类型理论：编程语言设计的基石

需积分: 7 34 浏览量更新于2024-07-20 收藏 1.64MB PDF 举报

"《实用编程语言基础》是罗伯特·哈珀编著的一本深入浅出的编程语言理论教材，该书主要围绕类型系统和结构操作语义为核心展开，为编程语言的概念提供了全面而严谨的定义。作者将静态类型和动态类型、基本数据类型（如联合类型和产品类型）、多态与抽象类型、动态分派、子类型和细化类型、符号和动态分类等核心概念逐一剖析，通过直观的方式呈现并结合基础数学工具进行讲解。书中的理论不仅适用于语言设计的实现，还为程序逻辑推理和语言属性的正式验证提供了框架。类型安全是其中的一个重要特性，作者通过实例展示了如何利用这些工具分析和证明语言的性质。修订版中，几乎每章都有练习题，旨在帮助读者巩固所学，同时新增了关于类型细化的章节，进一步扩展了内容深度。在本书中，作者强调类型是编程语言设计的核心原则，语法结构由定义其类型的构造规则决定，而语义则由这些构造之间的相互作用来确定。语言设计的合理性，即避免产生不明确的程序，实际上源于对类型结构的合理构建和管理。书中对诸如函数式编程、面向对象编程等各类语言特性的分析，都是在类型理论的大背景下进行的。静态分析关注的是程序在编译时的规则，比如类型检查，而动态分析则关注程序运行时的行为，如动态绑定和类型推断。这种全面的视角使得读者能够理解和比较不同语言的设计决策，并为实际编程实践提供坚实的基础。《实用编程语言基础》是一本兼具理论深度和实践指导价值的书籍，它不仅为学习者提供了理解编程语言的坚实基础，也为语言理论研究者和开发者提供了丰富的思考素材和工具。"

Preview

xvi CONTENTS

XVIII Equational Reasoning 471

47 Equational Reasoning for T 473

47.1 Observational Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

47.2 Logical Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

47.3 Logical and Observational Equivalence Coincide . . . . . . . . . . . . . . . . 479

47.4 Some Laws of Equality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

47.4.1 General Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

47.4.2 Equality Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

47.4.3 Induction Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

47.5 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

48 Equational Reasoning for PCF 485

48.1 Observational Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

48.2 Logical Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

48.3 Logical and Observational Equivalence Coincide . . . . . . . . . . . . . . . . 487

48.4 Compactness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

48.5 Co-Natural Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

48.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

49 Parametricity 495

49.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

49.2 Observational Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496

49.3 Logical Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

49.4 Parametricity Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503

49.5 Representation Independence, Revisited . . . . . . . . . . . . . . . . . . . . . 507

49.6 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

50 Process Equivalence 509

50.1 Process Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

50.2 Strong Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

50.3 Weak Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

50.4 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

XIX Appendices 517

A Finite Sets and Finite Functions 519

B Errata 521

Preview

4 1.1 Abstract Syntax Trees

1.1 Abstract Syntax Trees

An abstract syntax tree, or ast for short, is an ordered tree whose leaves are variables, and

whose interior nodes are operators whose arguments are its children. Ast’s are classiﬁed

into a variety of sorts corresponding to different forms of syntax. A variable stands for

an unspeciﬁed, or generic, piece of syntax of a speciﬁed sort. Ast’s may be combined by

an operator, which has both a sort and an arity, a ﬁnite sequence of sorts specifying the

number and sorts of its arguments. An operator of sort s and arity s

, . . . , s

combines

n ≥ 0 ast’s of sort s

, . . . , s

, respectively, into a compound ast of sort s. As a matter of

terminology, a nullary operator is one that takes no arguments, a unary operator takes one,

a binary operator two, and so forth.

The concept of a variable is central, and therefore deserves special emphasis. As in

mathematics a variable is an unknown object drawn from some domain, its range of signif-

icance. In school mathematics the (often implied) range of signiﬁcance is the set of real

numbers. Here variables range over ast’s of a speciﬁed sort. Being an unknown, the

meaning of a variable is given by substitution, the process of “plugging in” an object from

the domain for the variable in a formula. So, in school, we might plug in π for x in a poly-

nomial, and calculate the result. Here we would plug in an ast of the appropriate sort for

a variable in an ast to obtain another ast. The process of substitution is easily understood

for ast’s, because it amounts to a “physical” replacement of the variable by an ast within

another ast. We will shortly consider a generalization of the concept of ast for which the

substitution process is somewhat more complex, but the essential idea is the same, and

bears repeating: a variable is given meaning by substitution.

For example, consider a simple language of expressions built from numbers, addition,

and multiplication. The abstract syntax of such a language would consist of a single sort,

Exp, and an inﬁnite collection of operators that generate the forms of expression: num[ n]

is a nullary operator of sort Exp whenever n ∈ N; plus and times are binary operators of

sort Exp whose arguments are both of sort Exp. The expression 2 + (3 × x), which involves

a variable, x, would be represented by the ast

plus(num[2]; times(num[3]; x))

of sort Exp, under the assumption that x is also of this sort. Because, say, num[4], is an ast

of sort Exp, we may plug it in for x in the above ast to obtain the ast

plus(num[2]; times(num[3]; num[4])),

which is written informally as 2 + (3 × 4). We may, of course, plug in more complex ast’s

of sort Exp for x to obtain other ast’s as result.

剩余556页未读，继续阅读

GFelix

粉丝: 1
资源: 17

类型理论：编程语言设计的基石

Foundations for Programming Languages

Practical_Foundations_for_Programming_Languages

foundations of programming languages pdf

foundations of data science csdn

用qt和c++开发的系统所用的参考文献

foundations of machine learning答案

c primer plus网课推荐

foundations of mimo communication pdf

foundations of optimization 苏文藻

系统测试参考文献有哪些

最新资源