Abstract
To every partial inductive definitionD, a natural deduction calculusND(D) is associated. Not every such system will have the normalization property; specifically, there are definitionsD′ for whichND(D′) permits non-normalizable deductions. A lambda calculus is formulated where the terms are used as objects realizing deductions inND(D), and is shown to have the Church-Rosser property. SinceND(D) permits non-normalizable deductions, there will be typed terms which are non-normalizable. It will, for example, be possible to obtain a typed fixed-point operator.
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