Standard and normal reductions
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- by R. Hindley PDF
- Trans. Amer. Math. Soc. 241 (1978), 253-271 Request permission
Abstract:
Curry and Feys’ original standardization proof for $\lambda \beta$-reduction is analyzed and generalized to $\lambda \beta \eta$-reductions with extra operators. There seem to be two slightly different definitions of ’standard reduction’ in current use, without any awareness that they are different; it is proved that although these definitions turn out to be equivalent for $\lambda \beta$-reduction, they become different for $\lambda \beta \eta$ and for reductions involving extra operators, for example the recursion operator. Normal reductions are also studied, and it is shown that the basic normal-reduction theorem stays true when fairly simple operators like Church’s $\delta$ and Curry’s iterator Z are added, but fails for more complicated ones like the recursion operator R. Finally, a table is given summarizing the results, and showing how far the main theorems on $\lambda \beta$-reductions extend to reductions with various extra operators.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 241 (1978), 253-271
- MSC: Primary 03B40
- DOI: https://doi.org/10.1090/S0002-9947-1978-0492300-7
- MathSciNet review: 492300