Certified programming with dependent types : a pragmatic introduction to the Coq proof assistant

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Bibliographic Details
Main Author Chlipala, Adam, 1981-
Format Electronic eBook
LanguageEnglish
Published Cambridge, MA : The MIT Press, [2013]
Subjects
Automatic theorem proving > Computer programs.
Computer programming.
Coq (Electronic resource)
elektronické knihy
electronic books
Online AccessFull text
ISBN9780262317870
Physical Description1 online zdroj (xii, 424 pages)

Cover

Table of Contents:
  • Machine generated contents note: 1.Introduction
  • 1.1.Whence This Book?
  • 1.2.Why Coq?
  • 1.2.1.Based on a Higher-Order Functional Programming Language
  • 1.2.2.Dependent Types
  • 1.2.3.An Easy-to-Check Kernel Proof Language
  • 1.2.4.Convenient Programmable Proof Automation
  • 1.2.5.Proof by Reflection
  • 1.3.Why Not a Different Dependently Typed Language?
  • 1.4.Engineering with a Proof Assistant
  • 1.5.Prerequisites
  • 1.6.Using This Book
  • 1.6.1.Reading This Book
  • 1.6.2.The Tactic Library
  • 1.6.3.Installation and Emacs Setup
  • 2.Some Quick Examples
  • 2.1.Arithmetic Expressions over Natural Numbers
  • 2.1.1.Source Language
  • 2.1.2.Target Language
  • 2.1.3.Translation
  • 2.1.4.Translation Correctness
  • 2.2.Typed Expressions
  • 2.2.1.Source Language
  • 2.2.2.Target Language
  • 2.2.3.Translation
  • 2.2.4.Translation Correctness
  • I.Basic Programming and Proving
  • 3.Introducing Inductive Types
  • 3.1.Proof Terms
  • 3.2.Enumerations
  • 3.3.Simple Recursive Types
  • -3.4.Parameterized Types
  • 3.5.Mutually Inductive Types
  • 3.6.Reflexive Types
  • 3.7.An Interlude on Induction Principles
  • 3.8.Nested Inductive Types
  • 3.9.Manual Proofs about Constructors
  • 4.Inductive Predicates
  • 4.1.Propositional Logic
  • 4.2.What Does It Mean to Be Constructive?
  • 4.3.First-Order Logic
  • 4.4.Predicates with Implicit Equality
  • 4.5.Recursive Predicates
  • 5.Infinite Data and Proofs
  • 5.1.Computing with Infinite Data
  • 5.2.Infinite Proofs
  • 5.3.Simple Modeling of Nonterminating Programs
  • II.Programming with Dependent Types
  • 6.Subset Types and Variations
  • 6.1.Introducing Subset Types
  • 6.2.Decidable Proposition Types
  • 6.3.Partial Subset Types
  • 6.4.Monadic Notations
  • 6.5.A Type-Checking Example
  • 7.General Recursion
  • 7.1.Well-Founded Recursion
  • 7.2.A Nontermination Monad Inspired by Domain Theory
  • 7.3.Co-inductive Nontermination Monads
  • 7.4.Comparing the Alternatives
  • 8.More Dependent Types
  • 8.1.Length-Indexed Lists
  • -8.2.The One Rule of Dependent Pattern Matching in Coq
  • 8.3.A Tagless Interpreter
  • 8.4.Dependently Typed Red-Black Trees
  • 8.5.A Certified Regular Expression Matcher
  • 9.Dependent Data Structures
  • 9.1.More Length-Indexed Lists
  • 9.2.Heterogeneous Lists
  • 9.2.1.A Lambda Calculus Interpreter
  • 9.3.Recursive Type Definitions
  • 9.4.Data Structures as Index Functions
  • 9.4.1.Another Interpreter Example
  • 9.5.Choosing between Representations
  • 10.Reasoning about Equality Proofs
  • 10.1.The Definitional Equality
  • 10.2.Heterogeneous Lists Revisited
  • 10.3.Type Casts in Theorem Statements
  • 10.4.Heterogeneous Equality
  • 10.5.Equivalence of Equality Axioms
  • 10.6.Equality of Functions
  • 11.Generic Programming
  • 11.1.Reifying Datatype Definitions
  • 11.2.Recursive Definitions
  • 11.2.1.Pretty-Printing
  • 11.2.2.Mapping
  • 11.3.Proving Theorems about Recursive Definitions
  • 12.Universes and Axioms
  • 12.1.The Type Hierarchy
  • 12.1.1.Inductive Definitions
  • -12.1.2.Deciphering Baffling Messages about Inability to Unify
  • 12.2.The Prop Universe
  • 12.3.Axioms
  • 12.3.1.The Basics
  • 12.3.2.Axioms of Choice
  • 12.3.3.Axioms and Computation
  • 12.3.4.Methods for Avoiding Axioms
  • III.Proof Engineering
  • 13.Proof Search by Logic Programming
  • 13.1.Introducing Logic Programming
  • 13.2.Searching for Underconstrained Values
  • 13.3.Synthesizing Programs
  • 13.4.More on auto Hints
  • 13.5.Rewrite Hints
  • 14.Proof Search in Ltac
  • 14.1.Some Built-in Automation Tactics
  • 14.2.Ltac Programming Basics
  • 14.3.Functional Programming in Ltac
  • 14.4.Recursive Proof Search
  • 14.5.Creating Unification Variables
  • 15.Proof by Reflection
  • 15.1.Proving Evenness
  • 15.2.Reifying the Syntax of a Trivial Tautology Language
  • 15.3.A Monoid Expression Simplifier
  • 15.4.A Smarter Tautology Solver
  • 15.4.1.Manual Reification of Terms with Variables
  • 15.5.Building a Reification Tactic That Recurses under Binders
  • IV.The Big Picture
  • -16.Proving in the Large
  • 16.1.Ltac Antipatterns
  • 16.2.Debugging and Maintaining Automation
  • 16.3.Modules
  • 16.4.Build Processes
  • 17.Reasoning about Programming Language Syntax
  • 17.1.Dependent de Bruijn Indices
  • 17.2.Parametric Higher-Order Abstract Syntax
  • 17.2.1.Functional Programming with PHOAS
  • 17.2.2.Verifying Program Transformations
  • 17.2.3.Establishing Term Well-Formedness
  • 17.2.4.A Few Additional Remarks.

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