Deriving the usual denotational equations from the filter-model meaning

Establish that the standard structural denotational semantics equations for the parallel streaming lambda calculus can be derived from, and coincide with, the notion of meaning defined via the filter model; in particular, prove that the usual equation-by-equation meaning function matches the filter-model interpretation for all terms.

Background

Instead of defining denotational semantics by structural recursion on syntax, the paper assigns meanings via a filter model of computation and value formulae, which in turn induces a Scott-style model through ideal completion.

The authors explicitly conjecture that the conventional equation-based meaning function can be recovered from this filter-based meaning, but they leave the proof open, indicating a connection yet to be formally established.