Сервер протокола контекста модели (MCP), который предоставляет возможности SAT, SMT и решения ограничений для больших языковых моделей.
MCP Solver объединяет SAT, SMT и решение задач с ограничениями с LLM через протокол контекста модели, позволяя моделям ИИ интерактивно создавать, редактировать и решать:
Подробное описание архитектуры системы MCP Solver и теоретических основ см. в сопутствующей исследовательской статье: Стефан Сейдер, «MCP-Solver: Интеграция языковых моделей с системами программирования в ограничениях» , arXiv:2501.00539, 2024.
Related MCP server: mcp-optimizer
Далее item относится к некоторой части кода (MinZinc/Pysat/Z3), а model — к кодировке.
Название инструмента | Описание |
| Удалить все элементы из модели |
| Добавить новый элемент по указанному индексу |
| Удалить элемент по индексу |
| Заменить элемент по индексу |
| Получить текущее содержимое модели с пронумерованными элементами |
| Решить модель (с параметром тайм-аута) |
Python и менеджер проектов uv
Питон 3.11+
Требования для конкретного режима: MiniZinc, PySAT, Python Z3 (необходимые пакеты устанавливаются через pip)
Операционные системы: macOS, Windows, Linux (с соответствующими адаптациями)
Для работы MCP Solver требуются Python 3.11+, менеджер пакетов uv и специфичные для решателя зависимости (MiniZinc, Z3 или PySAT).
Подробные инструкции по установке для Windows, macOS и Linux см. на INSTALL.md .
Быстрый старт:
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 solversMCP Solver предоставляет три различных режима работы, каждый из которых интегрируется с различным бэкэндом решения ограничений. Каждый режим требует определенных зависимостей и предлагает уникальные возможности для решения различных классов проблем.
Режим MiniZinc обеспечивает интеграцию с языком моделирования ограничений MiniZinc со следующими функциями:
Богатое выражение ограничений с глобальными ограничениями
Интеграция с решателем ограничений Chuffed
Возможности оптимизации
Доступ к значениям решения через get_solution
Зависимости : Требуется пакет minizinc ( uv pip install -e ".[mzn]" )
Конфигурация : Для работы в режиме MiniZinc используйте:
mcp-solver-mznРежим PySAT позволяет взаимодействовать с набором инструментов решения задач Python SAT со следующими функциями:
Моделирование пропозициональных ограничений с использованием CNF (конъюнктивной нормальной формы)
Доступ к различным решателям SAT (Glucose3, Glucose4, Lingeling и т. д.)
Ограничения мощности (at_most_k, at_least_k, exact_k)
Поддержка решения булевых ограничений
Зависимости : Требуется пакет python-sat ( uv pip install -e ".[pysat]" )
Конфигурация : для запуска в режиме PySAT используйте:
mcp-solver-pysatРежим Z3 обеспечивает доступ к возможностям решения Z3 SMT (теории выполнимости по модулю) со следующими функциями:
Богатая система типов: логические значения, целые числа, действительные числа, битовые векторы, массивы
Решение ограничений с помощью квантификаторов
Возможности оптимизации
Библиотека шаблонов для общих шаблонов моделирования
Зависимости : Требуется пакет z3-solver ( uv pip install -e ".[z3]" )
Конфигурация : Для работы в режиме Z3 используйте:
mcp-solver-z3MCP Solver включает в себя клиент MCP для целей разработки, экспериментирования и диагностики, основанный на фреймворке агента ReAct . Этот клиент служит посредником между LLM и сервером MCP, облегчая перевод формулировок задач на естественном языке в формальные решения программирования ограничений.
# Install client dependencies
uv pip install -e ".[client]"
# Verify client installation and configuration
uv run test-setup-clientКлиенту требуется ключ API от поставщика LLM. Для Anthropic (LLM по умолчанию — Claude Sonnet 3.7) установите переменную среды ANTHROPIC_API_KEY . Ее можно установить в вашей среде или включить в файл .env в корне проекта.
Клиент также поддерживает других поставщиков LLM, включая OpenAI, Google (Gemini), OpenRouter и даже локальные модели через LM Studio. Вы можете указать, какую модель использовать, с помощью флага командной строки --mc . Подробности о форматах кода модели см. в INSTALL.md.
Клиент предоставляет специализированные команды для каждого решателя:
# 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>Это основано на примере Джорджа Джонсона (NYT, 13 июля 1999 г.).
Пользователь
Предположим, что театральный режиссер чувствует себя обязанным взять на роль либо свою инженю, актрису Альварес, либо своего племянника, актера Коэна, в постановке. Но мисс Альварес не будет играть в пьесе с мистером Коэном (ее бывшим любовником), и она требует, чтобы в актерский состав вошла ее новая страсть, актер Дэвенпорт. Продюсер, которому нужно отплатить за свои услуги, настаивает, чтобы актер Браниславский сыграл роль. Но мистер Браниславский не будет играть ни в одной пьесе с мисс Альварес или мистером Дэвенпортом. Может ли режиссер взять на роль актера?
Система: clear_model
Model cleared
Система: add_item (множественный)
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;
Система: solve_model
{'status': 'SAT', 'solution': Solution(alvarez=False, cohen=True, branislavsky=True, davenport=False, _checker=''), 'solve_time': 0.0}
Решение (в ролях Коэн и Браниславски, но не Альварес или Дэвенпорт) удовлетворяет всем ограничениям.
Пользователь
Проверьте, можете ли вы разместить n ферзей на шахматной доске nxn. Попробуйте n=10,20,30,40 и сравните время решения
Система: clear_model
Model cleared
Система: add_item (множественный)
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;
Система: solve_model (с n=10, 20, 30 и 40 путем изменения значения n)
Сравнение времени решения: n=10: 0,001sn=20: 0,005sn=30: 0,040sn=40: 0,043с
Решения существуют для всех протестированных размеров плат. Временная сложность увеличивается нелинейно, но остается управляемой до n=40.
Пользователь
Продавщица из Вены должна спланировать предстоящий тур по Австрии, посетив каждую столицу провинции по одному разу. Помогите найти кратчайший маршрут. Расстояния в км: 1=Вена, 2=Санкт-Пёльтен, 3=Айзенштадт, 4=Линц, 5=Грац, 6=Клагенфурт, 7=Зальцбург, 8=Инсбрук, 9=Брегенц
[Таблица матрицы расстояний предоставлена в сообщении пользователя]
Система: add_item (множественный)
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;
Система: solve_model
{'status': 'SAT', 'solution': Solution(objective=1564, succ=[2, 4, 1, 7, 3, 5, 9, 6, 8], _checker=''), 'solve_time': 0.002}
Оптимальный маршрут: Вена → Санкт-Пёльтен → Линц → Зальцбург → Брегенц → Инсбрук → Клагенфурт → Грац → Айзенштадт → Вена общим расстоянием 1564 км.
Вы можете оставить отзыв автору через эту форму .
Этот MCP Solver находится на стадии прототипа и должен использоваться с осторожностью. Пользователям рекомендуется экспериментировать, но любое использование в критических средах осуществляется на их страх и риск.
Данный проект лицензирован по лицензии MIT — подробности см. в файле LICENSE .
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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