lambdaI
Lambdai is a fictional formalism in the field of theoretical computer science, conceived as a variant of the lambda calculus that uses explicit indexing on variables to manage scope and resource usage. The term combines "lambda" with "i" to indicate indexed variables. In Lambdai, expressions are built from variables x_i, abstractions λx_i.M, and applications M N, where i is an index indicating the binding level or resource annotation. The indices support a canonical representation of binding and help avoid alpha-conversion because substitution can be performed with explicit indices.
Evaluation follows a beta-like rule, adapted to index-aware substitution, where the bound variable’s index is propagated
Lambdai is closely related to de Bruijn index representations and to the simply typed lambda calculus. It
Applications and usage are primarily academic, serving as a teaching tool for illustrating indexed binding and