Logic for Programmers
Logic for Programmers
About the Book
If I start a build at 3:05 PM and it takes 12 minutes to complete, when will the build be finished?
To answer this question, we need to how to manipulate numbers. The mathematics of numbers is called "arithmetic". Arithmetic shows us how to multiply two numbers, use fractions, determine which of two numbers is larger, and more.
If I have the conditional if(sensor_offline || inactive), and I know for sure thatsensor_offlineis true, does the value ofinactivematter?
To answer this question, we need to know how to manipulate booleans. The mathematics of booleans is called "logic". Logic shows us how to simplify a boolean expression, use sets, determine if one statement is stronger than another, and more.
But there is one key difference between arithmetic and logic. We were taught arithmetic in elementary school. Few of us were formally taught logic. Most programmers pick up a little logic by osmosis, but even that rarely exposes people to anything beyond the basics. This makes logic the single most useful topic in math a programmer can learn.
That is the goal of this book. Reading this will teach you the basics of logic and how to apply it to various everyday software problems, like testing code, designing a database, working out customer requirements, and more. Over 40 exercises are provided to help readers master the material. No prior math background required!
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The book's current status is BETA. Most of the content is in but I will be changing the prose and polishing based on reader feedback. I also need to give more attention to book layout, formatting, proofreading, and paying an artist for an Actually Good Cover Page. And there's always room for more useful exercises!
I will release new betas monthly, with the final 1.0 coming sometime mid-late 2025. If you buy the book now, you'll get all future version for free as well as input into how it develops. I'll be raising the price to 25 once 1.0 is ready.
New in v0.7:
- New fonts!
- Changed formatting and indentation for code blocks
- "Functional Correctness" chapter has new section on type invariants
- "Data Modeling" chapter has new example on finding design bugs via modeling
- "Conditionals" chapter now covers redundant conditionals more broadly
- Rewrote intro, "Why this book" section cleaner
- Incorporated various reader feedback
About the Author
Table of Contents
- Acknowledgements
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Part I: Introduction
- 1. Early access notes
- 2. A crash course in logic
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Part II: Techniques
- 1. Testing and property testing
- 2. Functional correctness and contracts
- 3. Case coverage and decision tables
- 4. Conditional simplification
- 5. Database constraints
- 6. Data modeling and formal specification
- 7. System modeling and TLA+
- 8. Constraint solving
- 9. Logic programming
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Part III: Appendices
- 1. Math notation
- 2. Rewrite rules
- 3. Other ideas in logic
- 4. Answers to Exercises
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