# The Delta-calculus: syntax and types

@article{Liquori2019TheDS, title={The Delta-calculus: syntax and types}, author={Luigi Liquori and Claude Stolze}, journal={ArXiv}, year={2019}, volume={abs/1803.09660} }

We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Salle', the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection type systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization…

## 7 Citations

### A Type Checker for a Logical Framework with Union and Intersection Types

- Computer ScienceFSCD
- 2020

We present the syntax, semantics, and typing rules of Bull, a prototype theorem prover based on the Delta-Framework, i.e. a fully-typed lambda-calculus decorated with union and intersection types, as…

### The Delta-framework

- MathematicsFSTTCS
- 2018

We introduce the Delta-framework, LF-Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection,…

### Manifest Contracts with Intersection Types

- Computer Science, MathematicsAPLAS
- 2019

A formal definition of PCFv$\Delta$H is given and its basic properties as a manifest contract system: preservation, progress, and value inversion are shown and it is shown that run-time checking does not affect essential computation.

### Non-idempotent Intersection Types in Logical Form

- MathematicsFoSSaCS
- 2020

It is shown that non-idempotent typing can be given a logical form in a system where formulas represent hereditarily indexed families of intersection types.

### Kripke Semantics for Intersection Formulas

- MathematicsACM Trans. Comput. Log.
- 2021

A notion of the Kripke-style model for intersection logic is proposed, and a game interpretation is used to prove soundness and completeness of the proposed semantics.

### Principality and approximation under dimensional bound

- Mathematics, Computer ScienceProc. ACM Program. Lang.
- 2019

Finite, computable bases are shown to span standard principal typings of a given term for sufficiently high dimension, thereby providing an approximation to standard principality by type inference, and capturing it precisely for sufficiently large dimensional parameter.

### A Typed Lambda Calculus with Gradual Intersection Types

- Computer ScienceProceedings of the 24th International Symposium on Principles and Practice of Declarative Programming
- 2022

This work incorporates intersection types and gradual types in a single typed calculus and defines an operational semantics with type cast annotations that proves several crucial properties of the type system, namely that types are preserved during compilation and evaluation and that the refined criteria for gradual typing holds.

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