Analysis of bounds for lengths of reductions in typed λ-calculus - Tigran M. Galoyan (Изд-во НАН РА)
We analyze bounds for the lengths of arbitrary reduction sequences of terms in typed λ-calculus, consider some estimates obtained by the other authors and compare these estimates. The cut elimination and normalization algorithms are also investigated in this paper. Thereafter we refine the estimates achieved in [3] (for pure implicational logic only) by supplement of η-conversion and then we extend evaluations to first-order logic.
Keywords: Mathematics