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CHAPTER 4. FORMAL DESCRIPTION OF LANGUAGE use .net vs 2010 ecc200 drawer tomake data matrix ecc200 on .net USD-8 streams through an op 2d Data Matrix barcode for .NET erating system pipe . This pipe could be implemented either by conveying the data values to Process_3 as soon as they are produced by Process_2 or by storing the output in a bu er or a le, then reading it back when the stream is closed.

A Semantic Basis. The formal semantic de nition of a language must include speci c de nitions of the details of the abstract machine that implements its semantics. Di erent language models include and exclude di erent elements of our abstract machine.

Many languages do not support a shared environment. The new functional languages do not support a program environment, except for prede ned symbols. The control elements, in particular, di er greatly from one language to the next.

We de ne the term semantic basis of a language to mean the speci c version of the abstract machine that de nes the language, together with the internal data structures and interpretation procedures that implement the abstract semantics. Layered on top of the semantic basis is the syntax of the language, which speci es the particular keywords, symbols, and order of elements to be used to denote each semantic unit it supports. The semantic basis of a language must de ne the kinds of objects that are supported, the primitive actions, and the control structures by which the objects and actions are linked together, and the ways that the language may be extended by new de nitions.

The features included in a semantic basis completely determine the power of a language; items left out cannot be de ned by the programmer or added by using macros. Where two di erent semantic units provide roughly the same power, the choice of which to include determines the character of the language and the style of programs that will be written in it. Thus a wise language designer gives careful thought to the semantic basis before beginning to de ne syntax.

. Lambda Calculus: A Minimal Semantic Basis It is perhaps surprising tha Data Matrix barcode for .NET t a very small set of semantic primitives, excluding goto and assignment, can form an adequate semantic basis for a language. This was proven theoretically by Church s work on lambda calculus.

14 Lambda calculus is not a programming language and is not directly concerned with computers. It has no programs or objects or execution as we understand them. It is a symbolic, logical system in which formulas are written as strings of symbols and manipulated according to logical rules.

We need to be knowledgeable about lambda calculus for three reasons. First, it is a complete system: Church has shown that it is capable of representing any computable function. Thus any language that can implement or emulate lambda calculus is also complete.

Second, lambda calculus gives us a starting point by de ning a minimal semantic basis for computation that is mathematically clean. As we examine real computer languages we want to distinguish between necessary features, nice features (extras), nonfeatures (things that the language. Church [1941].. 4.3. SEMANTICS Exhibit 4.10. Lambda calculu s formulas.

Formulas x ( x.((yy)x)) ( z.(y( z.

z))) (( z.(zy))x) Comments Any variable is a formula. Lambda expressions are formulas.

The body of this lambda expression is an application. Why is this formula an application . would be better o without), .net vs 2010 DataMatrix and missing features which limit the power of the language. The lambda calculus gives us a starting point for deciding which features are necessary or missing.

Finally, an extended version of lambda calculus forms the semantic basis for the modern functional languages. The Miranda compiler translates Miranda code into tree structures which can then be interpreted by an augmented lambda calculus interpreter. Lambda calculus has taken on new importance because of the recent research on functional languages.

These languages come exceedingly close to capturing the essence of lambda calculus in a real, translatable, executable computer language. Understanding the original formal system gives us some grasp of how these languages di er from C, Pascal, and LISP, and supplies some reason for the aspects of functional languages that seem strange at rst. Symbols, Functions, and Formulas There are two kinds of symbols in lambda calculus: A single-character symbol, such as y, used to name a parameter and called a variable.

Punctuation symbols ( , ) , . , and . These symbols can be combined into strings to form formulas according to three simple rules: 1.

A variable is a formula. 2. If y is a variable and F is a formula, then ( y.

F ) is a formula, which is called a lambda expression; y is said to be the parameter of the lambda expression, and F is its body. 3. If F and G are formulas, then (F G) is a formula, which is called an application.

Thus every lambda calculus formula is of one of three types: a variable, a lambda expression, or an application. Examples of formulas are given in Exhibit 4.10.

Lambda calculus di ers from programming languages in that its programs and its semantic domain are the same. Formulas can be thought of as programs or as the data upon which programs operate. A lambda expression is like a function: it speci es a parameter name and has a body that usually refers to that parameter.

15 An application whose rst formula is a lambda expression is like. The syntax de ned here suppo rts only one-argument functions. There is a common variant which permits multiargument functions. This form can be mechanically converted to the single-argument syntax.

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