类型与编程语言基础

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"Types and Programming Languages" 由 Benjamin C. Pierce 编著，是一部关于类型系统和编程语言理论的综合介绍。在计算机科学中，类型系统是编程语言理论的核心部分，它们用于规范和验证程序的结构和行为。类型系统的主要目标是确保程序的正确性，通过在编译时检测潜在的错误，如类型不匹配或无效的操作，从而减少运行时错误。本书深入探讨了这些系统的定义、结果和技巧，并对软件工程、语言设计、高性能编译器实现以及安全领域有重大应用。编程语言理论关注的是如何构建、分析和理解编程语言，而类型系统作为其中的一个关键概念，它不仅帮助我们理解程序的结构，还影响着语言的设计和实现。类型可以被看作是变量、表达式或函数的属性，定义了它们能够操作的数据类型。通过类型检查，我们可以确保程序中的操作是合法的，例如，不允许整数与字符串相加。类型系统和语言设计密切相关。类型系统的选择和设计直接影响着语言的使用方式和安全性。例如，静态类型语言在编译时强制执行类型检查，而动态类型语言则在运行时进行检查。每种策略都有其优缺点，静态类型可能提供更严格的错误检查，而动态类型则允许更灵活的编程风格。本书的胶囊历史部分可能回顾了类型系统的发展历程，从早期的简单类型系统到现代复杂的面向对象和函数式编程语言中的高级类型构造。这包括类型推断、类型系统的形式化模型，以及如类型别名、接口和泛型等概念的引入。此外，书中还可能讨论了其他相关阅读材料，引导读者进一步探索类型系统和编程语言理论的广泛研究领域。数学预科章节将涵盖集合论、关系、函数等基础概念，这些都是理解类型系统的基础。本著作使用 LaTeX 文档准备系统设置，表明了作者对技术细节的严谨态度。图书馆索引数据表明，这本书适合于计算机科学，特别是编程语言和类型理论的学习者和研究者。 "Types and Programming Languages" 是一本深入探讨类型系统和编程语言理论的权威教材，对于想要深入理解程序设计语言内部机制以及如何利用类型系统提高代码质量的开发者和学者来说，是一份宝贵的资源。

xvi Preface

30 31 3229

2 3

4 5 8

6 9

11 12

13 14 15 22

1816 19 26

Figure P-1: Chapter dependencies

Preface xvii

guages and type systems are mentioned only in passing, e.g, dependent types,

intersection types, and the Curry-Howard correspondence; short sections on

these topics provide starting points for further reading. Finally, except for a

brief excursion into a Java-like core language (Chapter 19), the book focuses

entirely on systems based on the lambda-calculus; however, the concepts and

mechanisms developed in this setting can be transferred directly to related

areas such as typed concurrent languages, typed assembly languages, and

specialized object calculi.

Required Background

The text assumes no preparation in the theory of programming languages,

but readers should start with a degree of mathematical maturity—in particu-

lar, rigorous undergraduate coursework in discrete mathematics, algorithms,

and elementary logic.

Readers should be familiar with at least one higher-order functional pro-

gramming language (Scheme, ML, Haskell, etc.), and with basic concepts of

programming languages and compilers (abstract syntax, BNF grammars, eval-

uation, abstract machines, etc.). This material is available in many excellent

undergraduate texts; I particularly like Essentials of Programming Languages

by Friedman, Wand, and Haynes (2001) and Programming Language Prag-

matics by Scott (1999). Experience with an object-oriented language such as

Java (Arnold and Gosling, 1996) is useful in several chapters.

The chapters on concrete implementations of typecheckers present signif-

icant code fragments in OCaml (or Objective Caml), a popular dialect of ML.

Prior knowledge of OCaml is helpful in these chapters, but not absolutely nec-

essary; only a small part of the language is used, and features are explained

at their ﬁrst occurrence. These chapters constitute a distinct thread from the

rest of the book and can be skipped completely if desired.

The best textbook on OCaml at the moment is Cousineau and Mauny’s

(1998). The tutorial materials packaged with the OCaml distribution (avail-

able at http://caml.inria.fr and http://www.ocaml.org) are also very

readable.

Readers familiar with the other major dialect of ML, Standard ML, should

have no trouble following the OCaml code fragments. Popular textbooks on

Standard ML include those by Paulson (1996) and Ullman (1997).

Course Outlines

An intermediate or advanced graduate course should be able to cover most

of the book in a semester. Figure P-2 gives a sample syllabus from an upper-

xviii Preface

level course for doctoral students at the University of Pennsylvania (two 90-

minute lectures a week, assuming minimal prior preparation in programming

language theory but moving quickly).

For an undergraduate or an introductory graduate course, there are a num-

ber of possible paths through the material. A course on type systems in pro-

gramming would concentrate on the chapters that introduce various typing

features and illustrate their uses and omit most of the metatheory and im-

plementation chapters. Alternatively, a course on basic theory and implemen-

tation of type systems would progress through all the early chapters, prob-

ably skipping Chapter 12 (and perhaps 18 and 21) and sacriﬁcing the more

advanced material toward the end of the book. Shorter courses can also be

constructed by selecting particular chapters of interest using the dependency

diagram in Figure P-1.

The book is also suitable as the main text for a more general graduate

course in theory of programming languages. Such a course might spend half

to two-thirds of a semester working through the better part of the book and

devote the rest to, say, a unit on the theory of concurrency based on Milner’s

pi-calculus book (1999), an introduction to Hoare Logic and axiomatic seman-

tics (e.g. Winskel, 1993), or a survey of advanced language features such as

continuations or module systems.

In a course where term projects play a major role, it may be desirable to

postpone some of the theoretical material (e.g., normalization, and perhaps

some of the chapters on metatheory) so that a broad range of examples can

be covered before students choose project topics.

Exercises

Most chapters include extensive exercises—some designed for pencil and pa-

per, some involving programming examples in the calculi under discussion,

and some concerning extensions to the ML implementations of these cal-

culi. The estimated diﬃculty of each exercise is indicated using the following

scale:

« Quick check 30 seconds to 5 minutes

«« Easy ≤ 1 hour

««« Moderate ≤ 3 hours

«««« Challenging > 3 hours

Exercises marked « are intended as real-time checks of important concepts.

Readers are strongly encouraged to pause for each one of these before mov-

ing on to the material that follows. In each chapter, a roughly homework-

assignment-sized set of exercises is labeled Recommended.

xx Preface

calculus. The new parts are set on a gray background to make the “delta”

from previous systems visually obvious.

An unusual feature of the book’s production is that all the examples are

mechanically typechecked during typesetting: a script goes through each chap-

ter, extracts the examples, generates and compiles a custom typechecker con-

taining the features under discussion, applies it to the examples, and inserts

the checker’s responses in the text. The system that does the hard parts of

this, called TinkerType, was developed by Michael Levin and myself (2001).

Funding for this research was provided by the National Science Foundation,

through grants CCR-9701826, Principled Foundations for Programming with

Objects, and CCR-9912352, Modular Type Systems.

Electronic Resources

A web site associated with this book can be found at the following URL:

http://www.cis.upenn.edu/~bcpierce/tapl

Resources available on this site include errata for the text, suggestions for

course projects, pointers to supplemental material contributed by readers,

and a collection of implementations (typecheckers and simple interpreters)

of the calculi covered in each chapter of the text.

These implementations oﬀer an environment for experimenting with the

examples in the book and testing solutions to exercises. They have also been

polished for readability and modiﬁability and have been used successfully by

students in my courses as the basis of both small implementation exercises

and larger course projects. The implementations are written in OCaml. The

OCaml compiler is available at no cost through http://caml.inria.fr and

installs very easily on most platforms.

Readers should also be aware of the Types Forum, an email list covering

all aspects of type systems and their applications. The list is moderated to

ensure reasonably low volume and a high signal-to-noise ratio in announce-

ments and discussions. Archives and subscription instructions can be found

at http://www.cis.upenn.edu/~bcpierce/types.

Acknowledgments

Readers who ﬁnd value in this book owe their biggest debt of gratitude to four

mentors—Luca Cardelli, Bob Harper, Robin Milner, and John Reynolds—who

taught me most of what I know about programming languages and types.

The rest I have learned mostly through collaborations; besides Luca, Bob,

Robin, and John, my partners in these investigations have included Martín

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