DeepAI AI Chat
Log In Sign Up

Linear Additives

by   Gianluca Curzi, et al.

We introduce 𝖫𝖠𝖬, a subsystem of 𝖨𝖬𝖠𝖫𝖫_2 with restricted additive rules able to manage duplication linearly, called linear additive rules. 𝖫𝖠𝖬 is presented as the type assignment system for a calculus endowed with copy constructors, which deal with substitution in a linear fashion. As opposed to the standard additive rules, the linear additive rules do not affect the complexity of term reduction: typable terms of 𝖫𝖠𝖬 enjoy linear strong normalization. Moreover, a mildly weakened version of cut-elimination for this system is proven which takes a cubic number of steps. Finally, we define a sound translation from 𝖫𝖠𝖬's proofs into 𝖨𝖬𝖫𝖫_2's linear lambda terms, and we study its complexity.


page 1

page 2

page 3

page 4


A type-assignment of linear erasure and duplication

We introduce LEM, a type-assignment system for the linear λ-calculus tha...

Exponentials as Substitutions and the Cost of Cut Elimination in Linear Logic

This paper introduces the exponential substitution calculus (ESC), a new...

Bouncing threads for infinitary and circular proofs

We generalize the validity criterion for the infinitary proof system of ...

Adding Negation to Lambda Mu

We present L, an extension of Parigot's λμ-calculus by adding negation a...

Admissible Tools in the Kitchen of Intuitionistic Logic

The usual reading of logical implication "A implies B" as "if A then B" ...

Towards Algorithmic Typing for DOT

The Dependent Object Types (DOT) calculus formalizes key features of Sca...

Probabilistic Soft Type Assignment

We model randomized complexity classes in the style of Implicit Computat...