Download PDFOpen PDF in browserA typed parallel lambda-calculus via 1-depth intermediate proofs22 pages•Published: May 27, 2020AbstractWe 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.
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