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Full abstraction of the filter model

Prove that the filter-model semantics assigning computation and value formulae to terms of the parallel streaming lambda calculus is fully abstract with respect to contextual equivalence induced by the paper’s approximate operational semantics; that is, show equivalence in the model if and only if contextual equivalence holds operationally.

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Background

The paper defines an approximate operational semantics with nondeterministic approximation steps and a denotational (filter-model) semantics, proving computational adequacy. It also shows that the filter model gives rise to a Scott-style domain model.

Drawing on classic results that connect parallel-or to full abstraction, the authors note their join operator encodes parallel-or and conjecture that this should yield full abstraction for their filter model, but they do not prove it.

References

We demonstrated how to encode parallel or using the join operator in #1{sec:por} and conjecture that, as a result, our filter model is fully abstract.

— Functional Meaning for Parallel Streaming (2504.02975 - Rioux et al., 3 Apr 2025) in Related Work, paragraph “Domain Theory and Concurrent Lambda Calculi”