probability

probability is an agent for coding agents from Verified-zkEVM/VCVio. It costs 0 tokens per session (6,961 once invoked), scanned A, original, Apache-2.0.

A guide to representing probability in software and mathematical proofs using measures, kernels, and probability computations. A measure describes how probability is distributed, while a kernel describes probability that depends on an environment or state.

In plain words
What is it for?
Use it when designing or proving probabilistic programs, evaluating distributions, modeling state-dependent probability, or translating between discrete probability notation and measure-based semantics.
Why use it?
It provides one agreed meaning for probability across different kinds of computations and keeps older discrete notation connected to the newer measure-based representation. This reduces confusion when moving between probability APIs and proofs.

Agent

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

agentmods
npx agentmods add agents/verified-zkevm/vcvio/probability
Clone the repo
git clone --depth 1 https://github.com/Verified-zkEVM/VCVio

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for probability

README.md
[![agentmods](https://agentmods.dev/badge/agents/verified-zkevm/vcvio/probability.svg)](https://agentmods.dev/agents/verified-zkevm/vcvio/probability)
Your own site
<a href="https://agentmods.dev/agents/verified-zkevm/vcvio/probability"><img src="https://agentmods.dev/badge/agents/verified-zkevm/vcvio/probability.svg" alt="Measured on agentmods" height="20"></a>
Per session 0 Only the description is in the session, so the agent can decide to use it. The body loads when it is invoked.
When invoked 6,961 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5 $0.00000 $0.06961
Opus 5 $0.00000 $0.03481
Sonnet 5 $0.00000 $0.01392
Haiku 4.5 $0.00000 $0.00696

Measured 3d ago against content hash 244f5608b015, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

probability scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 3d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

docs/agents/probability.md · 360 lines

How it starts

The opening of the file, as written. The whole thing — 360 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Probability Reasoning (EvalDist and ProbComp)

For the cross-project survey of SPMF, Mathlib measures and kernels, PolyFun coalgebraic limits, ArkLib, Bluebell/Iris, and possible long-term migration paths, see Probability Semantics for Computations: Landscape and Design Options. The accepted design for new work is Denotational Probability Semantics: use Mathlib measures for closed denotations, kernels for environment/state-indexed computations, effect-preserving outcome types for transformers, and keep Pr[...] as the discrete compatibility surface. docs/reading/ indexes the full design record.

The primary notation is now measure-valued: 𝒟[mx] : Measure α. The former finite distribution API is explicit as evalSPMF mx / 𝒮[mx]. Pr[...] remains the discrete compatibility façade; theorems probOutput_eq_evalSPMF_toMeasure, probEvent_eq_evalSPMF_toMeasure, and probFailure_eq_evalSPMF_toMeasure state its meaning through the explicit compatibility measure. Direct FreeM measure semantics has corresponding FreeM.evalDist_apply_singleton and FreeM.evalDist_apply_setOf coherence lemmas. This split is intentional. An unconditional Eq.rec law for Pr[...] only needs equality of result types in the discrete façade, whereas a measure denotation also depends on the selected MeasurableSpace; type equality does not identify those structures. We therefore do not install a blanket finite-type measurable-space instance.

evalDist_eq_evalSPMF_toMeasure is the sole deprecated whole-denotation bridge. It applies to the canonical compatibility adapter; measure-native semantics should remain on 𝒟[…] instead of round-tripping through the finite backend.

Core Definitions

Definition Type Notation Defined in
evalDist mx Measure α 𝒟[mx] EvalDist/Defs/Measure.lean
evalSPMF mx SPMF α 𝒮[mx] EvalDist/Defs/Basic.lean
probOutput mx x ℝ≥0∞ Pr[= x | mx] EvalDist/Defs/Basic.lean
probEvent mx p ℝ≥0∞ Pr[p | mx] EvalDist/Defs/Basic.lean
probFailure mx ℝ≥0∞ Pr[⊥ | mx] EvalDist/Defs/Basic.lean
support mx Set α EvalDist/Defs/Support.lean
finSupport mx Finset α EvalDist/Defs/Support.lean

Read the full file on GitHub · 360 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 3d ago First seen · 360 lines · 0 tokens per session scan A 244f5608b015

Subscribe to this mod's changes

probability is an agent published in the GitHub repository Verified-zkEVM/VCVio (142 stars, last pushed 4d ago), licensed Apache-2.0. It costs nothing until one of its globs matches a file; then it loads 6,961 tokens. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.

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