ON TYPED AND UNTYPED LAMBDA-TERMS

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Submitted: 2025-02-11; Published: 2025-02-11

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Abstract

Typedλ-terms that use variables of any order and don’t use constants oforder>1 are studied in the paper. An algorithm of translation of typedλ-terms to untypedλ-terms is presented. According to that algorithm, eachtyped termtis mapped to an untyped termt′. We study in which case typedtermst1,t2such thatt1→→β δt2correspond to untyped termst1′,t2′such thatt1′→→βt2′.