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

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 $λ_{\parallel}$, is a strongly normalizing parallel extension of the simply typed $λ$-calculus. Although simple, the $λ_{\parallel}$ reduction rules can model arbitrary process network topologies, and encode interesting parallel programs ranging from numeric computation to algorithms on graphs.

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