Logical Relations for Encryption

Logical Relation for Type
Abstraction (also standard)
The relation environment ϕ gives the relation ϕ(α)
between values of each abstract type α
ϕv 1 ∼ v 2 : α⇔ (v 1 , v 2 ) ∈ ϕ(α)
ϕpack σ 1 , e 1 as ∃α.τ
∼ pack σ 2 , e 2 as ∃α.τ : ∃α.τ⇔
ϕ, α a re 1 ∼ e 2 : τ for some r ⊆ σ 1 × σ 2
E.g., pack int, 〈1, λx. x mod 2〉 as ∃α.α×(α→int)
and pack int, 〈3, λx. x mod 2〉 as ∃α.α×(α→int)
can be related by taking α a {(1,3)}