# On the denotational semantics of Linear Logic with least and greatest fixed points of formulas

## TL;DR

This paper develops a denotational semantics for Linear Logic with fixed points across various models, and demonstrates how G{"o}del System T can be embedded into it, highlighting its expressive power.

## Contribution

It introduces a unified denotational semantics for Linear Logic with fixed points and embeds G{"o}del System T, enhancing understanding of their expressive capabilities.

## Key findings

- Denotational semantics for LL with fixed points in coherence spaces and totality models.
- Embedding of G{"o}del System T into LL with fixed points.
- Demonstrates expressive power and normalization properties of the system.

## Abstract

We develop a denotational semantics of Linear Logic with least and greatest fixed points in coherence spaces (where both fixed points are interpreted in the same way) and in coherence spaces with totality (where they have different interpretations). These constructions can be carried out in many different denotational models of LL (hypercoherences, Scott semantics, finiteness spaces etc). We also present a natural embedding of G{\"o}del System T in LL with fixed points thus enforcing the expressive power of this system as a programming language featuring both normalization and a huge expressive power in terms of data types.