abstract="The notion of parallel reduction is extracted from the Tait-Martin-Löf proof of the Church-Rosser theorem (for β-reduction). We define parallel β-, η- and βη-reduction by induction, and use them to give simple proofs of some fundamental theorems in λ-calculus; the normal reduction theorem for β-reduction, that for βη-reduction, the postponement theorem of η-reduction (in βη-reduction), and some others."

}

@book{Bar84,

author={H. P. Barendregt},

title={The Lambda Calculus Its Syntax and Semantics},