Generate High-Level TLA+ Model from Source Code

Create a TLA+ specification from source code by understanding the code's intent, abstracting implementation details, and focusing on the essential concurrent/distributed behavior.

Philosophy

TLA+ models should capture what the system does, not how it does it:

• Focus on state transitions and their effects
• Abstract away implementation details (memory management, error handling boilerplate)
• Identify the core concurrent/distributed behavior worth verifying
• Keep the model small enough to be tractable for model checking

Workflow Overview

┌─────────────────────────────────────────────────────────────────┐
│ Phase 1: Understand the Code                                    │
│   → What problem does it solve?                                 │
│   → What are the key functions and their purposes?              │
│   → What state is being managed?                                │
└─────────────────────────────────────────────────────────────────┘
                              ↓
┌─────────────────────────────────────────────────────────────────┐
│ Phase 2: Identify Abstractions                                  │
│   → What are the essential state variables?                     │
│   → What are the atomic actions?                                │
│   → What concurrency/ordering matters?                          │
└─────────────────────────────────────────────────────────────────┘
                              ↓
┌─────────────────────────────────────────────────────────────────┐
│ Phase 3: Write TLA+ Specification                               │
│   → Define constants and variables                              │
│   → Write Init and actions                                      │
│   → Define Next as disjunction of actions                       │
│   → Check specification syntax with TLC parser SANY             │
└─────────────────────────────────────────────────────────────────┘
                              ↓
┌─────────────────────────────────────────────────────────────────┐
│ Phase 4: Propose Properties                                     │
│   → Safety invariants                                           │
│   → Safety properties (what must be true at all times)          │
│   → Liveness properties (what must eventually happen)           │
└─────────────────────────────────────────────────────────────────┘

---

Phase 1: Understand the Code

Step 1.1: Identify the Problem Domain

Read the code and answer in English:

1. What is the overall purpose? (e.g., "thread-safe connection management", "distributed consensus", "producer-consumer queue")
2. What entities exist? (e.g., threads, processes, clients, servers, connections)
3. What resources are shared? (e.g., queues, counters, state machines)

Step 1.2: Catalog Functions and Their Purpose

For each significant function, document:

Function	Purpose (in English)	Side Effects	Concurrency Notes
functionName	What it does	State changes	Thread-safe? Atomic?

Focus on:

• Public API functions (entry points)
• State-modifying functions (mutators)
• Synchronization points (locks, atomics, barriers)

Skip:

• Getters/accessors (unless they have side effects)
• Utility functions (formatting, logging)
• Error handling boilerplate

Step 1.3: Identify State Variables

List all mutable state that affects the system's behavior:

State Variable	Type	Purpose	Accessed By
varName	int/enum/struct	What it tracks	Which functions

Look for:

• Atomic variables (concurrent state)
• Protected fields (mutex-guarded data)
• State enums (state machines)
• Reference counts
• Queues and buffers

Step 1.4: Identify Concurrency Patterns

Recognize common patterns in the code:

Pattern	Indicators	TLA+ Abstraction
State machine	Enum state, switch statements	pc variable with transitions
Reference counting	refCount, addRef/release	Counter variable
Producer-consumer	Queue with enqueue/dequeue	Sequence variable
Lock-based	Mutex lock/unlock	Optional: model explicitly or abstract
Lock-free	Atomics, CAS operations	Atomic state transitions
Connection lifecycle	Connect/disconnect, states	State machine per connection

---

Phase 2: Identify Abstractions

Step 2.1: Choose Abstraction Level

High-level modeling principles:

1. Collapse implementation details: Multiple C++ statements → one TLA+ action
2. Abstract data structures: std::vector<T> → finite set or sequence
3. Simplify types: uint32_t refCount → Nat (natural number)
4. Ignore memory management: smart pointers, allocation → just the logical state
5. Model only relevant concurrency: If code is thread-safe, model the logical operations

Step 2.2: Map Code Elements to TLA+

Source Code	TLA+ Abstraction
Class with state machine	Variables + PC states
enum State	Set of constants {State1, State2, ...}
std::atomic<T>	Variable (atomicity is implicit in TLA+)
compare_exchange	Guarded action with atomic state change
Thread/process	Element of Threads set, may have own pc[thread]
shared_ptr<T>	Logical pointer (present/absent), or reference count
Mutex-protected region	Single atomic action (if treating as atomic)
Queue	Seq(Element) with Append/Head/Tail
Counter	Nat with increment/decrement

Step 2.3: Decide What to Model

Include:

• State transitions that affect correctness
• Concurrent access patterns
• Ordering dependencies between operations

Exclude:

• Error handling paths (unless modeling failure modes)
• Logging and diagnostics
• Performance optimizations that don't affect correctness
• Memory management details

---

Phase 3: Write TLA+ Specification

Step 3.1: Module Header and Constants

---------------------------- MODULE ModuleName ----------------------------
EXTENDS Naturals, Sequences, FiniteSets

\* Configuration constants
CONSTANTS
    Threads,          \* Set of threads/processes
    MaxValue          \* Bounds for model checking

\* State constants (if using state machine)
CONSTANTS
    State_Init,
    State_Active,
    State_Done

Step 3.2: Variables

VARIABLES
    state,            \* Current state of the system
    counter,          \* Example counter variable
    pc                \* Program counter for each thread (if multi-threaded)

vars == << state, counter, pc >>

Step 3.3: Type Invariant

TypeOk ==
    /\ state \in {State_Init, State_Active, State_Done}
    /\ counter \in Nat
    /\ counter <= MaxValue
    /\ pc \in [Threads -> PCStates]

Step 3.4: Initial State

Init ==
    /\ state = State_Init
    /\ counter = 0
    /\ pc = [t \in Threads |-> PC_Start]

Step 3.5: Actions

For each significant operation identified in Phase 1:

\* Action: Description of what this action models. This description should describe the effect of the action on the state of the system and role of this code in the overall system behavior.
\* Source: functionName() in source.cpp
ActionName(thread) ==
    /\ pc[thread] = PC_Ready           \* Guard: when can this happen?
    /\ state = State_Active            \* Additional guards
    /\ counter' = counter + 1          \* State changes
    /\ pc' = [pc EXCEPT ![thread] = PC_Next]
    /\ UNCHANGED << state >>           \* Explicitly unchanged variables

Action naming conventions:

• Use descriptive names matching the source function
• Include thread/process parameter if per-entity
• Add comments referencing source code location

Step 3.6: Next State Relation

Next ==
    \/ \E t \in Threads : ActionName(t)
    \/ \E t \in Threads : AnotherAction(t)
    \/ SystemWideAction

\* Stuttering step (optional, for liveness)
Spec == Init /\ [][Next]_vars

Step 3.7: Check Specification Syntax with TLC Parser SANY

If available, check specification syntax with TLA+ MCP tool tlaplus_mcp_sany_parse.

---

Phase 4: Propose Properties

Step 4.1: Safety Invariants

Safety invariants are state exspressions that must be true in every state:

\* No negative counter
CounterNonNegative == counter >= 0

\* Mutual exclusion
MutualExclusion ==
    Cardinality({t \in Threads : pc[t] = PC_Critical}) <= 1

\* State consistency
StateConsistency ==
    state = State_Done => counter > 0

Check safety invariants with TLA+ MCP tool tlaplus_mcp_tlc_check.

Common safety patterns:

Pattern	Invariant
No overflow	counter <= MaxValue
Mutual exclusion	At most one thread in critical section
No resource leak	Resources acquired = resources released
State validity	State machine only in valid states

Step 4.2: Safety Properties

Safety properties are temporal properties that state what must be true at all times:

\* Actions happen in order
OrderedActions ==
    [][pc = PC_Step1 => (pc' = PC_Step2)]_pc

Check safety properties with TLA+ MCP tool tlaplus_mcp_tlc_check.

Step 4.2: Liveness Properties

Liveness properties state what must eventually happen:

\* Every thread eventually completes
EventualCompletion ==
    \A t \in Threads : <>(pc[t] = PC_Done)

\* Counter eventually increases
EventualProgress ==
    counter < MaxValue ~> counter >= MaxValue

\* If disconnect is requested, it eventually completes
DisconnectCompletes ==
    [](disconnectRequested => <>(state = State_Disconnected))

Check liveness properties with TLA+ MCP tool tlaplus_mcp_tlc_check.

---

Output Format

After completing the phases, present:

1. English Summary

## Code Analysis Summary

### Purpose
[One paragraph describing what the code does]

### Key Functions
- `function1`: [purpose]
- `function2`: [purpose]

### State Variables
- `var1`: [what it tracks]
- `var2`: [what it tracks]

### Concurrency Model
[How threads/processes interact]

2. TLA+ Specification

Complete, runnable TLA+ module.

3. Properties Summary

## Proposed Properties

### Safety Invariants
1. **InvariantName**: [what it ensures]
2. **InvariantName**: [what it ensures]

### Liveness Properties
1. **PropertyName**: [what must eventually happen]

### Recommended Checks
- [ ] Run TLC with small bounds first
- [ ] Verify TypeOk holds
- [ ] Check for deadlock

---

Example: Modeling a Reference Counter

Source code pattern:

std::atomic<int32_t> counter {0};

bool reserve() {
    if (counter.fetch_add(1) >= 0) {
        return true;
    } else {
        release();
        return false;
    }
}

void release() {
    if (counter.fetch_sub(1) == threshold) {
        finish();
    }
}

TLA+ abstraction:

VARIABLES counter, finished

Reserve(thread) ==
    /\ counter >= 0
    /\ counter' = counter + 1
    /\ UNCHANGED finished

Release(thread) ==
    /\ counter > 0
    /\ counter' = counter - 1
    /\ finished' = IF counter' = 0 THEN TRUE ELSE finished

\* Safety: counter never goes negative while active
CounterSafety == finished = FALSE => counter >= 0

---

Tips for Effective Modeling

1. Start simple: Model the happy path first, add error handling later
2. Use small bounds: Threads = {T1, T2}, MaxValue = 3 for initial checks
3. Name constants descriptively: State_Connecting not S1
4. Comment actions: Reference source code locations
5. Verify incrementally: Check TypeOk and basic invariants before complex properties
6. Abstract atomicity: If source uses locks, model locked region as single action

Common Pitfalls

Pitfall	Solution
Model too detailed	Focus on state changes, not implementation steps
Missing UNCHANGED	Every variable must be primed or in UNCHANGED
Unbounded state	Add finite bounds for model checking
Implicit assumptions	Make all preconditions explicit guards
Modeling syntax, not semantics	Understand what code does, not how it's written