Preface
1 Introducing functional programming
1.1 Computers and modelling
1.2 What is a function?
1.3 Pictures and functions
1.4 Types
1.5 The Haskell programming language
1.6 Expressions and evaluation
1.7 Definitions
1.8 Function definitions
1.9 Types and functional programming
1.10 Calculation and evaluation
1.11 The essence of Haskell programming
1.12 Domain-specific languages
1.13 Two models of Pictures
1.14 Tests, properties and proofs
2 Getting started with Haskell and GHCi
2.1 A first Haskell program
2.2 Using Haskell in practice
2.3 Using GHCi
2.4 The standard prelude and the Haskell libraries
2.5 Modules
2.6 A second example:pictures
2.7 Errors and error messages
3 Basic types and definitions
3.1 The Booleans:Bool
3.2 The integers:Integer and Int
3.3 Overloading
3.4 Guards
3.5 Characters and strings
3.6 Floating-point numbers:Float
3.7 Syntax
4 Designing and writing programs
4.1 Where do I start? Designing a program in Haskell
4.2 Solving a problem in steps:local definitions
4.3 Defining types for ourselves:enumerated types
4.4 Recursion
4.5 Primitive recursion in practice
4.6 Extended exercise:pictures
4.7 General forms of recursion
4.8 Program testing
5 Data types, tuples and lists
5.1 Introducing tuples and lists
5.2 Tuple types
5.3 Introducing algebraic types
5.4 Our approach to lists
5.5 Lists in Haskell
5.6 List comprehensions
5.7 A library database
6 Programming with lists
6.1 Generic functions:polymorphism
6.2 Haskell list functions in the Prelude
6.3 Finding your way around the Haskell libraries
6.4 The Picture example:implementation
6.5 Extended exercise:alternative implementations of pictures
6.6 Extended exercise:positioned pictures
6.7 Extended exercise:supermarket billing
6.8 Extended exercise:cards and card games
7 Defining functions over lists
7.1 Pattern matching revisited
7.2 Lists and list patterns
7.3 Primitive recursion over lists
7.4 Finding primitive recursive definitions
7.5 General recursions over lists
7.6 Example:text processing
8 Playing the game:IO in Haskell
8.1 Rock-Paper-Scissors:strategies
8.2 Why is IO an issue?
8.3 The basics of inputoutput
8.4 The do notation
8.5 Loops and recursion
8.6 Rock-Paper-Scissors:playing the game
9 Reasoning about programs
9.1 Understanding definitions
9.2 Testing and proof
9.3 Definedness,termination and finiteness
9.4 A little logic
9.5 Induction
9.6 Further examples of proofs by induction
9.7 Generalizing the proof goal
10 Generalization:patterns of computation
10.1 Patterns of computation over lists
10.2 Higher-order functions:functions as arguments
10.3 Folding and primitive recursion
10.4 Generalizing:splitting up lists
10.5 Case studies revisited
11 Higher-order functions
11.1 Operators:function composition and application
11.2 Expressions for functions:lambda abstractions
11.3 Partial application
11.4 Under the hood:curried functions
11.5 Defining higher-order functions
11.6 Verification and general functions
12 Developing higher-order programs
12.1 Revisiting the Picture example
12.2 Functions as data:strategy combinators
12.3 Functions as data:recognizing regular expressions
12.4 Case studies:functions as data
12.5 Example:creating an index
12.6 Development in practice
12.7 Understanding programs
13 Overloading, type classes and type checking
13.1 Why overloading?
13.2 Introducing classes
13.3 Signatures and instances
13.4 A tour of the built-in Haskell classes
13.5 Type checking and type inference:an overview
13.6 Monomorphic type checking
13.7 Polymorphic type checking
13.8 Type checking and classes
14 Algebraic types
14.1 Algebraic type definitions revisited
14.2 Recursive algebraic types
14.3 Polymorphic algebraic types
14.4 Modelling program errors
14.5 Design with algebraic data types
14.6 Algebraic types and type classes
14.7 Reasoning about algebraic types
15 Case study:Huffman codes
15.1 Modules in Haskell
15.2 Modular design
15.3 Coding and decoding
15.4 Implementation-Ⅰ
15.5 Building Huffman trees
15.6 Design
15.7 Implementation-Ⅱ
16 Abstract data types
16.1 Type representations
16.2 The Haskell abstract data type mechanism
16.3 Queues
16.4 Design
16.5 Simulation
16.6 Implementing the simulation
16.7 Search trees
16.8 Sets
16.9 Relations and graphs
16.10 Commentary
17 Lazy programming
17.1 Lazy evaluation
17.2 Calculation rules and lazy evaluation
17.3 List comprehensions revisited
17.4 Data-directed programming
17.5 Case study:parsing expressions
17.6 Infinite lists
17.7 Why infinite lists?
17.8 Case study:simulation
17.9 Proof revisited
18 Programming with monads
18.1 IO programming
18.2 Further IO
18.3 The calculator
18.4 The do notation revisited
18.5 Monads:languages for functional programming
18.6 Example:monadic computation over trees
19 Domain-specific languages
19.1 Programming languages everywhere
19.2 Why DSLs in Haskell?
19.3 Shallow and deep embeddings
19.4 A DSL for regular expressions
19.5 Monadic DSLs
19.6 DSLs for computation:generating data in QuickCheck
19.7 Taking it further
20 Time and space behaviour
20.1 Complexity of functions
20.2 The complexity of calculations
20.3 Implementations of sets
20.4 Space behaviour
20.5 Folding revisited
20.6 Avoiding recomputation:memoization
21 Conclusion
Appendices
A Functional,imperative and OO programming
B Glossary
C Haskell operators
D Haskell practicalities
E GHCi errors
F Project ideas
Bibliography
Index
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