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    Technology

    Iowa Type Theory Commute

    Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.

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    Copyright: ℗ & © 2020 Iowa Type Theory Commute

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    Latest Episodes:
    Indexed types and Curry-Howard for first-order quantifiers Jan 03, 2020
    Show notes

    I follow up on some comments I made about Curry-Howard for first-order quantifiers in the previous episode. Sheard's Omega language also mentioned (see links on <a href = "http://web.cecs.pdx.edu/~sheard/">his web page</a>). First-order quantifications turn into indexed types where the indices are not program expressions but come from another syntactic domain.

    The Curry-Howard Isomorphism for Propositional Logic Jan 02, 2020
    Show notes

    Discussion of the Curry-Howard isomorphism for the connectives of propositional logic (AND, OR, NOT, FALSE, IMPLIES). Initial consideration of Curry-Howard for first-order and higher-order logic. Dependent types.

    The Curry-Howard Isomorphism for Induction Dec 31, 2019
    Show notes

    In which I discover why the domino analogy for explaining induction always bothered me!

    Constructive proofs as programs Dec 21, 2019
    Show notes

    We consider the basic idea of the Curry-Howard isomorphism, that constructive proofs are essentially programs, and vice versa. Several simple examples. Why the law of excluded middle is not a legal constructive proof.

    Introduction to the Curry-Howard Isomorphism Dec 20, 2019
    Show notes

    The basic idea of the Curry-Howard isomorphism, and its connection to the contents of Chapters 1 and 2. Constructive proof. A famous nonconstructive proof.

    Functors and catamorphisms Dec 20, 2019
    Show notes

    More about the structured recusion scheme known as the catamorphism. Basic idea of functors.

    Structured Recursion Schemes for Point-Free Recursion Dec 18, 2019
    Show notes

    Review of basic application of category theory for functional programming. Recursion schemes are combinators that let you write point-free recursions.

    More on point-free programming and category theory Dec 17, 2019
    Show notes

    A few very basic ideas of categories and combinators. Also, the problem of understanding very concise code.

    Point-free programming and category theory Dec 17, 2019
    Show notes

    Relation of point-free functional programming to category theory.

    Concise code through point-free programming Dec 13, 2019
    Show notes

    Higher-order functions help make it possible to program in a point-free style, where we use combinators to connect functions, rather than calling the functions on inputs explicitly.

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