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invert

Read-onlyIdempotent

Swaps a contract’s inputs and outputs to produce its reciprocal environment view, enabling assume-guarantee reasoning from the environment perspective.

Instructions

Reciprocal (G, A): the contract seen from its environment. Inputs become outputs and outputs inputs.

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": {
      "contract": "<contract>"
    },
    "name": "invert"
  }
}

Input Schema

Name	Required	Description	Default
`name`	No
`contract`	Yes

Schema Changelog

Changes observed during successful MCP inspections.

Changed1 schema field changedv0.7.0Nov 2, 2026

addedInput schema / $defs / ContractSpec / properties / constants

Added value: +{
+  "additionalProperties": {
+    "anyOf": [
+      {
+        "type": "integer"
+      },
+      {
+        "type": "number"
+      }
+    ]
+  },
+  "description": "Named constants: name -> value; the formulas use the names (repair changes them)",
+  "title": "Constants",
+  "type": "object"
+}

Changed4 schema fields changedv0.4.2Oct 29, 2026

changedInput schema / $defs / ContractSpec / properties / inputs / additionalProperties / anyOf

Previous value: -[
-  {
-    "enum": [
-      "bool",
-      "real"
-    ],
-    "type": "string"
-  },
-  {
-    "maxItems": 2,
-    "minItems": 2,
-    "prefixItems": [
-      {
-        "type": "integer"
-      },
-      {
-        "type": "integer"
-      }
-    ],
-    "type": "array"
-  }
-]New value: +[
+  {
+    "enum": [
+      "bool",
+      "real"
+    ],
+    "type": "string"
+  },
+  {
+    "maxItems": 2,
+    "minItems": 2,
+    "prefixItems": [
+      {
+        "type": "integer"
+      },
+      {
+        "type": "integer"
+      }
+    ],
+    "type": "array"
+  },
+  {
+    "pattern": "^(signed |unsigned )?word\\[[1-9][0-9]*\\]$",
+    "type": "string"
+  }
+]

changedInput schema / $defs / ContractSpec / properties / inputs / description

Previous value: -"Input variables: \"bool\", [low, high], or \"real\""New value: +"Input variables: \"bool\", [low, high], \"real\", or \"word[n]\" (\"signed word[n]\")"

changedInput schema / $defs / ContractSpec / properties / outputs / additionalProperties / anyOf

Previous value: -[
-  {
-    "enum": [
-      "bool",
-      "real"
-    ],
-    "type": "string"
-  },
-  {
-    "maxItems": 2,
-    "minItems": 2,
-    "prefixItems": [
-      {
-        "type": "integer"
-      },
-      {
-        "type": "integer"
-      }
-    ],
-    "type": "array"
-  }
-]New value: +[
+  {
+    "enum": [
+      "bool",
+      "real"
+    ],
+    "type": "string"
+  },
+  {
+    "maxItems": 2,
+    "minItems": 2,
+    "prefixItems": [
+      {
+        "type": "integer"
+      },
+      {
+        "type": "integer"
+      }
+    ],
+    "type": "array"
+  },
+  {
+    "pattern": "^(signed |unsigned )?word\\[[1-9][0-9]*\\]$",
+    "type": "string"
+  }
+]

changedInput schema / $defs / ContractSpec / properties / outputs / description

Previous value: -"Output variables: \"bool\", [low, high], or \"real\""New value: +"Output variables: \"bool\", [low, high], \"real\", or \"word[n]\" (\"signed word[n]\")"

First observedv0.3.1Oct 27, 2026

TDQS

C2.9/5.0

Behavior3/5

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

Annotations already declare readOnlyHint, idempotentHint, and openWorldHint=false, so safety and purity are covered. The description adds the core behavioral semantic — that the returned contract has its input and output sets exchanged. It does not say whether the original contract object is untouched, whether guarantees/assumptions are also complemented or reordered, or what the optional name overrides.

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

Conciseness4/5

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

Two compact sentences, front-loaded with the defining transformation and free of filler. The parenthetical '(G, A)' is somewhat cryptic for anyone outside contract algebra, but the second sentence immediately disambiguates it.

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

Completeness2/5

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

There is no output schema, so the description should describe what is produced and how the optional name affects the result; it does neither. For a pure transformation tool taking a structured ContractSpec, an agent is left guessing about the return shape and about edge cases such as inverting a contract with assumptions/guarantees.

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

Parameters2/5

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

Schema description coverage is reported as 0%; the top-level 'name' parameter has no description anywhere, and the description never explains whether it renames the returned contract or labels it. The nested ContractSpec fields carry their own schema docs, but the description itself contributes no parameter-level meaning, so it does not compensate for the coverage gap.

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

Purpose4/5

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

The description names a specific transformation: a contract is viewed from its environment, with inputs and outputs swapped. 'Reciprocal' plus the input/output swap gives an agent a concrete mental model of the operation. It does not, however, use a plain verb or contrast the operation with related siblings such as divide, separate, or coimply, which also manipulate a contract's polarity.

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

Usage Guidelines2/5

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

There is no statement of when this operation is appropriate, what precondition the contract must satisfy (e.g. well-separatedness), or which sibling to use instead for related tasks like implication reordering. The agent must infer applicability purely from the mathematical gloss.

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