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
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computation first
Explore " computation first" with insightful episodes like "Adding a top type and allowing non-normalizing terms", "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" and "Iowa Type Theory Commute"" and more!
Episodes (3)
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).