Un servidor de Protocolo de Contexto de Modelo (MCP) que expone capacidades de resolución de restricciones, SAT y SMT a modelos de lenguaje grandes.
El solucionador MCP integra SAT, SMT y resolución de restricciones con LLM a través del protocolo de contexto de modelo, lo que permite que los modelos de IA creen, editen y resuelvan de forma interactiva:
Para obtener una descripción detallada de la arquitectura del sistema y los fundamentos teóricos del solucionador MCP , consulte el artículo de investigación adjunto: Stefan Szeider, "MCP-Solver: Integrating Language Models with Constraint Programming Systems" , arXiv:2501.00539, 2024.
Related MCP server: mcp-optimizer
A continuación, el elemento se refiere a alguna parte del código (MinZinc/Pysat/Z3) y el modelo a la codificación.
Nombre de la herramienta | Descripción |
| Eliminar todos los elementos del modelo |
| Agregar nuevo elemento en un índice específico |
| Eliminar elemento en el índice |
| Reemplazar elemento en el índice |
| Obtenga el contenido del modelo actual con elementos numerados |
| Resolver el modelo (con parámetro de tiempo de espera) |
Python y gestor de proyectos uv
Python 3.11+
Requisitos específicos del modo: MiniZinc, PySAT, Python Z3 (los paquetes necesarios se instalan mediante pip)
Sistemas operativos: macOS, Windows, Linux (con adaptaciones adecuadas)
MCP Solver requiere Python 3.11+, el administrador de paquetes uv y dependencias específicas del solucionador (MiniZinc, Z3 o PySAT).
Para obtener instrucciones de instalación detalladas para Windows, macOS y Linux, consulte INSTALL.md .
Inicio rápido:
git clone https://github.com/szeider/mcp-solver.git
cd mcp-solver
uv venv
source .venv/bin/activate
uv pip install -e ".[all]" # Install all solversEl solucionador MCP ofrece tres modos operativos distintos, cada uno de los cuales se integra con un backend de resolución de restricciones distinto. Cada modo requiere dependencias específicas y ofrece capacidades únicas para abordar diferentes tipos de problemas.
El modo MiniZinc proporciona integración con el lenguaje de modelado de restricciones MiniZinc con las siguientes características:
Expresión de restricción enriquecida con restricciones globales
Integración con el solucionador de restricciones Chuffed
Capacidades de optimización
Acceso a los valores de la solución mediante get_solution
Dependencias : Requiere el paquete minizinc ( uv pip install -e ".[mzn]" )
Configuración : Para ejecutar en modo MiniZinc, utilice:
mcp-solver-mznEl modo PySAT permite la interacción con el kit de herramientas de resolución de problemas SAT de Python con las siguientes características:
Modelado de restricciones proposicionales mediante CNF (Forma Normal Conjuntiva)
Acceso a varios solucionadores SAT (Glucose3, Glucose4, Lingeling, etc.)
Restricciones de cardinalidad (como máximo k, al menos k, exactamente k)
Soporte para la resolución de restricciones booleanas
Dependencias : Requiere el paquete python-sat ( uv pip install -e ".[pysat]" )
Configuración : Para ejecutar en modo PySAT, utilice:
mcp-solver-pysatEl modo Z3 proporciona acceso a las capacidades de resolución de Z3 SMT (teorías de módulo de satisfacción) con las siguientes características:
Sistema de tipos enriquecido: booleanos, enteros, reales, vectores de bits, matrices
Resolución de restricciones con cuantificadores
Capacidades de optimización
Biblioteca de plantillas para patrones de modelado comunes
Dependencias : Requiere el paquete z3-solver ( uv pip install -e ".[z3]" )
Configuración : Para ejecutar en modo Z3, utilice:
mcp-solver-z3El solucionador MCP incluye un cliente MCP para fines de desarrollo, experimentación y diagnóstico, basado en el framework del agente ReAct . Este cliente actúa como intermediario entre un LLM y el servidor MCP, facilitando la traducción de enunciados de problemas en lenguaje natural a soluciones formales de programación con restricciones.
# Install client dependencies
uv pip install -e ".[client]"
# Verify client installation and configuration
uv run test-setup-clientEl cliente requiere una clave API de un proveedor de LLM. Para Anthropic (el LLM predeterminado es Claude Sonnet 3.7), configure la variable de entorno ANTHROPIC_API_KEY . Puede configurarla en su entorno o incluirla en un archivo .env en la raíz del proyecto.
El cliente proporciona comandos especializados para cada solucionador backend:
# MiniZinc mode
uv run run-test mzn --problem <path/to/problem.md>
# PySAT mode
uv run run-test pysat --problem <path/to/problem.md>
# Z3 mode
uv run run-test z3 --problem <path/to/problem.md>Esto se basa en un ejemplo de George Johnson (NYT, 13 de julio de 1999).
Usuario
Supongamos que un director teatral se siente obligado a incluir en el reparto a su ingenua, la actriz Álvarez, o a su sobrino, el actor Cohen, en una producción. Pero la señorita Álvarez no quiere actuar con el señor Cohen (su antiguo amante) y exige que el reparto incluya a su nuevo amor, el actor Davenport. El productor, con sus propios favores que devolver, insiste en que el actor Branislavsky participe. Pero el señor Branislavsky no quiere actuar con la señorita Álvarez ni con el señor Davenport. ¿Puede el director incluir en el reparto a la obra?
Sistema: clear_model
Model cleared
Sistema: add_item (múltiple)
var bool: alvarez; var bool: cohen; var bool: branislavsky; var bool: davenport; constraint alvarez \/ cohen; % Must cast either Alvarez or Cohen constraint not (alvarez /\ cohen); % Alvarez won't work with Cohen constraint alvarez -> davenport; % If Alvarez is cast, Davenport must be cast constraint branislavsky; % Branislavsky must be cast constraint not (branislavsky /\ alvarez); % Branislavsky won't work with Alvarez constraint not (branislavsky /\ davenport); % Branislavsky won't work with Davenport solve satisfy;
Sistema: solve_model
{'status': 'SAT', 'solution': Solution(alvarez=False, cohen=True, branislavsky=True, davenport=False, _checker=''), 'solve_time': 0.0}
La solución (elegir a Cohen y Branislavsky, pero no a Alvarez o Davenport) satisface todas las restricciones.
Usuario
Comprueba si puedes colocar n reinas en un tablero de ajedrez de nxn. Prueba con n = 10, 20, 30, 40 y compara los tiempos de resolución.
Sistema: clear_model
Model cleared
Sistema: add_item (múltiple)
int: n = 10; array[1..n] of var 1..n: queens; constraint alldifferent(queens); constraint alldifferent([queens[i] + i | i in 1..n]); constraint alldifferent([queens[i] - i | i in 1..n]); solve satisfy;
Sistema: solve_model (con n=10, 20, 30 y 40 cambiando el valor de n)
Comparación de tiempos de resolución: n=10: 0,001 s n=20: 0,005 s n=30: 0,040 s n=40: 0,043 s
Existen soluciones para todos los tamaños de placa probados. La complejidad temporal aumenta de forma no lineal, pero se mantiene manejable hasta n=40.
Usuario
Una vendedora residente en Viena necesita planificar su próximo viaje por Austria, visitando cada capital de provincia una vez. Ayúdenme a encontrar la ruta más corta. Distancias en km: 1=Viena, 2=St. Pölten, 3=Eisenstadt, 4=Linz, 5=Graz, 6=Klagenfurt, 7=Salzburgo, 8=Innsbruck, 9=Bregenz.
[Tabla de matriz de distancias proporcionada en el mensaje del usuario]
Sistema: add_item (múltiple)
include "globals.mzn"; int: n = 9; array[1..n,1..n] of int: dist = [|0,65,60,184,195,319,299,478,631|65,0,125,119,130,254,234,413,566|60,125,0,184,157,281,261,440,593|184,119,184,0,208,252,136,315,468|195,130,157,208,0,136,280,459,629|319,254,281,252,136,0,217,391,566|299,234,261,136,280,217,0,188,343|478,413,440,315,459,391,188,0,157|631,566,593,468,629,566,343,157,0|]; array[1..n] of var 1..n: succ; var int: total_dist = sum(i in 1..n)(dist[i,succ[i]]); constraint circuit(succ); solve minimize total_dist;
Sistema: solve_model
{'status': 'SAT', 'solution': Solution(objective=1564, succ=[2, 4, 1, 7, 3, 5, 9, 6, 8], _checker=''), 'solve_time': 0.002}
Ruta óptima: Viena → St. Pölten → Linz → Salzburgo → Bregenz → Innsbruck → Klagenfurt → Graz → Eisenstadt → Viena con una distancia total de 1.564 km.
Puede proporcionar comentarios al autor a través de este formulario .
Este solucionador MCP se encuentra en fase de prototipo y debe utilizarse con precaución. Se anima a los usuarios a experimentar, pero cualquier uso en entornos críticos es bajo su propia responsabilidad.
Este proyecto está licenciado bajo la licencia MIT: consulte el archivo de LICENCIA para obtener más detalles.
Execute Python code in the persistent solving kernel.
Runs in the kernel set up by select_backend unless kernel_id overrides it. State persists across calls (variables, imports). Raise timeout (seconds, max 300) for long solver runs.
| Name | Required | Description | Default |
|---|---|---|---|
| code | Yes | ||
| timeout | No | ||
| kernel_id | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations, so the description carries the full burden. It usefully discloses that state (variables, imports) persists across calls and that timeout caps at 300 seconds, but says nothing about error behavior, sandboxing, or how execution output is captured/returned.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Four short lines, purpose front-loaded, with each remaining sentence adding a distinct operational fact (kernel source, state persistence, timeout cap). No filler or restated name text.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
No output schema exists, yet the description never describes what an execution returns (stdout, errors, result value), which is a meaningful gap for a code-execution tool. Kernel selection, persistence, and timeout behavior are covered, so the definition is workable but not complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate, and it does for two of three params: kernel_id is explained as overriding the kernel established by select_backend, and timeout is defined in seconds with a max of 300. The 'code' param is left implicit but is self-evident from the tool purpose.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb+resource ('Execute Python code') and adds the key qualifier that it runs in the persistent solving kernel, which differentiates it from a one-shot execution. It references select_backend for kernel setup, but never contrasts itself with submit_code, so sibling distinction is only partial.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
Gives implied usage guidance: raise the timeout for long solver runs, and rely on state persisting across calls. However, it never says when to prefer this over submit_code or when to instead use python_interrupt/python_reset, so the caller must infer routing.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Interrupt running code in the solving kernel (state is preserved).
| Name | Required | Description | Default |
|---|---|---|---|
| kernel_id | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It does disclose one meaningful trait — that state is preserved rather than discarded — but says nothing about what happens if nothing is running, whether interruption is cooperative, permissions, or the result of the call.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
A single front-loaded sentence with no filler; the verb and effect lead the reader immediately. It is efficient, though it is arguably too terse for the behavioral gaps it leaves.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a one-parameter tool with no output schema and no annotations, the description covers purpose and one behavioral note. It omits how to target a specific kernel and what the caller observes after interrupting, leaving the agent to guess at invocation details.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
One parameter (kernel_id, nullable, default null) has 0% schema description coverage, and the description adds no meaning: it never explains what kernel_id identifies, that it is optional, or what the default targets. The 'solving kernel' phrasing hints at a default target but is not tied to the parameter.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb ('interrupt') and resource ('running code in the solving kernel'), plus a scope qualifier ('state is preserved') that separates it from python_reset. It does not name siblings explicitly, so the differentiation is inferable rather than stated.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
Usage is implied by the verb: call it when running code needs to be stopped without losing kernel state. There is no explicit guidance on when to prefer this over python_reset, nor any prerequisite or condition (e.g., only valid while execution is in flight).
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Create a new kernel (no kernel_id) or reset one (with kernel_id).
Prefer select_backend, which installs the right solver packages for you. The kernel created or reset here becomes the target of bare python_exec calls.
| Name | Required | Description | Default |
|---|---|---|---|
| packages | No | ||
| kernel_id | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the behavioral burden. It usefully discloses that the created or reset kernel becomes the target of bare python_exec calls, but it does not mention that resetting may discard existing kernel state, nor does it explain the packages parameter's effect.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is three short sentences with no wasted text. The main behavior is front-loaded, followed by the alternative tool guidance and the downstream effect on python_exec.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a two-parameter, state-changing tool with no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It covers purpose and one parameter but leaves packages undocumented and does not describe reset side effects or state loss.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate for both parameters. It explains kernel_id's effect well by describing create-without vs reset-with, but it completely omits the packages parameter, leaving half the parameters undocumented.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description gives a specific verb and resource, and it clearly distinguishes the two modes: no kernel_id creates a new kernel, while a provided kernel_id resets one. It also names the related sibling tool select_backend, so the tool's role is immediately identifiable.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
It explicitly says to prefer select_backend when solver packages are needed, which is useful routing guidance. The create-vs-reset condition is also clear, though the description does not explicitly state when not to use python_reset or what prerequisites exist.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Check kernel state: active kernels, defined variables, packages.
| Name | Required | Description | Default |
|---|---|---|---|
| kernel_id | No |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden of behavioral disclosure. 'Check' implies a read-only operation, but it does not explicitly state that it is non-destructive, nor does it describe side effects, authorization needs, or rate limits. It only lists what is inspected, which is minimal behavioral context.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
A single, front-loaded sentence with no filler. It efficiently conveys the core purpose in one clause.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a simple no-required-parameter tool with no output schema, the description gives an outline of what is returned (kernels, variables, packages). However, it omits usage context and parameter semantics, leaving gaps an agent must infer.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The schema has 0% description coverage and the description never mentions the optional kernel_id parameter. It does not explain what the parameter does, when to supply it, or what the default behavior is when omitted.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description uses a specific verb 'Check' and resource 'kernel state', and enumerates the inspected items (active kernels, variables, packages). It is clear but does not differentiate this tool from siblings like python_exec or python_interrupt.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
No when-to-use guidance is given. The description does not say when to prefer this over python_exec or python_interrupt, nor does it state any prerequisites like requiring an active kernel.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Start solving a constraint problem: call this FIRST, once per problem.
Sets up a persistent IPython kernel preloaded with the backend's solver library and helper functions, and returns the modeling instructions for that backend. Calling it again recycles the kernel for a new problem (previous session state is cleared).
Backends:
pysat: Boolean satisfiability — feasibility, combinatorial search
maxsat: weighted optimization over Boolean constraints
z3: SMT — integers/reals/bitvectors, proofs, program verification
cpmpy: finite-domain constraint programming — scheduling, assignment, puzzles
clingo: Answer Set Programming — logic rules, defaults, reachability
didp: dynamic programming (state-space search) — routing, sequencing, packing
Unsure which backend fits? Read the resource mcp-solver://guide first.
Then iterate with python_exec (write, run, verify against the problem statement), and finish by calling submit_code with the final, verified, self-contained program. UNSAT / "no solution exists" is a valid outcome.
| Name | Required | Description | Default |
|---|---|---|---|
| solver | Yes |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden and delivers: persistent kernel lifetime, that re-invocation clears previous session state, that it returns modeling instructions, and that UNSAT is a legitimate terminal outcome. These are exactly the behavioral traits an agent needs and that the schema does not express.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Front-loaded imperative first sentence, then setup behavior, then the backend list, then the workflow tail. The bulleted backend table is dense with information and every line earns its place; no filler.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
No output schema exists, but the description says what is returned (modeling instructions) and sketches the full three-stage workflow ending in submit_code. For a single-parameter entry-point tool, an agent has everything required to select and invoke it correctly.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0% and the single 'solver' parameter has no enum, so the description must supply the value domain — and it does, enumerating all six backends with a one-line semantic gloss each (e.g. 'z3: SMT — integers/reals/bitvectors, proofs, program verification'). It does not explicitly state that these strings are the accepted values of the solver argument, so the mapping is inferred rather than stated.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
Specific verb+resource: 'Start solving a constraint problem' and sets up a persistent IPython kernel preloaded with the backend solver library. It explicitly positions itself against siblings by naming the full workflow (python_exec to iterate, submit_code to finish), so an agent can place it without opening other schemas.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
Explicit when-to-use ('call this FIRST, once per problem'), re-use semantics ('Calling it again recycles the kernel for a new problem'), an escape hatch for uncertainty ('Unsure which backend fits? Read the resource mcp-solver://guide first'), and the follow-on tools. Nothing is left to inference.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Submit the final, verified, self-contained solver program.
Call ONCE at the end, only after executing the program via python_exec and passing your verification. The code is syntax-checked; on success it is stored and linked as a resource (the server keeps the last 50).
| Name | Required | Description | Default |
|---|---|---|---|
| code | Yes |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden and does well: it discloses validation behavior (syntax-checked), the failure path, and what happens on success (stored and linked as a resource, server retains the last 50). It omits whether resubmission overwrites a prior submission and what an error response looks like.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Three short sentences, front-loaded with the action and artifact, then the timing constraint, then the side effect. No filler and nothing repeated from the schema.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a single-parameter submission tool with no annotations and no output schema, the description covers purpose, timing, validation, and persistence/retention. Remaining gaps (retry semantics, error format) are minor given the tool's simplicity.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 0% and the schema itself only says 'code: string', so the description has to define the payload; it does so by specifying the code must be the final, verified, self-contained solver program. It stops short of stating language/format constraints, but the payload's required qualities are communicated.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
States a specific verb (submit) plus the exact resource (the final, verified, self-contained solver program), which is distinct from the sibling execution/status tools. It does not explicitly name which sibling it is contrasted with, but the artifact it accepts is unambiguous.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
Gives explicit timing ('Call ONCE at the end'), an explicit prerequisite ('only after executing the program via python_exec and passing your verification'), and names the sibling tool involved. An agent cannot mistake when this should fire.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Recent tool additions, removals, and schema changes observed during successful MCP inspections.
v4.1.0python_execpython_interruptpython_resetpython_statusselect_backendsubmit_codeScored across 6 tools
Most tools are clearly distinct: python_status, python_interrupt, python_exec, and submit_code each have a unique role. The only mild overlap is between select_backend and python_reset (both create/configure kernels), but descriptions explicitly steer users to prefer select_backend, resolving the ambiguity.
Four tools share a consistent python_<action> prefix (python_status, python_interrupt, python_exec, python_reset), but select_backend and submit_code break this pattern with a verb_noun convention. Two coexisting conventions make it mixed but still readable.
Six tools is well-scoped for a constraint-solving workflow: backend setup, execution, kernel management, and final submission. Each tool earns its place with no redundancy.
The lifecycle (select_backend -> python_exec iterate -> submit_code, with status/interrupt/reset for kernel control) is well covered. Minor gaps: no tool to list or retrieve previously submitted solutions (only a resource mention), but core workflows are complete.
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