Cost-Aware Type Theory

11/07/2020
βˆ™
by   Yue Niu, et al.
βˆ™
0
βˆ™

Although computational complexity is a fundamental aspect of program behavior, it is often at odds with common type theoretic principles such as function extensionality, which identifies all functions with the same input-output behavior. We present a computational type theory called 𝐂𝐀𝐓𝐓 that has a primitive notion of cost (the number of evaluation steps). We introduce a new dependent function type "funtime" whose semantics can be viewed as a cost-aware version of function extensionality. We prove a collection of lemmas for 𝐂𝐀𝐓𝐓, including a novel introduction rule for the new funtime type. 𝐂𝐀𝐓𝐓 can be simultaneously viewed as a framework for analyzing computational complexity of programs and as the beginnings of a semantic foundation for characterizing feasible mathematical proofs.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
βˆ™ 07/09/2021

A cost-aware logical framework

We present calf, a cost-aware logical framework for studying quantitativ...
research
βˆ™ 05/24/2022

Modeling Asymptotic Complexity Using ACL2

The theory of asymptotic complexity provides an approach to characterizi...
research
βˆ™ 03/23/2021

Combinators: A Centennial View

We give a modern computational introduction to the S,K combinators inven...
research
βˆ™ 09/15/2023

A Two-Level Linear Dependent Type Theory

We present a type theory combining both linearity and dependency by stra...
research
βˆ™ 11/13/2019

Naive cubical type theory

This paper proposes a way of doing type theory informally, assuming a cu...
research
βˆ™ 04/14/2022

Puzzles of Existential Generalisation from Type-theoretic Perspective

The present paper addresses several puzzles related to the Rule of Exist...
research
βˆ™ 11/09/2017

Higher-order Cons-free Interpreters

Constructor rewriting systems are said to be cons-free if any constructo...

Please sign up or login with your details

Forgot password? Click here to reset