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18 State and Equality
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18.1 Boxes: A Canonical Mutable Structure
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18.2 Mutation and Types
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18.3 Mutation and Equality
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18.4 Another Equality Predicate
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18.5 A Hierarchy of Equality
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18.6 Space and Time Complexity
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18.7 What it Means to be Identical
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18.8 Comparing Functions
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19 Recursion and Cycles from Mutation
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19.1 Partial Definitions
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19.2 Recursive Functions
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19.3 Premature Evaluation
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19.4 Cyclic Lists Versus Streams
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20 Detecting Cycles
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20.1 A Running Example
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20.2 Types
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20.3 A First Checker
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20.4 Complexity
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20.5 A Fabulous Improvement
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20.6 Testing
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21 Avoiding Recomputation by Remembering Answers
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21.1 An Interesting Numeric Sequence
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21.1.1 Using State to Remember Past Answers
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21.1.2 From a Tree of Computation to a DAG
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21.1.3 The Complexity of Numbers
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21.1.4 Abstracting Memoization
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21.2 Edit-Distance for Spelling Correction
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21.3 Nature as a Fat-Fingered Typist
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21.4 Dynamic Programming
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21.4.1 Catalan Numbers with Dynamic Programming
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21.4.2 Levenshtein Distance and Dynamic Programming
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21.5 Contrasting Memoization and Dynamic Programming
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22 Partial Domains
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22.1 A Non-Solution
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22.2 Exceptions
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22.3 The Option Type
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22.4 Total Domains, Dynamically
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22.5 Total Domains, Statically
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22.6 Summary
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22.7 A Note on Notation
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23 Staging
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23.1 Problem Definition
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23.2 Initial Solution
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23.3 Refactoring
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23.4 Separating Parameters
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23.5 Context
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24 Factoring Numbers
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25 Deconstructing Loops
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25.1 Setup: Two Functions
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25.2 Abstracting a Loop
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25.3 Is It Really a Loop?
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25.4 Re-Examining for
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25.5 Rewriting Pollard-Rho
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25.6 Nested Loops
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25.7 Loops, Values, and Customization
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