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Oxyo (oxyo.si) — Cut Coding Agent Token & Quota Burn by up to 72%

by io.github.Eno654
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oxyo_prove_constraints

Read-onlyIdempotent

Solve bounded discrete constraint systems (action='satisfy' with optional minimize/maximize) or prove universal invariants (action='prove', returning a formal proof or minimal counterexample). Use for declarative constraint/invariant models; use oxyo_verify_python for general Python scripts.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "variables": "<variables>"
    },
    "name": "oxyo_prove_constraints"
  }
}

Input Schema

NameRequiredDescriptionDefault
claimNoBoolean invariant expression that must hold across all valid states (for action='prove').
senseNoOptimization direction ('minimize' or 'maximize') when `objective` is provided.minimize
actionNoChoose 'prove' to verify `assumptions => claim` universally, or 'satisfy' to find an assignment.prove
objectiveNoOptional arithmetic expression to optimize across valid assignments (for action='satisfy').
variablesYesBounded variable domain map, e.g. {'x': {'type': 'int', 'min': 0, 'max': 50}}.
assumptionsNoPrecondition boolean expressions constraining valid input states (for action='prove').
constraintsNoBoolean constraint expressions that a solution must satisfy (for action='satisfy').

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed7 schema fields changed
    • addedInput schema / properties / action / description
      Added value: +"Choose 'prove' to verify `assumptions => claim` universally, or 'satisfy' to find an assignment."
    • changedInput schema / properties / assumptions / description
      Previous value: -"Precondition constraints for action='prove'"New value: +"Precondition boolean expressions constraining valid input states (for action='prove')."
    • changedInput schema / properties / claim / description
      Previous value: -"Universal invariant expression to prove (for action='prove')"New value: +"Boolean invariant expression that must hold across all valid states (for action='prove')."
    • changedInput schema / properties / constraints / description
      Previous value: -"Symbolic constraints to satisfy (for action='satisfy')"New value: +"Boolean constraint expressions that a solution must satisfy (for action='satisfy')."
    • changedInput schema / properties / objective / description
      Previous value: -"Optional algebraic objective to optimize (for action='satisfy')"New value: +"Optional arithmetic expression to optimize across valid assignments (for action='satisfy')."
    • addedInput schema / properties / sense / description
      Added value: +"Optimization direction ('minimize' or 'maximize') when `objective` is provided."
    • changedInput schema / properties / variables / description
      Previous value: -"Map of variable specs, e.g. {'x': {'type': 'int', 'min': 1, 'max': 20}}"New value: +"Bounded variable domain map, e.g. {'x': {'type': 'int', 'min': 0, 'max': 50}}."
  2. First observed

TDQS

A4.6/5.0
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover safety (readOnlyHint, idempotentHint, destructiveHint=false, closed-world), so the bar is lower, and the description still adds real behavioral context: 'prove' returns a formal proof or a minimal counterexample, 'satisfy' returns an assignment, and optimization is optional. What is missing is guidance on complexity or time limits for these bounded systems, so it falls short of a 5.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two tight sentences with no filler: the capability statement comes first, the mode split comes second, and the sibling routing comes last. Every clause carries information an agent can act on.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a 7-parameter tool with nested objects and no output schema, the description does a solid job of explaining what 'prove' yields (proof or counterexample). It stops short of describing the shape of a 'satisfy' result (assignment plus objective value), which is the one gap an agent might want filled.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, so the baseline is 3, but the description goes further by linking parameters to modes — `minimize`/`maximize` only apply under 'satisfy' with an objective, while proving consumes the invariant. This cross-parameter relationship adds meaning beyond the per-field enum and type descriptions the schema already provides.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb and resource pair — solving bounded discrete constraint systems and proving universal invariants — and ties each to the `action` value ('satisfy' vs 'prove'). It also names the sibling it is not (`oxyo_verify_python`), so an agent can distinguish it from alternatives without opening any schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines5/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

It gives explicit routing: use this for declarative constraint/invariant models, use `oxyo_verify_python` for general Python scripts. The condition that selects the alternative is stated directly rather than implied, which is exactly what an agent needs to choose between the two.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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