Evidence-Tracked Tape Semantics for Probabilistic Computation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915991703781376 |
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| author | Cohen, Liron Samara, Tomer |
| author_facet | Cohen, Liron Samara, Tomer |
| contents | A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of randomness and correlation visible, and an extensional layer obtained by interpreting tapes under a chosen probability measure.
We develop an evidence-tracked tape semantics using the monadic-core-to-evidenced-frame pipeline (and its induced realizability tripos), obtaining a higher-order logic in which entailments are witnessed by uniform evidence transformers. Quantitative statements are recovered by interpretation: once a tape measure is fixed, probabilities and expectations arise by extracting numerical summaries from tape-indexed predicates, and entailments yield sound inequalities, with an almost-sure quotient supporting probability-one reasoning. We also study intensional principles that are lost at the level of laws, including proof-relevant transport along realizable tape-rewiring maps and a canonical splitting discipline for stream tapes enforcing independent draws. Finally, we relate tape-based reasoning to an extensional law semantics via pushforward, isolating a probability-one must abstraction as a sound summary of tape-based proofs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_07259 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Evidence-Tracked Tape Semantics for Probabilistic Computation Cohen, Liron Samara, Tomer Logic in Computer Science A standard intensional account of probabilistic computation represents a randomized program as a deterministic computation that consumes an explicit random tape. This yields a two-layer perspective: an intensional layer that makes reuse of randomness and correlation visible, and an extensional layer obtained by interpreting tapes under a chosen probability measure. We develop an evidence-tracked tape semantics using the monadic-core-to-evidenced-frame pipeline (and its induced realizability tripos), obtaining a higher-order logic in which entailments are witnessed by uniform evidence transformers. Quantitative statements are recovered by interpretation: once a tape measure is fixed, probabilities and expectations arise by extracting numerical summaries from tape-indexed predicates, and entailments yield sound inequalities, with an almost-sure quotient supporting probability-one reasoning. We also study intensional principles that are lost at the level of laws, including proof-relevant transport along realizable tape-rewiring maps and a canonical splitting discipline for stream tapes enforcing independent draws. Finally, we relate tape-based reasoning to an extensional law semantics via pushforward, isolating a probability-one must abstraction as a sound summary of tape-based proofs. |
| title | Evidence-Tracked Tape Semantics for Probabilistic Computation |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2605.07259 |