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An overlapping feature of type theory and type systems.

11
votes
Type theories have multiple uses, and with each kind of usage comes a different notion of correctness. They two key uses are As a foundation of mathematics. In this context correctness means primari …
answered Apr 4 '14 by Martin Berger
8
votes
Quite a bit is know about this. The concept of Pure Type Systems (PTS) is useful for showing Church-Rosser (CR) for large classes of typed $\lambda$-calculi. Paraphrasing (1): PTS with only β reduct …
answered Dec 15 '15 by Martin Berger
3
votes
"Types are the leaven of computer programming; they make it digestible." Robin Milner
answered Jul 11 '21 by Martin Berger
4
votes
1answer
Programming languages with dependent types and/or higher-kinded types feature what might be called compile-time computation at the type-level. This is usually defined as follows (I'm omitting some de …
asked Aug 3 '15 by Martin Berger
6
votes
Inductive types have been studied heavily and many variants exist. A well-known introduction to inductive definitions is P. Aczel, An Introduction to Inductive Definitions which was originally pub …
answered Mar 29 '14 by Martin Berger
4
votes
A practical example of an axiom behaving badly you ask, what about this? 0 = 1 The Coquand paper referred to might be [ 1 ], where he shows that dependent ITT (Martin-Löf's intuitionistic type the …
answered Dec 19 '15 by Martin Berger