A typed parallel lambda-calculus via 1-depth intermediate proofs

22 pages•Published: May 27, 2020

Federico Aschieri, Agata Ciabattoni and Francesco Antonio Genco

Abstract

We introduce a Curry–Howard correspondence for a large class of intermediate logics characterized by intuitionistic proofs with non-nested applications of rules for classical disjunctive tautologies (1-depth intermediate proofs). The resulting calculus, we call it λ∥, is a strongly normalizing parallel extension of the simply typed λ-calculus. Although simple, the λ∥ reduction rules can model arbitrary process network topologies, and encode interesting parallel programs ranging from numeric computation to algorithms on graphs.

Keyphrases: functional programming languages, hypersequent calculi, intermediate logics, lambda calculus, natural deduction, type theory

In: Elvira Albert and Laura Kovacs (editors). LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 68-89.

Links:	https://easychair.org/publications/paper/hPQJ
	https://doi.org/10.29007/g15z

BibTeX entry

@inproceedings{LPAR23:typed_parallel_lambda_calculus,
  author    = {Federico Aschieri and Agata Ciabattoni and Francesco Antonio Genco},
  title     = {A typed parallel lambda-calculus via 1-depth intermediate proofs},
  booktitle = {LPAR23. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Elvira Albert and Laura Kovacs},
  series    = {EPiC Series in Computing},
  volume    = {73},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/hPQJ},
  doi       = {10.29007/g15z},
  pages     = {68-89},
  year      = {2020}}

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