• Journal for History of Mathematics
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• v.17 no.4
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• pp.45-64
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• 2004

The lambda calculus is a mathematical formalism in which functions can be formed, combined and used for computation that is defined as rewriting rules. With the development of the computer science, many programming languages have been based on the lambda calculus (LISP, CAML, MIRANDA) which provides simple and clear views of computation. Furthermore, thanks to the "Curry-Howard correspondence", it is possible to establish correspondence between proofs and computer programming. The purpose of this article is to make available, for didactic purposes, a subject matter that is not well-known to the general public. The impact of the lambda calculus in logic and computer science still remains as an area of further investigation.stigation.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.45-56
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• 2010

Sequent Calculus is a symmetrical version of the Natural Deduction which Gentzen restructured in 1934, where he presents 'Hauptsatz'. In this thesis, we will examine why the Cut-Elimination Theorem has such an important status in Proof Theory despite of the efficiency of the Cut Rule. Subsequently, the dynamic side of Curry-Howard correspondence which interprets the system of Natural Deduction as 'Simply typed $\lambda$-calculus', so to speak the correspondence of Cut-Elimination and $\beta$-reduction in $\lambda$-calculus, will also be studied. The importance of this correspondence lies in matching the world of program and the world of mathematical proof. Also it guarantees the accuracy of program.

• The Transactions of the Korea Information Processing Society
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• v.7 no.9
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• pp.2807-2814
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• 2000

In this paper, we suggest a visual language supporting collaboration with functional attributes. The visual language is a set of visual sentences that consist of object icons and operators. The object icon is a user who participates in collaboration. And, the operator means interactive relations between users according to a point of collaborative time. The functional attributes that support various computing orders provide flexibility of interactive relations on collaboration. Also, using representation both synchronous and asynchronous relations in collaboration, the visual language supports efficiently collaboration than conventional visual languages. And, functional attributes of visual sentences are analyzed using $\lambda$ expressions.

• Korean Journal of Logic
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• v.6 no.2
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• pp.49-67
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• 2003

조합논리는 기본적으로 정해진 해석이 없는 순수한 형태만을 가지고 추상적으로 연산하는 관점에 관한 논리로서, 논리학을 기호학적 관점에서 볼 수 있는 토대를 제공해 준다. 조합논리의 특징은 연산자가 피연산자도 될 수 있다는 사실에 있으며 그래서 동일한 연산자가 그 자신의 피연산자도 될 수 있다. 이 논문에서 우리는 기본연산자들의 직관적 개념과 형식적 개념을 소개하고 연산자 대수에 내해 검토하고 나서 조합논리와 $\lambda$-연산의 번역가능성에 다해 알아보겠다. 조합논리에 유형의 개념을 추가하면 자연언어 분석에서 아주 효율적인데 기본유형인 대상자 명제 이외의 어떤 요소라도 함수자로 나타낼 수 있는데 이들은 조합자의 특수한 경우로서 파생유형들이다.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.8
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• pp.11-19
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• 1994

The matching probability P(ο/$\lambda$), of the signal sequence(ο) observed for a finite time interval with a HMM (Hidden Markov Model $\lambda$) indicates the probability that signal comes from the given model. By utilizing the fact that the probability represents matching score of the observed signal with the model we can recognize an unknown signal pattern by comparing the magnitudes of the matching probabilities with respect to the known models. Because the algorithm however uses floating point variables during the computing process hardware implementation of the algorithm requires floating point units. This paper proposes an integer algorithm which uses positive integer numbers rather than float point ones to compute the matching probability so that we can economically realize the algorithm into hardware. The algorithm makes the model parameters integer numbers by multiplying positive constants and prevents from divergence of data through the normalization of variables at each step. The final equation of matching probability is composed of constant terms and a variable term which contains logarithm operations. A scheme to make the log conversion table smaller is also presented. To analyze the qualitive characteristics of the proposed algorithm we attatch simulation result performed on two groups of 10 hypothetic models respectively and inspect the statistical properties with repect to the model order the magnitude of scaling constants and the effect of the observation length.

• The Journal of the Korea institute of electronic communication sciences
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• v.19 no.2
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• pp.335-343
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• 2024

Real-time target signal processing techniques for FMCW LiDAR are described in this paper. FMCW LiDAR is gaining attention as the next-generation LiDAR for self-driving cars because of its detection robustness even in adverse environmental conditions such as rain, snow and fog etc. in addition to its long range measurement capability. The hardware architecture which is required for high-speed data acquisition, data transfer, and parallel signal processing for frequency-domain signal processing is described in this article. Fourier transformation of the acquired time-domain signal is implemented on FPGA in real time. The paper also details the C-FAR algorithm for ensuring robust target detection from the transformed target spectrum. This paper elaborates on enhancing frequency measurement resolution from the target spectrum and converting them into range and velocity data. The 3D image was generated and displayed using the 2D scanner position and target distance data. Real-time target signal processing and high-resolution image acquisition capability of FMCW LiDAR by using the proposed parallel signal processing algorithms based on FPGA architecture are verified in this paper.

• Korean Journal of Optics and Photonics
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• v.8 no.3
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• pp.189-193
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• 1997

Aspheric pick-up lenses are increasingly used in consumer products such as computer and multimedia, as their mass production has become possible owing to the injection molding process. However still much work needs to be done for more effective manufacture of aspheric lenses, one area of which is the in-line inspection of produced lenses. In this paper, we present a lateral-shearing interferometer that has specially been designed to have a high immunity to external vibration and atmospheric disturbance. The interferometer comprises four prisms. They are directly attached to each other using an immersion oil so that relative sliding motions between the prisms are allowed. Their relative displacement can readily generate necessary lateral-shearing and phase-shifting to determine the wavefront of the beam collimated by the lens under inspection. A special phase-measuring algorithm of arbitrary-bucket is adopted to compensate the phase-shifting error caused by the thickness reduction in the immersion oil. Zernike polynomial fitting has done for determinating quantitative aberration of aspheric pick-up lenses. The interferometer built in this work is robust to external mechanical vibration and atmospheric disturbance so that experimental results show that it has a repeatability of less than λ/100.