Jean Vuillemin. Correct and optimal implementations of recursion in a simple programming language. Journal of Computer and System Sciences, 9(3):332--354, 1974.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....each signature to the full class of standard algebras. mapping each signature to the class of standard algebras where all functions except if Gamma then Gamma else are strict. 15 3. The operator mapping each signature to the class of standard algebras where all functions are sequential ([Vui74]) On the other hand the operator TG mentioned above is not of great interest in this framework, since we do not want to require that all functions of an algebra are explicitelly listed in the parameter part of a module. For instance we could define a module list of elements that we want to ....

Jean Vuillemin. Correct and optimal implementations of recursion in a simple programming language. Journal of Computer and System Sciences, 9:332--354, 1974.

.... simultaneously, the leftmost outermost rule says that from all calls which do not occur as arguments of other calls only the leftmost one has to be replaced, and the leftmost innermost rule says that from all calls which are free from other calls only the leftmost one has to be replaced; see e.g. [4]. If patterns are allowed in routine declarations, then the computation rules are a little bit more complicated. Simpli cation executes operations of the pre de ned datatypes and evaluates conditionals. Operational semantics de ned in the just sketched manner executes a functional program by ....

....system. Although the detailed appearance of its windows depends on resources de ned in two con guration les, when working with it the screen typically looks as in Figure 2. The tree depicted in the tree window of this picture represents an expression which may occur when the call list2stree([7,2,8,1,4,5,2,3,5,8,1,9]) is evaluated. From the user s point of view, roughly spoken the KIEL system consists of two main components. The rst main component is the workspace. It holds a program of the system s programming language and the expressions to be evaluated. Programs are loaded into the system from an ....

Vuillemin J.: Correct and optimal implementation of recursion in a simple programming language. Journal of Computer and System Sciences 9, 332-354 (1974)

....function f such that f( x) whenever x i = for some i. It follows from ordinary recursion theory that a strict function is computable i it is recursive. 3 Monotone functions In [Sazonov75] it is proved that a monotone function is PCF computable i it is an e ectively sequential function [Vuillemin75]. In [Trakhtenbrot76] it is shown that the e ectively sequential functions are precisely those de nable from computable strict functions and if by composition. Since computable strict functions are recursive we have: 3 Theorem 1 (Sazonov, Trakhtenbrot) A monotone function is PCFde nable i ....

Vuillemin, J., Correct and optimal implementations of recursion in a simple programming language, Journal of Computer and System Science 9 (1975), 332-354 9

....program analysis (for example, strictness analysis) so that the needless work inherent in normal order evaluation might somehow be controlled. Such optimal and correct implementations were known for recursion schemas, but not ones where higherorder functions could be passed as rst class values [Vui74]. In elaborating his notion of optimal reduction, L evy introduced a labelled variant of calculus where all subterms of an expression are annotated with labels that Supported by CONFER. y Supported by ONR Grant N00014 93 1 1015, NSF Grant CCR 9619638, and the Tyson Foundation. 1 code the ....

Jean Vuillemin. Correct and optimal implementation of recursion in a simple programming language. J. Computer and System Sciences 9:3, pp. 332-354.

.... , affects the semantics. However, the transformation is not intended for comparing cbv and cbn parameter passing and giving a uniform semantic framework. 1. 4 Starting Points The denotational semantics we define is a fixed point semantics like those for recursive applicative program schemes ([32, 33, 23, 10, 4, 12, 7]) While the concept of a base datatype is central to this field, viewing the semantics of a whole program as a data type is inspired by algebraic specifications ( 35] We define reduction semantics as operational semantics, but due to pattern matching we cannot use the simple reduction semantics ....

....not even that unusual. The first one is more closely related to the cbn semantics of recursive applicative program schemes than our cbn semantics. In the theory of recursive applicative program schemes cbn refers just to the evaluation of function operations. The major part of the literature ([32, 21, 23, 10, 20]) considers only flatly ordered base data types (interpretations) because the flat order permits simpler proofs. The second mixture has even been implemented in versions of the functional programming language Hope ( 11] thereby combining the expressiveness of infinite data structures with the ....

J. Vuillemin. Correct and optimal implementations of recursion in a simple programming language. Journal of Computer and System Sciences, 9:332--354, 1974.

....the full class of standard algebras. 2. The operator = strict mapping each signature to the class of standard algebras where all functions except if Gamma then Gamma else are strict. 3. The operator mapping each signature to the class of standard algebras where all functions are sequential ([Vui74]) On the other hand the operator TG mentioned above is not of great interest in this framework, since we do not want to require that all functions of an algebra are explicitelly listed in the parameter part of a module. For instance we could define a module list of elements that we want to ....

Jean Vuillemin. Correct and optimal implementations of recursion in a simple programming language. Journal of Computer and System Sciences, 9:332--354, 1974.

....power to help with still relevant tasks. 4. Time and Space Lazy evaluation [9] call by name) using evaluate once thunks is an optimal strategy for evaluating applicative expressions on a single processor, in the sense that the minumum number of reductions (procedure calls) are made [17,3]. However, when more than one processor is available to evaluate the expression, it is not clear what strategy would be optimal. If nothing is known about the particular expression being evaluated, we conjecture that any reasonable strategy must allocate one processor to lazy evaluation, with the ....

Vuillemin, Jean. "Correct and Optimal Implementations of Recursion in a Simple Programming Language". JCSS 9 (1974), 332-354.

....from rule is not terminating, thus improving termination as in lazy reduction strategies. In fact, termination of ## for this TRS can be formally established (see below) 3.3. 3 Safe Computations The concept of safe computation is the operational counterpart of the semantic concept of strictness [Lal93, Vui74]. Given a Scott domain 3 D, a function f : D k # D is strict in the i th argument if f(x 1 , x i 1 , #, x k ) #. By interpreting (as usual) the bottom element of a domain as a nonterminating computation, the strictness information can be used to define a computation ....

J. Vuillemin. Correct and optimal implementation of recursion in a simple programming language.<F5.483e+05> Journal of Computer and System<F5.359e+05> Sciences, 9(3):332--354, 1974.

....analysis (for example, strictness analysis) so that the needless work inherent in normal order evaluation might somehow be controlled. Such optimal and correct implementations were known for recursion schemas, but not ones where higherorder functions could be passed as first class values [Vui74]. In elaborating his notion of optimal reduction, L evy introduced a labelled variant of calculus where all subterms of an expression are annotated with labels that Supported by CONFER. y Supported by ONR Grant N00014 93 1 1015, NSF Grant CCR 9619638, and the Tyson Foundation. code the ....

Jean Vuillemin. Correct and optimal implementation of recursion in a simple programming language. J. Computer and System Sciences 9:3, pp. 332-354.

....answer under lazy evaluation, since lazy evaluation will certainly introduce sufficient delays to insure that the delayed expressions are executable. In fact, if there is any evaluation order which will produce an answer from a program, lazy evaluation will also produce an answer to that program [42]. Laziness grants an additional flexibility to the programmer: the ability to create and manipulate infinite data structures. A well known example in literature is the sieve of Eratosthenes for finding prime numbers [15] The program works by defining an infinite list of integers, and using this ....

J. Vuillemin. Correct and optimal implementation of recursion in a simple programming language. Journal of Computer and System Sciences, 9(3):332-354, Dec 1974.

No context found.

Jean Vuillemin. Correct and optimal implementations of recursion in a simple programming language. Journal of Computer and System Sciences, 9(3):332--354, 1974.

No context found.

Jean Vuillemin, Correct and Optimal Implementations of Recursion in a Simple Programming Language, JCSS, Vol. 9, No. 3, pp. 322-354, 1974.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC