Certainty by Construction
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Certainty by Construction

Software and Mathematics in Agda

About the Book

Agda is not just a programming language; it's a completely new way of thinking about software, and mathematical objects at large. This book is on successfully wielding Agda: teaching everything you need to know to get productive in modeling problems and in verifying your solutions.

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  • Categories

    • Functional Programming
    • Mathematics
    • Computer Science
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About the Author

Sandy Maguire
Sandy Maguire

Sandy might best be described somewhere between independent researcher and voluntarily-unemployed bum. At the ripe old age of 27 he decided to quit his highly-lucrative engineering job and decide to focus more on living than on grinding for the man. It's what you might call a work in progress.

He regularly writes about Haskell and Agda at reasonablypolymorphic.com.

Sandy Maguire

Episode 117

Table of Contents

  • Preface
  • The Co-blub Paradox
    • A World Without Execution?
  • Introduction to Agda
    • Modules and Imports
    • Syntax Highlighting
    • Types
    • Dealing with Unicode
    • A Note on Syntax
    • Operators
    • Agda’s Computational Model
    • Records and Tuples
    • Function Types
    • The Curry/Uncurry Isomorphism
    • Implicit Arguments
    • Wrapping Up
  • An Exploration of Numbers
    • Natural Numbers
    • A Note on Algebraic Data Types
    • Playing with Naturals
    • Induction
    • Two Notions of Evenness
    • Constructing Evidence
    • Addition
    • Termination Checking
    • Multiplication and Exponentiation
    • Semi-subtraction
    • Integers
  • Proof Objects
    • Constructivism
    • Propositions as Types
    • Hard to Prove or Simply False?
    • The Equality Type
    • Congruence
    • Identities
    • Symmetry and Involutivity
    • Transitivity
    • Mixfix Parsing
    • Equational Reasoning
    • Ergonomics, Associativity and Commutativity
    • Facts About Natural Numbers
  • Decidability
    • Negation
    • Bottom
    • Inequality
    • Negation Considered as a Callback
    • Intransitivity of Inequality
    • Decidability
    • Binary Trees
    • Binary Search Trees
    • Insertion into BSTs
    • Intrinsic vs Extrinsic Proofs
    • An Intrinsic BST
  • Quotients
    • Setoids
    • Constructions on Setoids
  • Functions, Big and Small
    • Matrices
    • The Row-Major Representation
    • Function Representation
    • Matrices as Functions
  • Ring Solving
    • Canonical Forms
    • Sketching Out a Ring Solver
  • Isomorphism
    • More Setoids
    • Formalizing Isomorphisms
    • Injectivity
    • Surjectivity
    • Showing the Bijection
    • Moving Forwards
  • Algebraic Structures
    • More Monoids
    • Monoid Homomorphisms
    • Semigroups
  • Countability
    • Finite Types
  • Partially Ordered Sets
    • Examples of Posets
    • The Poset of Substrings
    • Meets and Joins
    • Duality
  • Theorems about Monoids
    • Free Constructions

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