Examples in Relational Type Theory
I discuss how to define internalized relational typings, implicit products, and two forms of natural number types, in RelTT.
Iowa Type Theory Commute
en-usDecember 23, 2020
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relational semantics
Explore " relational semantics" with insightful episodes like "Examples in Relational Type Theory", "The Semantics of Relational Types", "The Types of Relational Type Theory" and "Introducing Relational Type Theory" from podcasts like ""Iowa Type Theory Commute", "Iowa Type Theory Commute", "Iowa Type Theory Commute" and "Iowa Type Theory Commute"" and more!
Episodes (4)
The Semantics of Relational Types
In this episode, I discuss the semantics of the proposed six type constructors of RelTT.
The Types of Relational Type Theory
This episode continues the introduction of RelTT by presenting the types of the language. Because the system is based on binary relational semantics, we can include binary relational operators like composition and converse as type constructs! Strange. The language also promotes terms to relations, by viewing them as functions and then taking their graphs as the relational meaning.
Iowa Type Theory Commute
en-usDecember 15, 2020
Introducing Relational Type Theory
This episode begins Chapter 11 of the podcast, on Relational Type Theory. This is a new approach to type theory that I am developing. The idea is to design a type system based on the binary relational semantics for types, which we considered in Chapter 10. This episode recalls some of that semantics.