A confluent non-idempotent intersection type system for lambda-calculus induces a factorization of derivation spaces into garbage-free prefixes and garbage using a variant of the Grothendieck construction.
There are three subcases, depending on whether the step t′→ # s′ takes place at the root, inside u′, or inside r′ i for some i = 1..n , 3.1 Reduction at the root
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Factoring Derivation Spaces via Intersection Types (Extended Version)
A confluent non-idempotent intersection type system for lambda-calculus induces a factorization of derivation spaces into garbage-free prefixes and garbage using a variant of the Grothendieck construction.