lambda calculus

Recently more idle, intend to tidy up the previous study on the language of the program knowledge. The main content is to design the program language while writing the interpreter to implement it. This knowledge is essentially derived from programming Languages and Lambda calculi and essentials of programming Languages these two books. I remember the high School Olympiad training when the teacher said: "To solve problems must grasp the definition." "

1. g9yuanyon's blog: translated a series of lambda calculus articles, which are very popular and part of gossip. There are also a small amount of supplementary information for the original. Http://blog.csdn.net/g9yuayon/article/details/7909532. markcc 'blog good math bad math: Here there is the original G9 translation article, the next few G9 no translation, but very enlightening Http://goodmath.blogspot.c

language"? The problem is the so-called "entscheidungsproblem,decision" (problem). The study of this problem eventually led to the birth of theoretical computer science: Alonzo Chuchi and Alan Turing in their respective ways to answer the question in a negative way. In the study of this problem, they first studied the intuitive concept of "decidable" and gave a formal definition and explanation, further putting the problem into a "computable" (computable) problem, and finally defining it as "co

: Z≡λx.xf¬f If it works on 0, it will unfold as follows: Z0≡0f¬f≡ (ΛSZ.Z) (f¬) f≡¬f≡t If the function is on a positive integer n, it expands to the following (2 for example): Z2≡2f¬f≡ (Λsz.s (S (z))) (f¬) F≡f (F (¬))) f≡faf≡fA≡f (¬) As the example shows, no matter how many F (f (f ()) are nested internally, the returned result is F, because it is all in the form of FAF.After that, you can define a comparison function. Before you do this, you need to defi

This one is connected to the back of the first lambda calculus. Tell me something about maths. Often something that seems easy to understand, once described correctly, becomes extremely troublesome. In software engineering, there is a similar situation: 20% of the code to achieve the core functionality, leaving 80% of the code to deal with the boundary situation. As a result, most of the text in the so-cal

Y Combo: \f. (\x.f (XX)) (\x.f (XX)), accepts a function, returns a higher order functionThe y combination is used to generate anonymous recursive functions.What is anonymous recursive function, consider the following C language recursive functionint sum (int n) { return n = = 0? 0:n + sum (n-1);}This function calls itself recursively, calling itself the name of the function body, which is called Sum,sum internal with the name sum, recursive calls to their ownIn

x in T1 is replaced with T2.Example: (λx.x) y→y(λx.x (λx.x)) (u r) →u R (λx.x)"Because the abstract body:x (λx.x) on the left, only the first X is free. 】The term is called redex("reducible expression"), and the above rule overrides a redex, called Beta-reduction.Third, the Lambda-calculus evaluation strategy:1.full Beta-reduction:any Redex is reduced at any time.2.normal Order strategy: The leftmost and m

on point spectrumThe establishment of Banach algebraic symbolic calculus is derived from three heuristic points, one is the establishment of the vector value integral, the other is the whole pure function theory, especially the Cauchy integral formula. The third is the wide existence of strong all-pure B-valued function in Banach algebra. The foundation of the establishment is the perfect spectrum theory.Let's start with a brief discussion of vector-

1. Differential Application 1.1 Differential 1.1.1 monotonicity, extremum and asymptote of unary functionThe derivative gives the direction of the function, which is very useful for the graphical properties of our analytic functions, and here we use the knowledge of calculus to understand the nature of the function. The effect of the first derivative on the function is the most direct one, where first-order derivative is seen. For the constant functio

Calculus learning turning? It's a strange story. In fact, Calculus, like a car, turns slowly. In November 11, 1675, German mathematician Leibniz wrote the points and differential symbols in his notebook: Attention and D. This was the beginning of calculus. He insisted that differential dx is an infinitely small number (infinitesimal), So he developed paradoxing p

The mean value theorem for definite integrals:The definition of the integral itself is simple, but in the teaching process people often remember only its calculation method, in the introduction of the concept of integral, often it is tightly tied to the calculation method, in fact, in the simple definition of integrals, the basic theorem of calculus tells us the calculation method of integral.Basic theorem of calculus:Can see, it is based on such a ba

Original article link "If people don't believe in the simplicity of mathematics, they just don't realize the complexity of life ." -- Johnvon norann Dec mainly discusses extra points in discrete situations, which are used in the computer field. We know that it is impossible to use a computer to process geometric images completely smooth (the computer is a discretization world consisting of 0 and 1 ), the concept of Dec also provides us with a better tool to portray discrete ry. For example,

JAVA 8 Lambda Expressions-Lambda Expressions, lambda-lambdaLambda expressions Lambda expressions are defined in java standard proposal JSR 335. Java 8 introduces Lambda expressions and is considered to be the biggest new feature of Java 8.

Document directory 2.1 variables and functions 2.2 functions and Calculus 2.3 limit and Calculus 3.1 micro-Learning 3.2 points 5.1 law of opposites 5.2 examples of corresponding points Now we have started a round of postgraduate mathematics review, using the sixth edition of Tongji higher mathematics. For postgraduate entrance exams, it is a good teaching material, and all the knowledge points a

Learn the big map/aerial view of functional programming and give the scheme code before you have mastered the various language details of scheme. This means that we do not need to read the source code, but the introduction here as a follow-up study of the large map, so that they know where the body;At the beginning of 1930s, Alonzo Church,1903-1995 , a Arenzo Chuchi at Princeton University, developed a new form system (formal system), lambda Operatio

In 1960 Abraham Robinson (1918-1974) solved the three hundred year old problem of giving a rigorous development of the calculus based on infinitesimals. Robinson's achievement was oneThe major mathematical advances of the twentieth century. This is an exposition of Robinson's Infinitesimal calculus at the advanced undergraduate level. It is entirely self-contained but is Keyed to the 2000 digital edition of

When it comes to calculus, everyone is unfamiliar, and people who go to college are basically the ones who have been on it, and countless people are hanging on that tall tree every semester ... Liberal arts students in the "University of Mathematics" in the look of its face, engineering students in the "higher mathematics" and it met, and science students in the "mathematical analysis" see its true colors. But to tell the truth, compared with other ab

It seems to us that calculus is called "decentralization" in secondary school, but in the Russian context it is necessary, not "decentralized", to teach calculus at the secondary level. This is why. Let's get things straight, and we can't just talk. According to the research of the School of Mathematics Science of Beijing Normal University, the course of "algebra and Mathematical Analysis preliminary" in 10

Looking back, in 1908, calculus (also known as "micro-accumulation") was introduced into China. At the beginning, only a few people in China knew about calculus. After liberation, especially after the proposal of "entering science" in 1956, China began to learn about the Soviet Union in an all-round way. At that time, the Soviet scholar fekhincz wrote the "calculus