Logic & Applications

Big logic johndcook.com/blog/applied-l…

Use of Formal Methods at Amazon Web Services research.microsoft.com/en-us/um/peopl… [pdf]

The halting problem: You cannot write a program that can tell whether an arbitrary program will complete or run forever.

'Every good idea will be discovered twice: once by a logician and once by a computer scientist.' -- @PhilipWadler

Fun with combinators doisinkidney.com/posts/2020-10-…

The Algebra of Logic gutenberg.org/ebooks/10836

Glivenko's theorem: If φ is a propositional formula, then φ is a classical tautology if and only if ¬ ¬ φ is an intuitionistic tautology.

A formal proof of the Kepler conjecture arxiv.org/abs/1501.02155

Proofs and programs johndcook.com/blog/2016/09/0…

In minimal modal logic, there can be infinitely many inequivalent modalities, sequences of boxes and diamonds. In S4 there are only 7. In S5 there are 3.

The Church numeral for a non-negative integer n is λxy. x^n y

The Open Logic Project openlogicproject.org/about/

'There may, indeed, be other applications of the system [i.e. lambda calculus] than its use as a logic.' -- Alonzo Church, 1932

Beta reduction: The difference typing makes johndcook.com/blog/2016/09/1…

The first problem proved to be undecidable was the equivalence of arbitrary lambda expressions.

Sequent calculus cheat sheet antitypical.com/posts/2021-08-…

Ligatures for logic johndcook.com/blog/2022/10/0…

“I wish my wish would not be granted!” — Douglas Hofstadter

Intuitionistic implication A ⇒ B can be represented in linear logic as !A ⊸ B.

Gödel proved in 1932 that intuitionistic logic has no interpretation as a finite-valued logic. The proof was only two pages long.

A Timeline for Logic, λ-Calculus, and Programming Language Theory by Dana Scott fm.csl.sri.com/SSFT15/Timelin… [pdf]