Appendices to “Environmental Bisimulations for Higher-Order Languages”
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چکیده
On these elements, clause (1.b) is immediate: if C[Ṽ ] is a value, then also C[W̃ ] is a value and they are in E. This is sufficient, because E∈ X . Clause (1.a) is proved by an induction on C. The details are easy: the only possible case is C = C1C2; we use the fact that if λx.P E λx.Q, and V E W , and E ∈ Y , then (P{V/x}, Q{W/x}) ∈ XE′ for some E ′ with E ⊆ E ′, which follows from the definition of bisimulation (we exploit here the peculiarity of clause (2) of environmental bisimulations on abstractions). The requirements for elements of the form
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