PAL (Program-Aided Language Models)
Language models are brilliant at understanding problems but unreliable at arithmetic. PAL separates these concerns — the model translates reasoning into Python code, then hands execution to an interpreter that never makes a calculation error.
Introduced: PAL (Program-Aided Language Models) was published in 2023 by Gao et al. The core idea is elegantly simple: instead of having the language model both reason about a problem and compute the answer, PAL has the model generate Python code that encodes the reasoning process, then executes that code via an external Python interpreter to obtain the final answer. This division of labor avoids the well-documented arithmetic and logical errors that plague pure language-based reasoning.
Modern LLM Status: PAL was a breakthrough showing that LLMs could use code as a reasoning medium rather than natural language. In 2026, this insight is fundamental — virtually all AI coding assistants and agent frameworks use code execution as a reasoning tool. The original PAL concept of “think in code, execute for accuracy” is now standard practice. Modern systems like Claude, GPT-4, and Gemini natively support code execution environments, making PAL’s approach seamlessly integrated rather than requiring explicit prompting.
Think in Code, Execute for Accuracy
Language models excel at understanding natural language problems and decomposing them into logical steps. But when those steps involve arithmetic, date calculations, or multi-variable tracking, the model’s “mental math” frequently fails. Even a model that perfectly understands the structure of a word problem can stumble on 47 × 23 or lose track of running totals across a dozen transactions.
PAL decouples understanding from computation. The model reads the problem and translates its reasoning into Python code — variable assignments, loops, conditionals, function calls. This code is the reasoning chain, expressed in a language where every step is unambiguous and executable. The code then runs in a real Python interpreter, which handles all arithmetic with perfect precision.
Think of it as hiring a brilliant analyst who cannot do arithmetic to work alongside a calculator. The analyst reads the problem, decides what calculations are needed, writes them down as instructions — and the calculator executes them flawlessly. Together, they are far more reliable than either alone.
When a model reasons in natural language, it can say “47 times 23 is 1,081” and no one catches the error until the final answer is wrong (it is actually 1,081 — but try 47 × 38 and watch errors compound). In code, 47 * 23 is executed by the interpreter and returns 1081 every time. PAL’s insight is that the model should reason about what to compute, not perform the computation itself. This separation eliminates an entire category of LLM errors.
The PAL Process
Four stages from natural language problem to verified answer
Read and Understand the Problem
The language model reads the natural language problem and identifies the key quantities, relationships, and constraints. This is the step where the model’s natural language understanding shines — parsing ambiguous phrasing, identifying relevant information, and filtering out distractors.
“A farmer has 3 fields. The first field produces 120 bushels of wheat, the second produces 85, and the third produces 1.5 times as much as the first two combined. How many total bushels does the farmer harvest?”
Translate Reasoning into Python Code
Instead of computing the answer in natural language, the model writes Python code that represents each reasoning step as a variable assignment or expression. The code reads like a structured proof: each line corresponds to one logical step, making the reasoning fully transparent and verifiable.
field_1 = 120field_2 = 85field_3 = 1.5 * (field_1 + field_2)total = field_1 + field_2 + field_3print(total)
Execute Code in Python Interpreter
The generated code is sent to an external Python interpreter for execution. The interpreter handles all arithmetic, data manipulation, and logic with machine precision. No rounding errors, no arithmetic mistakes, no lost variables — the computation is exact.
Interpreter runs: field_3 = 1.5 * (120 + 85) = 1.5 * 205 = 307.5; total = 120 + 85 + 307.5 = 512.5. Output: 512.5.
Return the Verified Answer
The interpreter’s output becomes the final answer. Because the code itself serves as an interpretable reasoning chain, anyone can review it to verify that the logic is correct — checking both the model’s understanding and the computation. Always review the generated code to confirm it correctly represents the problem before relying on the output.
Final answer: “The farmer harvests 512.5 total bushels of wheat.” The code serves as a verifiable proof — each variable maps to a quantity in the problem, and the interpreter guarantees the math is correct.
See the Difference
Why code-based reasoning eliminates arithmetic errors
Chain-of-Thought Only
A school has 4 classrooms. Room A has 28 students, Room B has 31, Room C has 26, and Room D has 33. If 15% of all students are absent today, how many students are present?
Total students: 28 + 31 + 26 + 33 = 118. 15% of 118 is about 17.7, so roughly 18 absent. 118 minus 18 = 100 students present. (Note: verify these calculations independently.)
PAL
room_a = 28room_b = 31room_c = 26room_d = 33total = room_a + room_b + room_c + room_dabsent = total * 0.15present = total - absentprint(f"Total: {total}, Absent: {absent}, Present: {present}")
Total: 118, Absent: 17.7, Present: 100.3. Every step is exact, the reasoning chain is verifiable in the code, and no precision is lost. Always review the generated code to confirm it correctly models the problem.
Natural Language Works Too
While structured frameworks and contextual labels are powerful tools, LLMs are exceptionally good at understanding natural language. As long as your prompt contains the actual contextual information needed to create, answer, or deliver the response you’re looking for — the who, what, why, and constraints — the AI can produce complete and accurate results whether you use a formal framework or plain conversational language. But even in 2026, with the best prompts, verifying AI output is always a necessary step.
PAL in Action
See how code-based reasoning produces verifiable, precise answers
“A bakery makes 240 loaves of bread per day. They sell 60% in the morning and 25% of the remainder in the afternoon. How many loaves are left at closing? If each unsold loaf costs $3.50 in wasted ingredients, what is the daily waste cost?”
Generated Code:
daily_production = 240
morning_sold = daily_production * 0.60
after_morning = daily_production - morning_sold
afternoon_sold = after_morning * 0.25
remaining = after_morning - afternoon_sold
waste_cost = remaining * 3.50
print(f"Remaining: {remaining}, Waste cost: ${waste_cost}")
Interpreter Output: Remaining: 72.0, Waste cost: $252.0
Final answer: 72 loaves remain at closing, costing $252.00 in wasted ingredients daily. Review the code logic to confirm it matches the problem’s intent before acting on these numbers.
“A project started on January 15, 2025 and has a 90-day deadline. The team works 5 days per week (no weekends). What is the actual calendar completion date accounting for weekends?”
Generated Code:
from datetime import date, timedelta
start = date(2025, 1, 15)
work_days_needed = 90
current = start
days_worked = 0
while days_worked < work_days_needed:
current += timedelta(days=1)
if current.weekday() < 5:
days_worked += 1
print(f"Completion: {current}")
Interpreter Output: Completion: 2025-05-23
Final answer: The project completes on May 23, 2025 (accounting for weekends, 126 calendar days for 90 work days). This excludes holidays — verify against your actual work calendar.
“You invest $5,000 at 4.5% annual interest compounded monthly. After 3 years, you add another $2,000 and continue for 2 more years at the same rate. What is the final balance?”
Generated Code:
principal_1 = 5000
rate = 0.045
monthly_rate = rate / 12
months_phase_1 = 3 * 12
balance_after_3yr = principal_1 * (1 + monthly_rate) ** months_phase_1
balance_after_deposit = balance_after_3yr + 2000
months_phase_2 = 2 * 12
final_balance = balance_after_deposit * (1 + monthly_rate) ** months_phase_2
print(f"Final balance: ${final_balance:.2f}")
Interpreter Output: Final balance: $8,370.42
Final answer: After 5 years, the final balance is $8,370.42. The code shows exactly how each phase of the investment compounds. This is a mathematical model — consult a financial professional for actual investment decisions.
When to Use PAL
Best for problems where computation must be exact
Perfect For
Multi-step arithmetic, algebra, and quantitative reasoning where a single calculation error invalidates the entire answer.
Problems involving calendar arithmetic, time zone conversions, or scheduling — areas where LLMs are notoriously unreliable without code support.
Compound interest, amortization schedules, portfolio calculations — any financial reasoning where precision matters and errors have real-world consequences.
When you need to filter, sort, aggregate, or transform structured data and need deterministic, reproducible results.
Skip It When
Writing, summarizing, or answering questions that involve no computation — the code layer adds unnecessary complexity without benefit.
When the reasoning involves semantic judgments that cannot be expressed as code — consider Chain of Code (CoC) which extends PAL with the LMulator for these hybrid scenarios.
When you cannot run Python code — PAL’s entire advantage comes from the interpreter. Without it, use Chain-of-Thought with explicit step-by-step reasoning instead.
Use Cases
Where PAL delivers the most value
Educational Math Problems
Solve multi-step math problems with a visible, verifiable code chain that shows students exactly how each step connects to the next — perfect for teaching problem-solving structure.
Business Metrics Dashboards
Calculate KPIs, conversion rates, growth percentages, and projections from raw business data with guaranteed arithmetic accuracy across multi-step computations.
Scientific Calculations
Unit conversions, statistical analyses, and formula evaluations where the model understands the science but the math must be precise — no rounding errors allowed.
Scheduling and Planning
Calculate project timelines, resource allocation, and scheduling conflicts using date arithmetic that accounts for weekends, holidays, and time zones.
Audit and Compliance Calculations
Tax computations, regulatory threshold checks, and financial compliance calculations where errors have legal consequences and every step must be auditable.
Inventory Management
Track stock levels, calculate reorder points, and compute supply chain logistics where running totals across hundreds of transactions must be exactly right.
Where PAL Fits
PAL pioneered the code-as-reasoning paradigm
PAL’s insight — that language models should generate code rather than compute answers directly — is now so fundamental that it is built into the architecture of modern AI systems. When Claude runs Python code, when GPT-4 uses the Code Interpreter, or when Gemini executes calculations, they are all following the principle PAL established: let language models do what they do best (understand and translate), and let code interpreters do what they do best (compute precisely).
Related Techniques
Explore the code reasoning family of techniques
Think in Code, Execute for Accuracy
Try PAL’s code-based reasoning approach on your own computational problems or explore more code reasoning techniques.