach to provide objects with memory. In order to obtain a reasonable calculus of programs, the programming language is extended to provide two sorts of lambda binding and an explicit dereferencing construct. There have been recent improvements in this calculus, but the problem ....

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Felleisen, M. The calculi of lambda-v-cs conversion: A syntactic theory of control and state in imperative higher-order programming languages, Ph.D. thesis, Indiana University. 1987

....As can be expected, higher order control operators are even more expressive than their first order counterparts. 1. 2 Prior motivating work The expressiveness of control operators comes at a cost they invalidate many of the familiar laws of reasoning that hold for functional languages [14]. As Meyer and Riecke observed, terms that once behaved identically now act very differently, suggesting that control operators are unreasonable [35] In technical terms, the operational equivalence relation that identifies interchangeable terms for a functional language is not a subset of the ....

M. Felleisen. The Calculi of Lambda-v-CS-Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

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Matthias Felleisen. The Calculi of Lambda-v-CS-Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, 1987.

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Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

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Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

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Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

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Matthias Felleisen. The Calculi of #-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987. 42

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Matthias Felleisen. The Calculi of l-v-CS Conversion: A Syntactic Theory of Control and State in Imperative HigherOrder Programming Languages. PhD thesis, Department of Computer Science, Indiana University, Bloomington, Indiana, August 1987.

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Matthias Felleisen. The Calculi of v -CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages. PhD thesis, Indiana University, Bloomington, IN, 1987. 18

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