mcp-z3-prover
Server Quality Checklist
Latest release: v0.1.0
- Disambiguation5/5
Each tool has a clear, distinct purpose: variable creation for different types (bool, int, real) with separate creation of constants and variables, constraint addition, solving, optimization, model retrieval, listing, and reset. No overlap.
Naming Consistency5/5All tool names follow a consistent snake_case verb_noun pattern (e.g., create_int_var, add_constraint, get_model_value). No mixing of conventions.
Tool Count5/511 tools is well-scoped for a constraint solver. Each tool serves a necessary function without being overly granular or too sparse.
Completeness4/5Covers the core workflow: variable creation, constraints, solving, and model retrieval. Minor gaps exist, such as no push/pop for incremental solving or constraint deletion, but the essential operations are present.
Average 3.6/5 across 11 of 11 tools scored.
See the Tool Scores section below for per-tool breakdowns.
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- 0 commits in the last 12 weeks
- Last stable release on
- No critical vulnerability alerts
- No high-severity vulnerability alerts
- No code scanning findings
- CI is failing
This repository is licensed under MIT License.
This repository includes a README.md file.
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How is the quality score calculated?
The overall quality score combines two components: Tool Definition Quality (70%) and Server Coherence (30%).
Tool Definition Quality measures how well each tool describes itself to AI agents. Every tool is scored 1–5 across six dimensions: Purpose Clarity (25%), Usage Guidelines (20%), Behavioral Transparency (20%), Parameter Semantics (15%), Conciseness & Structure (10%), and Contextual Completeness (10%). The server-level definition quality score is calculated as 60% mean TDQS + 40% minimum TDQS, so a single poorly described tool pulls the score down.
Server Coherence evaluates how well the tools work together as a set, scoring four dimensions equally: Disambiguation (can agents tell tools apart?), Naming Consistency, Tool Count Appropriateness, and Completeness (are there gaps in the tool surface?).
Tiers are derived from the overall score: A (≥3.5), B (≥3.0), C (≥2.0), D (≥1.0), F (<1.0). B and above is considered passing.
Tool Scores
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must bear the full burden. It does not disclose potential side effects, naming rules, what happens if the variable already exists, or required permissions. Behavior is opaque beyond the basic action.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness3/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is very concise (one sentence) but lacks structure or front-loading of key points. While no word is wasted, it is overly minimal for a standard description.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (1 parameter, output schema exists), the description is adequate but does not cover error scenarios or return value details. It meets basic needs but leaves gaps for an AI agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% and the description adds no extra meaning beyond the schema's own description of the 'name' parameter. Baseline 3 is appropriate as the description is not misleading but adds no value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Create') and the resource ('Real (floating-point) variable'), effectively distinguishing from sibling tools like create_int_var and create_bool_var.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool versus alternatives, such as when to create a variable vs. a constant, or any prerequisites. Usage context is entirely implied.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries full burden but only says 'Create'. It does not disclose side effects (e.g., whether creating a duplicate constant is allowed), state modifications, or what happens in the solver context. This is minimal information.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single sentence with no wasted words. It is concise and front-loaded, though it lacks a more structured format.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the low complexity (1 parameter, high schema coverage, output schema present), the description is minimally adequate. However, it misses usage context and behavioral details that could help an agent choose this tool over alternatives.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so the schema already documents the parameter. The description adds 'with the given value' but does not elaborate on constraints or valid ranges beyond the schema, meeting the baseline expectation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description 'Create an integer constant with the given value' clearly states the action (create) and the resource (integer constant), and it distinguishes from sibling tools like 'create_int_var' or 'create_bool_var' which create variables of different types.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use an integer constant versus an integer variable or other siblings. No prerequisites or context are provided, leaving the agent without decision support.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, and the description contains no behavioral details beyond creation. It does not disclose side effects, permissions, or whether the variable is tied to a specific model.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness4/5Is the description appropriately sized, front-loaded, and free of redundancy?
Single sentence, no superfluous words. Efficient but very minimal; slightly more context would improve usability without harming conciseness.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
With an output schema present, the description does not need to explain return values. However, for a creation tool, missing details about variable scope, existence checks, or error handling leaves it incomplete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% (only parameter 'name' is fully described in schema). The description adds no extra meaning beyond 'with the given name', so it meets baseline but does not exceed.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
Description clearly states the action (create), resource (integer variable), and the input (name). It is specific enough to distinguish from sibling tools like create_bool_var or create_int_constant.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance on when to use this tool versus alternatives such as create_int_constant or create_real_var. The description does not specify context or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description lacks details on side effects, such as whether the variable is added to an existing model, implications for solver state, or any constraints on name uniqueness. With no annotations, the agent gets minimal insight into the tool's behavior.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, short sentence that efficiently conveys the primary action. It is front-loaded and contains no redundant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema (which likely covers return values), the description does not address context like when to choose this tool over siblings or what state changes occur. For a simple tool with one parameter, it is adequate but not comprehensive.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema already describes the 'name' parameter as 'The name of the boolean variable to create.' The description only adds 'with the given name,' which adds no new meaning. Schema coverage is 100%, so the baseline is 3, and no extra value is provided.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the action ('Create'), the resource ('Boolean variable'), and the scope ('with the given name'). This distinguishes it from sibling tools like create_int_var or create_real_var by specifying the data type.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives like create_int_var or create_real_var. There is no mention of prerequisites, context, or scenarios where one type is preferred.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations exist, so the description carries full burden. It only states creation without disclosing side effects, return behavior, or state changes. The tool likely returns a result (output schema exists) but this is not mentioned.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
A single, front-loaded sentence with no unnecessary words. Every part earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple tool with one parameter and an output schema, the description is minimally complete. However, lacking usage guidance and behavioral details, it does not fully aid an AI agent in correct invocation.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with a clear parameter description. The description adds no new meaning beyond 'with the given value' which merely restates the schema. Baseline 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states 'Create a real constant with the given value.' with a specific verb (create) and resource (real constant), and it distinguishes from sibling tools like create_int_constant and create_real_var.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No guidance is provided on when to use this tool versus alternatives, such as create_int_constant or create_real_var. There are no prerequisites, when-not-to-use, or context hints.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must disclose behavioral traits. It fails to mention side effects, error handling (e.g., on timeout or UNSAT), or whether the solver state is modified. The description only states basic function with no details on limitations or behavioral nuances.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is two sentences, concise and front-loaded with the primary purpose. Every sentence adds value without redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness2/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Despite having an output schema, the description lacks essential context such as ordering dependencies (e.g., constraints must be added first) and behavior on timeout or UNSAT. Given the tool's complexity as a solver, the description is incomplete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so the baseline is 3. The description does not add any further meaning to the 'timeout_ms' parameter beyond what the schema already provides, so no extra value.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves the current problem and checks constraints for satisfiability, returning a model if SAT. This verb-resource combination is specific and distinguishes it from siblings like 'optimize' and 'get_model_value'.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies use after adding constraints but does not explicitly state when to use this tool versus alternatives like 'optimize'. No exclusions or context are provided, missing guidance on when not to use it.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavior. It mentions 'after solving' but does not specify what happens if called before solving, with an invalid variable, or whether it requires the model to be solved. Lacks details on errors or side effects.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is a single, front-loaded sentence that conveys the core purpose without any wasted words. Every part earns its place.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness3/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's simplicity (one parameter, output schema exists), the description adequately states its purpose and condition. However, it lacks information on error behavior and prerequisites beyond 'after solving', which is a gap for a query tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100% with a clear example for the only parameter. The tool description adds no additional meaning beyond the schema, so baseline 3 is appropriate.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the verb 'Get the value of', the resource 'a variable from the model', and a condition 'after solving'. This distinguishes it from sibling tools like list_variables which only list variable names, not values.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines3/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implies usage after solving but does not explicitly state when not to use it or mention alternatives like list_variables for listing variable names. No guidance on prerequisites or error conditions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior2/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations provided, the description carries full burden. It only says 'Add a constraint to the solver' without disclosing side effects, reversibility, state modifications, or error conditions. The behavioral impact is minimally described.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
Three concise sentences: first states purpose, second provides parameter formatting guidance, third mentions API support. No fluff, front-loaded, every sentence serves a clear function.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple one-parameter tool with an output schema, the description covers the core behavior and input format. It does not mention return values or solver state prerequisites, but these are minor gaps given the tool's straightforward nature.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100% with a single parameter. The description adds valuable context: variable reference patterns ('bool:x', 'int:y', 'real:z') and syntax support, which significantly clarifies the expected input beyond the schema's brief description.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states 'Add a constraint to the solver' with a specific verb and resource. It further explains variable reference syntax and supported API, making the purpose unambiguous. Sibling tool names like 'solve' and 'optimize' indicate differentiation.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives. While it's implied that constraints are added before solving or optimizing, the description does not state prerequisites, when not to use, or how it relates to sibling tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior3/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the burden. It states it 'finds the optimal value subject to all added constraints', indicating dependency on prior constraint addition. However, it does not disclose side effects on the model or mention return behavior beyond what an output schema may cover.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
Extremely concise: two sentences that front-load the core purpose and follow with context. Every word adds value with no redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness4/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity of optimization, the description adequately covers the tool's role. It mentions the objective and constraints, and the output schema likely handles return values. Slight gap: no mention of solver state or reusability.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters3/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, so the description adds no extra parameter meaning beyond the schema. The baseline of 3 is appropriate as the description does not expand on parameter usage or validation.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves an optimization problem with maximize/minimize. It uses a specific verb+resource ('Solve with an optimization objective') and distinguishes from sibling tools like 'solve' which likely performs a general solve.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines2/5Does the description explain when to use this tool, when not to, or what alternatives exist?
No explicit guidance on when to use this tool versus alternatives such as 'solve'. The description does not mention prerequisites or exclusions, leaving the agent without clear context for selection.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description fully discloses the tool's effects: clearing all solver state. It also shows the return value via an example, providing full transparency.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise, front-loaded with a summary, uses bullet points for clarity, and includes a relevant example. Every sentence adds value.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given no parameters and no annotations, the description covers purpose, usage, return value, and provides an example. It is complete for this simple tool.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters4/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, so the baseline score is 4. The description correctly does not attempt to explain parameters.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool resets the solver state, listing exactly what is cleared (variables, constants, constraints, model data). This distinguishes it from sibling tools that add or query state.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description explicitly says 'Useful when starting a new problem,' indicating when to use it. It does not mention when not to use it or alternatives, but the context is clear enough.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
- Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries full burden. It clearly states the return format and includes an example, indicating this is a read-only query with no side effects.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5Is the description appropriately sized, front-loaded, and free of redundancy?
The description is extremely concise, with two sentences and an example. It front-loads the core purpose immediately.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has no parameters, an output schema exists (per context), and the description fully explains the return structure with an example, it is completely adequate for an agent to invoke correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The tool has zero parameters, and the description correctly mentions none. The example confirms no input is required. Schema coverage is 100%, so no additional information is needed.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Purpose5/5Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states 'List all created variables' with a specific verb and resource, distinguishing it from sibling tools like create_int_var and solve. The example reinforces the exact functionality.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Usage Guidelines4/5Does the description explain when to use this tool, when not to, or what alternatives exist?
The description implicitly tells when to use (to retrieve all variable references) but does not explicitly exclude scenarios or mention alternatives. Given sibling tools are entirely different operations, the context is clear enough.
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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