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Total Functional Programming
 Journal of Universal Computer Science
, 2004
"... We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Chur ..."
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Cited by 31 (1 self)
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We now define the notion, already discussed, of an effectively calculable function of positive integers by identifying it with the notion of a recursive function of positive integers (or of a lambdadefinable function of positive integers). The phrase in parentheses refers to the apparatus which Church had developed to investigate this and other problems in the foundations of mathematics: the calculus of lambda conversion. Both the Thesis and the lambda calculus have been of seminal influence on the development of Computing Science. The main subject of this article is the lambda calculus but I will begin with a brief sketch of the emergence of the Thesis. The epistemological status of Church’s Thesis is not immediately clear from the above quotation and remains a matter of debate, as is explored in other papers of this volume. My own view, which I will state but not elaborate here, is that the thesis is empirical because it relies for its significance on a claim about what can be calculated by mechanisms. This becomes clearer in
Incremental Mature Garbage Collection
, 1993
"... Many programming languages provide automatic garbage collection to reduce the need for memory management related programming. However, traditional garbage collection techniques lead to long and unpredictable delays and are therefore not satisfactory in a number of settings, such as interactive syste ..."
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Many programming languages provide automatic garbage collection to reduce the need for memory management related programming. However, traditional garbage collection techniques lead to long and unpredictable delays and are therefore not satisfactory in a number of settings, such as interactive systems, where nondisruptive behavior is of paramount importance. Advanced techniques, such as generationbased collection, alleviate the problem somewhat by concentrating collection efforts on small but hopefully gainful areas of memory, the socalled young generations. This approach reduces the need for collecting the remaining large memory area, the old generation, but in no way obviates it. Traditionally, conventional techniques have been employed for old generation collection, leading to pauses which, although less frequent, are still highly disruptive. Recently, however, Hudson & Moss have introduced a new algorithm, the Train Algorithm, for performing efficient incremental collection of o...
On Arithmetical FirstOrder Theories allowing Encoding and Decoding of Lists
, 1998
"... In Computer Science, ntuples and lists are usual tools; we investigate both notions in the framework of firstorder logic within the set of nonnegative integers. Gödel had firstly shown that the objects which can be defined by primitive recursion schema, also can be defined at firstorder, using na ..."
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In Computer Science, ntuples and lists are usual tools; we investigate both notions in the framework of firstorder logic within the set of nonnegative integers. Gödel had firstly shown that the objects which can be defined by primitive recursion schema, also can be defined at firstorder, using natural order and some coding devices for lists. Secondly he had proved that this encoding can be defined from addition and multiplication. We show this can be also done with addition and a weaker predicate, namely the coprimeness predicate. The theory of integers equipped with a pairing function can be decidable or not. The theory of decoding of lists (under some natural condition) is always undecidable. We distinguish the notions encoding of ntuples and encoding of lists via some properties of decidabilityundecidability. At last, we prove it is possible in some structure to encode lists although neither addition nor multiplication are definable in this structure. Résumé On utilise couramment en informatique les nuplets et les listes sur un ensemble donné; nous étudions ces deux notions dans le cadre de la logique du premier ordre et pour l’ensemble des entiers naturels. Gödel a montré que les objets définis par un schéma de récurrence primitive sont définissables au premier ordre avec la relation d’ordre et le codage des listes, euxmêmes définissable avec l’addition et la multiplication; nous montrerons que ce codage peut également s’effectuer avec l’addition et un prédicat plus faible que la multiplication, à savoir la coprimarité. On montre aussi que les notions de nuplets et de listes se distinguent par des arguments de décidabilitéindécidabilité. La théorie des entiers munis d’une fonction de couplage peutêtreou non décidable. Par contre la théorie du décodage des listes, soumise à une certaine condition naturelle, est toujours indécidable. On montre enfin qu’il existe des structures dans lesquelles on peut coder les listes sans pour autant que l’addition (et donc l’ordre) et la multiplication ne soient définissables.