Quadratic type checking for objective type theory

02/01/2021
by   Benno van den Berg, et al.
0

We introduce a modification of standard Martin-Lof type theory in which we eliminate definitional equality and replace all computation rules by propositional equalities. We show that type checking for such a system can be done in quadratic time and that it has a natural homotopy-theoretic semantics.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
11/19/2019

Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality

In type theory with an impredicative universe of propositions and a proo...
research
05/12/2020

MathZero, The Classification Problem, and Set-Theoretic Type Theory

AlphaZero learns to play go, chess and shogi at a superhuman level throu...
research
09/15/2023

MetaOCaml Theory and Implementation

Quasi-quotation (or, code templates) has long been used as a convenient ...
research
10/15/2022

A tutorial on implementing De Morgan cubical type theory

This tutorial explains (one way) how to implement De Morgan cubical type...
research
03/12/2021

An extensible equality checking algorithm for dependent type theories

We present a general and user-extensible equality checking algorithm tha...
research
07/17/2019

Shallow Embedding of Type Theory is Morally Correct

There are multiple ways to formalise the metatheory of type theory. For ...
research
02/17/2018

Design and Implementation of the Andromeda Proof Assistant

Andromeda is an LCF-style proof assistant where the user builds derivabl...

Please sign up or login with your details

Forgot password? Click here to reset