notation

A notation reference for OracleSpec, probability, and related mathematical expressions in the VCVio codebase. It also explains the newer notation that should be used in new code.

In plain words
What is it for?
Looking up what expressions such as Pr[...] or A →ₒ B mean and choosing the correct notation when editing formal code or comments.
Why use it?
It reduces confusion when older code uses different symbols from the current conventions.

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/notation
Clone the repo
git clone --depth 1 https://github.com/Verified-zkEVM/VCVio
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 1,559 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 $0.01559
Opus 5 $0.00000 $0.00779
Sonnet 5 $0.00000 $0.00312
Haiku 4.5 $0.00000 $0.00156

Measured 3d ago against content hash bf7dd57ef277, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

notation 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/notation.md · 86 lines

How it starts

The opening of the file, as written. The whole thing — 86 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Notation Reference

OracleSpec Notations

Notation Meaning Defined in
A →ₒ B Singleton oracle spec (OracleSpec.ofFn) VCVio/OracleComp/OracleSpec.lean
[]ₒ Empty oracle spec (emptySpec) VCVio/OracleComp/OracleSpec.lean
spec₁ + spec₂ PFunctor coproduct (dependent Sum.rec) VCVio/OracleComp/OracleSpec.lean
⊂ₒ SubSpec relation VCVio/OracleComp/Coercions/SubSpec.lean
∘ₛ QueryImpl composition VCVio/OracleComp/SimSemantics/QueryImpl/Constructions.lean

Probability Notations

Notation Meaning Defined in
𝒟[mx] primary Measure denotation, evalDist mx VCVio/EvalDist/Defs/Measure.lean
𝒮[mx] explicit finite adapter, evalSPMF mx VCVio/EvalDist/Defs/Basic.lean
Pr[= x | mx] probOutput mx x VCVio/EvalDist/Defs/Basic.lean
Pr[p | mx] probEvent mx p VCVio/EvalDist/Defs/Basic.lean
Pr[⊥ | mx] probFailure mx VCVio/EvalDist/Defs/Basic.lean
Pr[cond | var ← src] probEvent src (fun var => cond) VCVio/EvalDist/Defs/Basic.lean

NOTE: Legacy code and comments may still use the old [= x | comp] notation (without Pr prefix). Always use Pr[...] in new code.

Pr[...] is a discrete compatibility notation. Use probOutput_eq_evalDist, probEvent_eq_evalDist, or probFailure_eq_evalDist to move a scalar statement to 𝒟[...].

Sampling Notations

Notation Meaning Defined in
$ᵗ T uniformSample T (type-level uniform) VCVio/OracleComp/Constructions/SampleableType.lean
$ xs uniformSelect xs (can fail on empty) VCVio/OracleComp/ProbComp.lean
$! xs uniformSelect! xs (never fails) VCVio/OracleComp/ProbComp.lean
$[0..n] uniformFin n (uniform Fin (n+1)) VCVio/OracleComp/ProbComp.lean
$[n⋯m] uniformRange n m (uniform over range) VCVio/OracleComp/ProbComp.lean

Read the full file on GitHub · 86 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 · 86 lines · 0 tokens per session scan A bf7dd57ef277

Subscribe to this mod's changes

notation 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 1,559 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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