ABSTRACT
This research proposes a program to characterize Lawvere-Tierney topologies for computational effects beyond CPS, including state, exceptions, nondeterminism, and probabilistic computation. It develops a framework connecting monad-induced effects, evidenced frames, Lawvere-Tierney topologies, and sheafification.
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Key findings
Establishes a deep connection between double negation topology and CPS computations.
Proposes specific topology candidates for various computational effects.
Outlines a research agenda for establishing semantic correspondences.
Limitations & open questions
Research is in the proposal stage, requiring further exploration and validation.