Adding a top type and allowing non-normalizing terms
Curry-style typing and realizability make it sensible to allow a top type to type every term, even non-normalizing ones.
Iowa Type Theory Commute
en-usFebruary 05, 2020
On this page
type theory design 1
Explore " type theory design 1" with insightful episodes like "Adding a top type and allowing non-normalizing terms", "Intersection types using Curry-style typing", "Curry-style versus Church-style, and the nature of type annotations", "More on Computation First, and Basic Idea of Realizability" and "Types should be erased for executing and reasoning about programs" from podcasts like ""Iowa Type Theory Commute", "Iowa Type Theory Commute", "Iowa Type Theory Commute", "Iowa Type Theory Commute" and "Iowa Type Theory Commute"" and more!
Episodes (5)
Intersection types using Curry-style typing
Intersection types internalize the idea that a term has two types. Curry-style typing is generally needed for this to be nontrivial.
Iowa Type Theory Commute
en-usFebruary 04, 2020
Curry-style versus Church-style, and the nature of type annotations
In Curry-style typing annotations -- for example, the types of bound variables -- are erased, and not truly (semantically) part of the term. In Church-style, they are intrinsic to the term and are truly there. Discussion of some of the practicalities of Curry-style typing, in particular type annotations versus proving typings.
More on Computation First, and Basic Idea of Realizability
Types are specifications whose semantics is explained in terms of computation, which is thus conceptually prior. Realizability is a way of explaining the semantics of types.
Iowa Type Theory Commute
en-usJanuary 29, 2020
Types should be erased for executing and reasoning about programs
In which I argue that type information should be erased from programs by the compiler both for final execution and also for reasoning (in a language with dependent types, for example, where we can reason about program execution statically).