Code-Execution Decision — emit-code-vs-reason

> One-liner: LMs are unreliable calculators but reliable coders. When the answer needs > determinism and precision — arithmetic, exact data manipulation, deterministic transforms — > emit code and run it. When the answer needs judgment, taste, or open-ended synthesis, reason > in natural language. The cost of getting this gate wrong is silent: prose arithmetic > hallucinates a plausible-looking wrong number, and over-coding a judgment task burns a > sandbox round-trip for nothing.

This is an enhancement overlay. DSPy already gives you dspy.ProgramOfThought (PoT) — the mechanism for write-then-execute. What it does not give you is the decision rubric for when to reach for it. That rubric is this skill. Cross-link the sibling agentsop-output-format-by-model]] (which decides how code-shaped content should be serialized) and agentsop-test-fix-loop]] (which closes the execute → error → retry loop).

1. 何时激活 (When to activate)

Activate this skill before committing a step to a reasoning strategy whenever the task has a verifiable, deterministic core — or whenever you catch an agent doing arithmetic in prose.

| Trigger | Signal | |---|---| | Arithmetic / math | "compute the compound interest", "what's 17.5% of $4,392.18", multi-step word problems, unit conversions, date deltas | | Precise data manipulation | "sort these 240 rows by the third column", "dedupe and count", "join these two lists on id", "parse this CSV and sum column B" | | Deterministic transforms | regex extraction, string reformatting, base conversion, hashing, sorting, set operations | | Symbolic / combinatorial | "how many distinct permutations", "solve this system of equations", calendar/scheduling math | | You see a model doing math in prose | "Let me add: 1,204 + 8,991 + ... = 10,195" — almost always worth a code check | | Choosing a DSPy module | deciding between ChainOfThought and ProgramOfThought for a signature dspy.ai/learn/programming/modules/] |

Anti-triggers (do NOT reach for code execution):

• The task is judgment: tone, summarization, ranking by quality, "is this reply empathetic?", design tradeoffs, open-ended explanation.
• The "computation" is trivial and within the model's reliable range (single-digit arithmetic, a 3-item count) — the sandbox round-trip costs more than it saves.
• No sandbox is available and the determinism requirement is soft.
• The output's consumer is a human reading prose, and an approximate answer is acceptable.

2. 核心心智模型 (Core mental model)

> LMs are unreliable calculators but reliable coders.

A language model predicts the next token, not the correct value. When you ask it to add 48,217 + 9,884 in prose, it emits the most plausible-looking digit sequence — which is frequently wrong, and wrong in a way that looks right. The same model can write 48217 + 9884 as a Python expression flawlessly, because emitting the program is a pattern-matching task it is genuinely good at, and the Python interpreter is a deterministic oracle. This decoupling — model writes the recipe, interpreter computes the result — is the entire thesis of Program-of-Thought (PoT) arXiv 2211.12588] and PAL arXiv 2211.10435].

            ┌────────────────────────────────────────────────────────┐
            │  THE GATE: does this answer need determinism/precision?  │
            └────────────────────────────────────────────────────────┘
                       │                                  │
              YES (computable)                     NO (judgment)
                       │                                  │
                       ▼                                  ▼
            ┌─────────────────────┐            ┌─────────────────────┐
            │ EMIT CODE           │            │ REASON IN PROSE     │
            │ model writes recipe │            │ model is the engine │
            │ interpreter = oracle│            │ no oracle exists    │
            └─────────────────────┘            └─────────────────────┘
                       │
                       ▼
            sandbox → run → feed result back into LM → LM narrates/uses it

Two failure modes the gate prevents:

| Failure | Mechanism | Symptom | |---|---|---| | Under-coding (reason when you should compute) | LM hallucinates a calculation it cannot reliably perform | A confident, wrong, plausible-looking number; off-by-one counts; arithmetic that "looks" right | | Over-coding (compute when you should reason) | LM wraps a judgment task in a sandbox round-trip that adds no determinism | Wasted latency + cost; brittle code that encodes a subjective rubric as if it were a formula; print("the tone is friendly") |

Why the asymmetry matters. Under-coding fails silently — the wrong number propagates downstream and no exception fires. Over-coding fails loudly and cheaply — you notice the useless sandbox call. So the default lean, when genuinely uncertain and a verifiable core exists, is toward code. But "genuinely uncertain" is the operative phrase: most judgment tasks are not close calls.

The format corollary (from agentsop-output-format-by-model]]): once you decide to emit code, emit it as code in a fenced block / single string field — never nested inside JSON sub-structure. Code-in-JSON measurably degrades the code itself (Aider: 61%→20% on GPT-4 Turbo). The execution decision and the serialization decision are two separate gates; pass both.

3. SOP 工作流 (Decision workflow)

A three-step gate. Run it per step, not per task — one task can have computable steps and judgment steps interleaved.

Step 1 — Classify the step: deterministic-computable vs judgment

Ask: "Is there a single correct answer that a program could verify?"

• Yes → computable. Arithmetic, sorting, parsing, counting, set/regex ops, symbolic math, anything with a checkable ground truth. → Step 2.
• No → judgment. Quality ranking, tone, summarization, design choice, open synthesis. → reason in prose. Stop here.
• Mixed → decompose. "Summarize these sales and tell me the total" = a judgment summary step + a computable total step. Route each independently. The total goes to code; the summary stays prose.

A useful tiebreaker for the "trivial computable" gray zone: if the model would be embarrassed to get it wrong and you'd reach for a calculator yourself, emit code. If you'd do it in your head without a second thought, prose is fine.

Step 2 — If computable, emit + run code

1. Emit the computation as a real program (Python is the PoT default; the interpreter is the oracle).
2. Keep the code minimal and side-effect-free for the computation — read inputs, compute, print/return the result. No network, no filesystem unless the task is I/O.
3. Serialize the code per agentsop-output-format-by-model]]: fenced block or single string field, not JSON-nested.

Step 3 — Sandbox → run → feed result back into the LM

1. Sandbox choice (see §4 op #3, cross-link agentsop-output-format-by-model]] for the wire shape): DSPy ProgramOfThought uses a Python interpreter (Deno/PythonInterpreter sandbox in recent versions); OpenAI Code Interpreter runs in a managed container; Anthropic code-execution tool runs in a sandboxed VM; LangChain PythonREPLTool runs in-process and is unsandboxed — treat as untrusted-input-hostile.
2. Run the code in the sandbox; capture stdout / return value / traceback.
3. Feed the result back into the LM — this is the step under-coders forget. The code produces a value; the LM must consume it to narrate, format, or chain into the next step. PoT is "code computes, LM contextualizes," not "code replaces the LM."
4. Error → retry (cross-link agentsop-test-fix-loop]]): on traceback, feed the error back to the LM, regenerate the code, re-run. Bound the retries (DSPy ProgramOfThought defaults to max_iters ≈ 3). After the bound, fall back to prose reasoning or surface the failure — do not loop forever.

Exit criterion: the step produces either (a) a code-derived value the LM has consumed, or (b) a prose judgment, with the gate decision recorded so a reviewer can audit why code was or wasn't used.

4. 操作模型 (Operations: Trigger → Action → Output → Evidence)

Seven operations. Each row is a reusable move.

| # | Op | Trigger | Action | Output | Evidence | |---|---|---|---|---|---| | 1 | Computable-vs-judgment gate | Any step about to be reasoned | Apply §3 Step 1: single verifiable answer? | Route to code or prose | PoT premise: decouple compute from reasoning arXiv 2211.12588] | | 2 | Decompose mixed steps | Step has both a number and a narrative | Split into computable sub-step (code) + judgment sub-step (prose) | Two routed sub-steps | Mirrors mixed-content split in agentsop-output-format-by-model]] §5 Case B | | 3 | Sandbox choice | Decided to emit code | Pick interpreter by trust + capability: DSPy PoT (Python sandbox), OpenAI Code Interpreter (managed container), Anthropic code-exec (VM), LangChain PythonREPLTool (unsandboxed, in-process) | Chosen runtime | DSPy modules dspy.ai/learn/programming/modules/]; LangChain PythonREPLTool docs | | 4 | Result-back-into-LM | Code produced a value | Inject stdout/return value into the next LM turn so the model narrates/uses it | LM-consumed result | PoT design: code computes, LM contextualizes arXiv 2211.12588] | | 5 | Error retry (bounded) | Code raised a traceback | Feed error to LM, regenerate, re-run; cap at max_iters (~3) then fall back | Fixed code or graceful fallback | DSPy ProgramOfThought max_iters; see agentsop-test-fix-loop]] | | 6 | Precision escalation | Prose answer involves multi-step arithmetic | Re-route the arithmetic to code even if prose started it | Code-verified number | "LMs are unreliable calculators" — PAL arXiv 2211.10435] | | 7 | Over-coding veto | About to sandbox a judgment task | Stop: no deterministic core → reasoning, not code | Prose reasoning, no sandbox call | §5 Case B; avoids wasted round-trip |

In DSPy terms, op #1 is exactly the choice between dspy.ChainOfThought (prose reasoning) and dspy.ProgramOfThought (emit+run) for a signature — the dspy skill lists the modules but this overlay supplies the when.

5. 困境决策案例 (Dilemma cases)

Case A — Arithmetic in prose hallucinates → PoT fixes it (under-coding)

Trigger: A finance-summary agent step: "Given these 14 line items, compute the total, the 8.25% tax, and the grand total." The agent is a dspy.ChainOfThought module emitting prose.

Constraints:

• 14 multi-digit addends + a percentage + a sum-of-sums. Well outside reliable mental-math range.
• The number flows into an invoice — wrong is expensive and silent.
• A Python sandbox is available.

Decision steps:

1. Gate (§3 Step 1): "Is there a single verifiable answer?" Yes — the total is a fact, not a judgment. → computable.
2. Recognize the under-coding failure mode. Prose chain-of-thought will emit a plausible

running sum that is frequently off by some digits, and no exception will fire. This is the silent failure the gate exists to prevent.

1. Switch the module from ChainOfThought to ProgramOfThought. The model now emits

subtotal = sum([...]); tax = round(subtotal * 0.0825, 2); total = subtotal + tax and the interpreter computes it exactly.

1. Feed the result back (op #4): the LM receives total = 4,217.93 and narrates the invoice

line. Code computed; LM contextualized.

1. Serialize per agentsop-output-format-by-model]]: the generated code goes in a fenced block, not a

JSON program field — code-in-JSON would degrade it.

Outcome: The arithmetic is now deterministic and auditable. PoT-style code execution is the documented fix for exactly this class of error arXiv 2211.12588, arXiv 2211.10435].

Extractable operation: Multi-step arithmetic in prose is a smell. Re-route it to code (op #6).

Case B — Over-coding a judgment task wastes a sandbox round-trip (over-coding)

Trigger: A support-triage agent step: "Read this customer message and decide whether the tone is hostile, neutral, or warm." An over-eager engineer wires it through ProgramOfThought because "code is more reliable."

Constraints:

• "Tone" has no single verifiable answer — it is a judgment.
• The sandbox round-trip adds latency + cost.
• Forcing it into code produces something like if "!!!" in msg: tone = "hostile" — a brittle

rule that encodes a subjective rubric as if it were a formula, and is worse than the model's native judgment.

Decision steps:

1. Gate (§3 Step 1): "Single verifiable answer a program could check?" No — tone is

judgment. → reason in prose. Stop.

1. Invoke the over-coding veto (op #7). There is no deterministic core to delegate to an

oracle. Code adds no determinism — it just relocates the same judgment into worse, hard-coded heuristics.

1. Cost it out. The sandbox call adds a full round-trip (and a code-gen + parse step) for

zero precision gain. This is pure waste — the loud, cheap failure mode.

1. Keep it as ChainOfThought (or Predict). The LM is the right engine for judgment.
2. Counter-check: if a later spec adds "and count how many exclamation marks" — that

sub-step is computable; decompose (op #2) and route the count to code, the tone to prose.

Outcome: No sandbox call. The judgment stays where judgment belongs. Over-coding is a real and common anti-pattern: not everything benefits from an interpreter, only things with a verifiable deterministic core.

Extractable operation: No verifiable answer → no code. Veto the sandbox round-trip (op #7).

Case C — Mixed step: summary + total (decompose)

Trigger: "Summarize this quarter's sales narrative and give me the exact total revenue."

Constraints: One sentence contains both a judgment (summary) and a computation (total).

Decision steps:

1. Gate → mixed. Decompose (op #2).
2. Route the total to ProgramOfThought: code sums the figures, interpreter verifies.
3. Route the summary to ChainOfThought: prose synthesis, no oracle exists.
4. Feed the code result back into the prose step so the narrative cites the exact, verified total.

Outcome: Each sub-step uses its correct engine. This is the execution-decision analogue of the mixed-content two-pass pattern in agentsop-output-format-by-model]] §5 Case B.

Extractable operation: One task ≠ one strategy. Gate per step, decompose mixed steps.

6. 反模式与边界 (Anti-patterns & boundaries)

Anti-patterns

1. Code for everything ("code is always more reliable"). False. Code is more reliable only

where a deterministic, verifiable answer exists. For judgment tasks, code just hard-codes a subjective rubric and adds a wasted round-trip (Case B). The interpreter is an oracle only for computable questions.

1. Reasoning for arithmetic ("the model can just add it"). The headline failure. LMs are

unreliable calculators; multi-step prose arithmetic hallucinates plausible wrong numbers, silently (Case A). Any non-trivial computation → code arXiv 2211.12588].

1. Emitting code but never feeding the result back. PoT is "code computes, LM contextualizes."

If the value never re-enters the LM turn, you have a dangling computation the agent can't use or narrate (op #4).

1. Unbounded error-retry loops. On a traceback, regenerate-and-rerun is correct — but cap it

(max_iters ≈ 3) and fall back to prose or surface the failure. Infinite code-repair loops burn cost. See agentsop-test-fix-loop]].

1. Nesting generated code inside JSON sub-structure. The execution decision says emit code;

agentsop-output-format-by-model]] says emit it as a fenced block / single string, never as nested JSON — code-in-JSON degrades the code (Aider 61%→20%). Pass both gates.

1. Treating LangChain PythonREPLTool as a safe sandbox. It runs in-process, unsandboxed.

Fine for trusted self-authored code; hostile to untrusted input. Use a real sandbox (OpenAI Code Interpreter container, Anthropic code-exec VM, DSPy's interpreter) when inputs are untrusted.

1. Over-decomposing trivial computation. A 3-item count or single-digit add does not need a

sandbox round-trip; the tax exceeds the benefit. The gate is for non-trivial computation.

Boundaries (when this gate doesn't fire)

• No sandbox available and determinism is soft. Sometimes you must reason in prose because

there is no interpreter; accept the precision risk and flag it.

• The model is overwhelmingly capable for a tiny computation. Frontier models reliably handle

small arithmetic; the round-trip isn't worth it below a complexity threshold.

• The task is one-shot exploration with no downstream consumer of the precise value.
• Latency-critical paths where a sandbox round-trip violates a hard SLA and an approximate

answer is acceptable — a deliberate, documented tradeoff, not a default.

7. 跨框架对照 (Ecosystem cross-reference)

How major frameworks expose the emit-code-vs-reason mechanism. This skill operates at the decision layer; each framework supplies the mechanism.

DSPy ProgramOfThought dspy.ai/learn/programming/modules/]

The canonical declarative version. A signature compiled with dspy.ProgramOfThought(Sig) makes the LM emit Python, runs it in an interpreter sandbox, and feeds the result back — with bounded retry on error (max_iters). The sibling dspy skill lists ChainOfThought vs ProgramOfThought as module choices but does not give the decision rubric; this overlay is that rubric. Use ProgramOfThought exactly when §3 Step 1 returns "computable."

OpenAI Code Interpreter / Assistants code tool

A managed container that the model can write Python into and execute, with files and state persisted across turns. Heavier and stateful — good for data-analysis sessions (load CSV, compute, plot). Same gate applies: route computable steps in, keep judgment in chat.

Anthropic code-execution tool

A sandboxed VM exposed as a tool; the model emits code, it runs, results return to the conversation. First-party, sandboxed — safe for untrusted inputs. The execution-decision gate maps directly: offer the tool, but the model/agent should only invoke it for computable steps.

LangChain PythonREPLTool

A tool wrapping a Python REPL. Runs in-process and is unsandboxed — powerful and dangerous. Use only for trusted, self-authored computation; never expose it to untrusted input without an external sandbox. The decision rubric is identical; the safety profile is worst-in-class.

Cross-framework summary

Framework            | Mechanism                | Sandbox     | Result-back
---------------------|--------------------------|-------------|------------
DSPy PoT             | ProgramOfThought module  | Python intp | automatic (max_iters)
OpenAI Code Interp.  | Assistants code tool     | container   | persisted state
Anthropic code-exec  | code-execution tool      | VM (safe)   | into conversation
LangChain            | PythonREPLTool           | NONE (proc) | manual wiring

Every framework can be mis-invoked — pointed at a judgment task (over-code) or skipped for a computation (under-code). This overlay is the gate that decides invocation, regardless of which mechanism is underneath.

Quick reference card

┌──────────────────────────────────────────────────────────────────────┐
│                  EMIT-CODE-VS-REASON DECISION CARD                   │
├──────────────────────────────────────────────────────────────────────┤
│ Single verifiable answer a program could check?                      │
│   YES → EMIT CODE → sandbox → run → feed result back into LM         │
│   NO  → REASON IN PROSE (no oracle exists for judgment)              │
│   MIXED → decompose; route each sub-step independently               │
├──────────────────────────────────────────────────────────────────────┤
│ Arithmetic / parse / sort / count / regex / symbolic → CODE          │
│ Tone / quality / summary / design / synthesis        → PROSE         │
│ "summary AND total"                                  → SPLIT         │
├──────────────────────────────────────────────────────────────────────┤
│ LMs are unreliable calculators but reliable coders.                  │
│ Under-coding fails SILENTLY (wrong plausible number).                │
│ Over-coding fails LOUDLY+CHEAPLY (wasted sandbox round-trip).        │
│ When genuinely uncertain AND a verifiable core exists → lean CODE.   │
├──────────────────────────────────────────────────────────────────────┤
│ NEVER:                                                               │
│  • code a judgment task (over-coding veto)                          │
│  • do multi-step arithmetic in prose (under-coding)                 │
│  • forget to feed the code result back into the LM                  │
│  • nest generated code in JSON (see [[agentsop-output-format-by-model]])     │
│  • loop code-repair unbounded (see [[agentsop-test-fix-loop]])               │
│  • trust LangChain PythonREPLTool on untrusted input (unsandboxed)  │
└──────────────────────────────────────────────────────────────────────┘

引用源 (Citations)

Primary anchors:

• Program of Thoughts (PoT) — Chen et al., arXiv 2211.12588 — decouple computation from reasoning; LM writes code, interpreter computes.
• PAL: Program-aided Language Models — Gao et al., arXiv 2211.10435 — LM as coder, runtime as deterministic solver.
• DSPy ProgramOfThought module — dspy.ai/learn/programming/modules/] — emit+run+retry mechanism.

Framework / API docs:

• OpenAI Code Interpreter / Assistants code tool — platform.openai.com/docs/assistants/tools/code-interpreter]
• Anthropic code-execution tool — docs.anthropic.com/en/docs/agents-and-tools/tool-use/code-execution-tool]
• LangChain PythonREPLTool — python.langchain.com/docs/integrations/tools/python] (unsandboxed; in-process).

Companion / overlaid skills:

• dspy-sop-skill/SKILL.md — ships ProgramOfThought but not this decision rubric (the gap this overlay fills).
• d-output-format-by-model-skill/SKILL.md — sibling: once you emit code, how to serialize it (PoT for math/parse; code never nested in JSON). Cross-linked as agentsop-output-format-by-model]].
• test-fix-loop — the execute → error → retry loop this skill defers to for bounded code repair. Cross-linked as agentsop-test-fix-loop]].