scholarly journals Using the General Intensional Programming System (GIPSY) for Evaluation of Higher-Order Intensional Logic (HOIL) Expressions

2010 ◽  
Author(s):  
Serguei A. Mokhov ◽  
Joey Paquet
Keyword(s):  
Higher Order ◽  
Intensional Logic ◽  
Programming System ◽  
Intensional Programming

Intensionality

1995 ◽  
Author(s):  
E. A. Ashcroft ◽  
A. A. Faustini ◽  
R. Jaggannathan ◽  
W. W. Wadge
Keyword(s):  
Programming Languages ◽  
Large Scale ◽  
Possible Worlds ◽  
Second Generation ◽  
Formal System ◽  
Intensional Logic ◽  
Declarative Languages ◽  
Computer Scientists ◽  
Intensional Programming ◽  
Large Scale Integration

The intensional programming language, Lucid, described in Chapter 1 is based directly on intensional logic, a family of mathematical formal systems that permit expressions whose value depends on hidden contexts or indices. Our use of intensional logic is one in which the hidden contexts or indices are integers or tuples of integers. Intensional logic, as used to give semantics to natural language, uses a much more general notion of context or index. Of course, intensional logic is hardly the first example of a formal system of interest to both logicians and computer scientists. The language LISP (invented by McCarthy and others in the early sixties [34]) was originally intended to be an adaptation of the lambda calculus, although it diverged in its treatment of variable-binding and higher-order functions. Shortly after, however, Landin produced ISWIM, the first true functional language [30]. These “logical” programming languages such as ISWIM are in many respects vastly superior to the more conventional ones. They are much simpler and better defined and yet at the same time more regular and more powerful. These languages are notationally closer to ordinary mathematics and are much more problem-oriented. Finally, programs are still expressions in a formal system, and are still subject to the rules of the formal system. It is therefore much easier to reason formally about their correctness, or to apply meaningpreserving transformations. With these languages, programming really is a respectable branch of applied mathematical logic. These logic-based (or declarative) languages at first proved difficult to implement efficiently, and interest in declarative languages declined soon after the promising initial work of McCarthy and Landin. Fortunately, the advent of large scale integration and new compiling technology reawakened interest in declarative languages, and brought about a series of new “second generation” declarative languages, such as Prolog [12] and Miranda [44]. Lucid itself was one of these second generation declarative languages. Lucid is based not so much on classical logical systems as on the possible worlds approach to intensional logic—itself a relatively new branch of logic [43] which reached maturity during the period (1965-75) in which declarative programming languages were in eclipse.

scholarly journals Higher-order functional languages and intensional logic

1999 ◽  
Vol 9 (5) ◽  
pp. 527-564 ◽  
Author(s):  
P. RONDOGIANNIS ◽  
W. W. WADGE
Keyword(s):  
Broad Class ◽  
Higher Order ◽  
Final Outcome ◽  
Intensional Logic ◽  
New Technique ◽  
Functional Languages ◽  
Order Zero ◽  
Functional Program ◽  
Source Program ◽  
Context Manipulation

In this paper we demonstrate that a broad class of higher-order functional programs can be transformed into semantically equivalent multidimensional intensional programs that contain only nullary variable definitions. The proposed algorithm systematically eliminates user-defined functions from the source program, by appropriately introducing context manipulation (i.e. intensional) operators. The transformation takes place in M steps, where M is the order of the initial functional program. During each step the order of the program is reduced by one, and the final outcome of the algorithm is an M-dimensional intensional program of order zero. As the resulting intensional code can be executed in a purely tagged-dataflow way, the proposed approach offers a promising new technique for the implementation of higher-order functional languages.

Multidimensional Programming

1995 ◽  
Author(s):  
E. A. Ashcroft ◽  
A. A. Faustini ◽  
R. Jaggannathan ◽  
W. W. Wadge
Keyword(s):  
Formal System ◽  
Visual Programming ◽  
Intensional Logic ◽  
Software Systems ◽  
Programming System ◽  
Natural Languages ◽  
The Past ◽  
Advanced Students ◽  
Multidimensional Programming ◽  
Multidimensional Objects

This book describes a powerful language for multidimensional declarative programming called Lucid. Lucid has evolved considerably in the past ten years. The main catalyst for this metamorphosis was the discovery that Lucid is based on intensional logic, one commonly used in studying natural languages. Intensionality, and more specifically indexicality, has enabled Lucid to implicitly express multidimensional objects that change, a fundamental capability with several consequences which are explored in this book. The author covers a broad range of topics, from foundations to applications, and from implementations to implications. The role of intensional logic in Lucid as well as its consequences for programming in general is discussed. The syntax and mathematical semantics of the language are given and its ability to be used as a formal system for transformation and verification is presented. The use of Lucid in both multidimensional applications programming and software systems construction (such as a parallel programming system and a visual programming system) is described. A novel model of multidimensional computation--education--is described along with its serendipitous practical benefits for harnessing parallelism and tolerating faults. As the only volume that reflects the advances over the past decade, this work will be of great interest to researchers and advanced students involved with declarative language systems and programming.

Other Uses of Intensionality

1995 ◽  
Author(s):  
E. A. Ashcroft ◽  
A. A. Faustini ◽  
R. Jaggannathan ◽  
W. W. Wadge
Keyword(s):  
Intensional Logic ◽  
Creation Myth ◽  
Intensional Programming

In Chapter 2 we presented what is essentially a creation myth of intensional programming—that far-sighted researchers studied intensional logic and then applied this knowledge by designing a language that embodied intensional principles. In fact, the whole project grew out of a more modest attempt to make fairly conventional Pascal-style programming mathematically acceptable. Indexed sequences were originally added so that programs which, in Pascal, used for-loops and reassignment, could be rewritten as equations involving temporal operators.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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