Removing recursive types from the elementary affine lambda calculus reduces the predicate type !Str⊸!!Bool from polynomial time to exactly the regular languages, while the fixpoint version gains a Church-encoding-only characterization of FP and k-FEXPTIME.
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On the Elementary Affine Lambda-Calculus with and Without Fixed Points
Removing recursive types from the elementary affine lambda calculus reduces the predicate type !Str⊸!!Bool from polynomial time to exactly the regular languages, while the fixpoint version gains a Church-encoding-only characterization of FP and k-FEXPTIME.