Studia Logica 103 (6):1225-1244 (2015)

Abstract
The third author gave a natural deduction style proof system called the \-calculus for implicational fragment of classical logic in. In -calculus, 2015, Post-proceedings of the RIMS Workshop “Proof Theory, Computability Theory and Related Issues”, to appear), the fourth author gave a natural subsystem “intuitionistic \-calculus” of the \-calculus, and showed the system corresponds to intuitionistic logic. The proof is given with tree sequent calculus, but is complicated. In this paper, we introduce some reduction rules for the \-calculus, and give a simple and purely syntactical proof to the theorem by use of the reduction. In addition, we show that we can give a computation model with rich expressive power with our system
Keywords $${{\lambda}{\rho}}$$ λ ρ -calculus  Curry–Howard isomorphism  Intuitionistic logic  Proof theory
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DOI 10.1007/s11225-015-9616-1
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