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coimply

Read-onlyIdempotent

Computes the coimplication of two assume-guarantee contracts: the smallest contract C such that the second refines C ∨ first, supporting LTL refinement checks.

Instructions

Coimplication, the adjoint of disjunction: the smallest contract C such that second refines the disjunction of C and first. (A2 | !A1, (G2 & !G1) | (A1 & !A2)), with first = (A1, G1).

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": {
      "first": "<first>",
      "second": "<second>"
    },
    "name": "coimply"
  }
}

Input Schema

Name	Required	Description	Default
`name`	No
`first`	Yes
`second`	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

B3.2/5.0

Behavior4/5

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

Annotations already establish read-only, idempotent, closed-world behavior. The description adds the exact output formula for the resulting contract's assumptions and guarantees, which is valuable behavioral context, though it omits return format and error behavior.

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 dense sentences with no filler, front-loaded with the operation name and definition. The formula is essential to the operation, so the brevity is appropriate.

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?

For a complex contract-algebra operation with no output schema and low parameter description coverage, the definition is too sparse. It does not explain how to supply first/second/name or what the returned contract looks like beyond the formula.

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?

Top-level schema coverage is 0%; the description mentions first = (A1, G1) and uses A2/G2 for second, but never explains the name parameter or clearly defines second's structure. It only partially compensates for the missing parameter documentation.

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 the operation and defines it precisely as the adjoint of disjunction with a formal condition. This distinguishes it from disjoin, though it does not explicitly contrast with the sibling imply.

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?

No when-to-use guidance or alternatives are given. The mathematical condition implies the operation but does not tell an agent when to choose it over imply, disjoin, or conjoin.

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