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12
evolution and application of functional programming languages
 ACM Computing surveys
, 1989
"... The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda ’ ..."
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The foundations of functional programming languages are examined from both historical and technical perspectives. Their evolution is traced through several critical periods: early work on lambda calculus and combinatory calculus, Lisp, Iswim, FP, ML, and modern functional languages such as Miranda ’ and Haskell. The fundamental premises on which the functional programming methodology stands are critically analyzed with respect to philosophical, theoretical, and pragmatic concerns. Particular attention is paid to the main features that characterize modern functional languages: higherorder functions, lazy evaluation, equations and pattern matching, strong static typing and type inference, and data abstraction. In addition, current research areassuch as parallelism, nondeterminism, input/output, and stateoriented computationsare examined with the goal of predicting the future development and application of functional languages.
Artificial Intelligence and Literary Creativity: Inside the Mind of BRUTUS, a Storytelling Machine
"... Professor Hart, and Hart had often saidto others and to himselfthat he was honored to help Dave secure his wellearned dream. Well before the defense, Striver gave Hart a penultimate copy of his thesis. Hart read it and told Dave that it was absolutely firstrate, and that he would gladly sig ..."
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Cited by 42 (16 self)
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Professor Hart, and Hart had often saidto others and to himselfthat he was honored to help Dave secure his wellearned dream. Well before the defense, Striver gave Hart a penultimate copy of his thesis. Hart read it and told Dave that it was absolutely firstrate, and that he would gladly sign it at the defense. They even shook hands in Hart's booklined office. Dave noticed that Hart's eyes were bright and trustful, and his bearing paternal. At the defense, Dave thought that he eloquently summarized Chapter 3 of his dissertation. There were two quest2ons, one from Professor Rodman and one from Dr. Teer; Dave answered both, apparently to everyone's satisfaction. There were no further objections. Professor Rodman signed. He slid the tome to Teer; she too signed, and then slid it in front of Hart. Hart didn't move. "Ed?" Rodman said. Hart still sat motionless. Dave felt slightly dizzy. "Edward, are you going to sign?" Later, Hart sat alone in his office, in his big leather
A Modal Herbrand Theorem
, 1996
"... We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of firstorder modal logic  we use the device of predicate abstraction, something that has ..."
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Cited by 7 (3 self)
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We state and prove a modal Herbrand theorem that is, we believe, a more natural analog of the classical version than has appeared before. The statement itself requires the enlargement of the usual machinery of firstorder modal logic  we use the device of predicate abstraction, something that has been considered elsewhere as well. This expands the expressive power of modal logic in a natural way. Our proof of the modal version of Herbrand's theorem uses a tableau system that takes predicate abstraction into account. It is somewhat simpler than other systems for the same purpose that have previously appeared. 1 Introduction In classical logic, Herbrand's famous theorem of 1930 plays many roles. Herbrand seems to have thought of it as something like a constructive completeness theorem [12, 13]. Robinson cited it as the foundation of automated theorem proving [15]. It has been applied to derive results on decidability [3]. But despite its fundamental nature, it has remained remarkably...
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
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Cited by 4 (2 self)
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Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection ” to his view that machines can think. Logicomathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do. Key words: artificial intelligence, ChurchTuring thesis, computability, effective procedure, incompleteness, machine, mathematical objection, ordinal logics, Turing, undecidability The ‘skin of an onion ’ analogy is also helpful. In considering the functions of the mind or the brain we find certain operations which we can express in purely mechanical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains, we find a further skin to be stripped off, and so on. Proceeding in this way, do we ever come to the ‘real ’ mind, or do we eventually come to the skin which has nothing in it? In the latter case, the whole mind is mechanical (Turing, 1950, p. 454–455). 1.
What does it mean to say that logic is formal?
, 2000
"... Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and ..."
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topicneutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this
Categories, structures, and the fregehilbert controversy: The status of metamathematics
 Philosophia Mathematica, 13:61–77. Pagenumbers in
, 2005
"... There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I th ..."
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There is a parallel between the debate between Gottlob Frege and David Hilbert at the turn of the twentieth century and at least some aspects of the current controversy over whether category theory provides the proper framework for structuralism in the philosophy of mathematics. The main issue, I think, concerns the place and interpretation of metamathematics in an algebraic or structuralist approach to mathematics. Can metamathematics itself be understood in algebraic or structural terms? Or is it an exception to the slogan that mathematics is the science of structure? The slogan of structuralism is that mathematics is the science of structure. Rather than focusing on the nature of individual mathematical objects, such as natural numbers, the structuralist contends that the subject matter of arithmetic, for example, is the structure of any collection of objects that has a designated, initial object and a successor relation that satisfies the induction principle. In the contemporary scene, Paul Benacerraf’s classic
History of Constructivism in the 20th Century
"... notions, such as `constructive proof', `arbitrary numbertheoretic function ' are rejected. Statements involving quantifiers are finitistically interpreted in terms of quantifierfree statements. Thus an existential statement 9xAx is regarded as a partial communication, to be supplemented by providi ..."
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notions, such as `constructive proof', `arbitrary numbertheoretic function ' are rejected. Statements involving quantifiers are finitistically interpreted in terms of quantifierfree statements. Thus an existential statement 9xAx is regarded as a partial communication, to be supplemented by providing an x which satisfies A. Establishing :8xAx finitistically means: providing a particular x such that Ax is false. In this century, T. Skolem 4 was the first to contribute substantially to finitist 4 Thoralf Skolem 18871963 History of constructivism in the 20th century 3 mathematics; he showed that a fair part of arithmetic could be developed in a calculus without bound variables, and with induction over quantifierfree expressions only. Introduction of functions by primitive recursion is freely allowed (Skolem 1923). Skolem does not present his results in a formal context, nor does he try to delimit precisely the extent of finitist reasoning. Since the idea of finitist reasoning ...
Reflections On Formalism And Reductionism In Logic And Computer Science
"... This report contains a preprint (paper 1) and a reprint (paper 2). The first develops some epistemological views which were hinted in the second, in particular by stressing the need of a greater role of geometric insight and images in foundational studies and in approaches to cognition. The second p ..."
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This report contains a preprint (paper 1) and a reprint (paper 2). The first develops some epistemological views which were hinted in the second, in particular by stressing the need of a greater role of geometric insight and images in foundational studies and in approaches to cognition. The second paper is the "philosophical" part of a lecture in Type Theory, whose technical sections, omitted here, have been largely subsumed by subsequent publications (see references). The part reprinted below discusses more closely some historical remarks recalled in paper 1. 1. Reflections on formalism and reductionism in Logic and Computer Science (pp. 1  9)
Sentences, 92
"... al nets, 26, 31, 3638, 52 neuroscience, 58 Noel, R., xiii O'Connell, R., xi OSCAR, 6 Papadias, D., 59 paragraph grammar, 194 Peck, M., 101 Piaget, J., 60 pictorial reasoning, 34 pictorial representation, 34 pictorialism, 46 Pinker, S., 59 Plato, xviii plot generation, 191 Poirot,H., ..."
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al nets, 26, 31, 3638, 52 neuroscience, 58 Noel, R., xiii O'Connell, R., xi OSCAR, 6 Papadias, D., 59 paragraph grammar, 194 Peck, M., 101 Piaget, J., 60 pictorial reasoning, 34 pictorial representation, 34 pictorialism, 46 Pinker, S., 59 Plato, xviii plot generation, 191 Poirot,H.,147 Pollock, J., 6 Poltrino,T.,xii Porush, D., xii proactive behavior, 179, 191 process level, 165 production rules, 173 Propp, V., 154 Psotka, J., 50 Racter, 22 Rapaport, W., 76 reactive behavior, 178, 191 reader response theory, xiii register machines, 38 ROALD, 151 robots, xvi, xvii, 6, 7, 21, 34, 57, 63 housecleaning, xviii Sancho Panza, 92 scenario, 194 Schwartz,D.,56 Searle, J., 53, 55, 68 selfreference familiar reference, 188 Ferrucci, D., xi, 10 Fetzer, J., xiv fiction belletristic, xii, xv, xxiv, 152 Fleming, I., 157, 159 FLEX, 170 Ford , K . , x i v Fort i er, S., 56 free will, xii Freud, S., xv Fuentes , C . , 64 Funt , B . , 61 Galbraith, M.,