An extended type system with lambda-typed lambda-expressions (extended version)

03/17/2018
by   Matthias Weber, et al.
0

We present the type system d, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. d extends existing lambda-typed systems by an existential abstraction operator as well as propositional operators. β-reduction is extended to also normalize negated expressions using a subset of the laws of classical negation, hence d is normalizing both proofs and formulas which are handled uniformly as functional expressions. d is using a reflexive typing axiom for a constant τ to which no function can be typed. Some properties are shown including confluence, subject reduction, uniqueness of types, strong normalization, and consistency. We illustrate how, when using d, due to its limited logical strength additional axioms must be added both for negation and for the mathematical structures whose deductions are to be formalized.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/21/2018

An extended type system with lambda-typed lambda-expressions

We present the system d, an extended type system with lambda-typed lambd...
research
04/09/2021

A Constructive Logic with Classical Proofs and Refutations (Extended Version)

We study a conservative extension of classical propositional logic disti...
research
01/08/2021

Polymorphic System I

System I is a simply-typed lambda calculus with pairs, extended with an ...
research
08/13/2018

The Delta-framework

We introduce the Delta-framework, LF-Delta, a dependent type theory base...
research
01/04/2023

Grammar construction methods for extended deterministic expressions

Extended regular expressions with counting and interleaving are widely u...
research
09/21/2021

Adding Negation to Lambda Mu

We present L, an extension of Parigot's λμ-calculus by adding negation a...
research
05/07/2019

A Type Theory for Defining Logics and Proofs

We describe a Martin-Löf-style dependent type theory, called Cocon, that...

Please sign up or login with your details

Forgot password? Click here to reset