Call-by-Value Non-determinism in a Linear Logic Type Discipline

@article{DazCaro2013CallbyValueNI,
  title={Call-by-Value Non-determinism in a Linear Logic Type Discipline},
  author={Alejandro D{\'i}az-Caro and Giulio Manzonetto and Michele Pagani},
  journal={ArXiv},
  year={2013},
  volume={abs/1312.4507}
}
We consider the call-by-value λ-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard’s second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough… 

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References

SHOWING 1-10 OF 26 REFERENCES

Complexity of Strongly Normalising λ-Terms via Non-idempotent Intersection Types

TLDR
A typing system for the λ-calculus, with nonidempotent intersection types, and a result that is the counterpart of de Carvalho's result for linear head-reduction sequences.

A relational semantics for parallelism and non-determinism in a functional setting

Collapsing non-idempotent intersection types

TLDR
This work construction of a new model, which features a new duality, is presented, and how to use it for reducing normalization results in idempotent intersection types to purely combinatorial methods is explained.

Lambda-Calculi for (Strict) Parallel Functions

We introduce two ?-calculi and show that they are expressive for two canonical domains of parallel functions. The first calculus is an enrichment of the lazy, call-by-name ?-calculus with

A Filter Model for Concurrent lambda-Calculus

TLDR
Type-free lazy $\lambda$-calculus is enriched with angelic parallelism and demonic nondeterminism, and the induced logical semantics is fully abstract.

Free-Algebra Models for the pi-Calculus

TLDR
A novel algebraic description for models of the @p-calculus is obtained, and an existing construction is validated as the universal such model, and it is generalised to prove that all free-algebra models are fully abstract.

Linear-algebraic lambda-calculus: higher-order, encodings, and confluence

TLDR
A minimal language combining higher-ordercomputation and linear algebra is introduced, and the confluence of the calculus is proved, this is the main result.

Domains and lambda-calculi

TLDR
This chapter discusses the development of lambda-calculi in CCC's of algebraic dcpo's, as well as its applications in recursion theory and category theory.