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.
Then there exists a context C2 such that C1 = C⟨C2⟩, and we have that t{{ x := ¯s}} = C2⟨(λ ℓ′ y.u )¯r⟩
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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.