Compositional Characterizations of λ-Terms Using Intersection Types

A Behavioural Model for Klop's Calculus

“…We denote by derivability in this system. It is easy to verify that strengthening and weakening are admissible rules in this system: Γ, x: σ S : τ x ∈ F V (S) Γ S : τ Γ S : τ x ∈ Γ Γ, x: σ S : τ The type assignment system enjoys a Generation Lemma whose restriction to Λ is proved in [3]. The proof of the last clause which is the only new clause follows easily by induction on deductions.…”

Tailoring Filter Models

“…Before characterizing (restricted) filter models we need a technical result on typing properties of strongly normalizing terms: for a proof see [13].…”

Verification of Substitution Theorem Using HOL

“…The proof in Ref. [2] is complicated and confusing. We can simplify their proof by using AC(M, S , n).…”

“…The formalization of the proof of Lemma 2.8, which is Lemma A13 of Ref. [2], is given in Ref. [8] and the details of its verification will be fully discussed in another paper.…”