// Moved from docs/05-operations/refinement/capa.adoc to docs/working/archive/operations/refinement/capa.adoc on 2026-06-16 (docs reorg Phase 2)
= StarForth C↔Isabelle Refinement Defect Tracking
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== Overview

This document tracks all discrepancies between the Isabelle formal theories and the C implementation.

**Purpose:** Serve as a Corrective Action/Preventive Action (CAPA) log for the iterative refinement process.
Each defect/discrepancy receives a unique ID, root cause analysis, corrective action plan, and verification status.

**Process:**
1. Compare Isabelle theory (spec) to C code (implementation) 2. For each discrepancy, create a DEFECT entry 3. Decide: Fix theory?
Fix code?
Revise both?
4. Execute corrective action 5. Prove refinement or update CAPA 6. Close defect when verified

[cols="1,2,1,2"]
|===
| **Phase** | **Scope** | **Status** | **Target Date**

| 1 | vm.c core stack/execution | Not started | TBD
| 2 | Root-level *.c utilities | Not started | TBD
| 3 | Test harness integration | Not started | TBD
| 4 | Primitive dictionary (Forth words) | Not started | TBD
| 5 | VM expansion & iteration | Not started | TBD
|===

---

== Summary Statistics

[cols="1,1,1,1,1"]
|===
| Total Defects | Open | In Progress | Resolved | Not Applicable

| 0 | 0 | 0 | 0 | 0
|===

*Last Updated:* {docdate}

---

== DEFECT Template

[source]
----
== DEFECT-NNN: <Brief Title>

[cols="1,3"]
|===
| **ID** | DEFECT-NNN
| **Phase** | N - <Phase Name>
| **Component** | <file.c>::<function>
| **Theory** | <Theory.thy>::<definition/lemma>
| **Status** | OPEN / IN-PROGRESS / CLOSED / NOT-APPLICABLE
| **Severity** | CRITICAL / HIGH / MEDIUM / LOW
| **Priority** | P0 / P1 / P2 / P3
| **Date Created** | YYYY-MM-DD
| **Date Closed** | YYYY-MM-DD (if applicable)
|===

=== Description

Concise description of the discrepancy between theory and code.

Example: "Theory requires precondition X, but code doesn't enforce it"

=== Root Cause Analysis

[ ] **Theory is incorrect** - Specification was wrong/incomplete
[ ] **Code is incorrect** - Implementation doesn't match spec
[ ] **Both need revision** - Specification incomplete, code needs update
[ ] **Misunderstanding** - Actually aligned, just poorly communicated
[ ] **Environmental** - External constraint discovered

*Explanation:*
(Detailed analysis of why the discrepancy exists)

=== Impact

**Correctness Impact:** (Does this break the property being proven? Yes/No/Unknown)

**Scope:** (How many functions/operations affected?)

**Risk:** (Could this cause runtime failure if unresolved?)

=== Corrective Action Plan

**Option A (Recommended):**
(Action description)

[source,c]
----
// Code change example if applicable
----

**Option B (Alternative):**
(Alternative approach)

**Rationale for selection:**
(Why Option A is best)

=== Verification Plan

**Step 1:** (First validation step)

**Step 2:** (Refinement proof to attempt)

**Step 3:** (Testing/validation)

**Success Criteria:** (How do we know it's resolved?)

=== Implementation Status

- [ ] Corrective action approved
- [ ] Code changes implemented
- [ ] Theory updated (if needed)
- [ ] Refinement proof started
- [ ] Refinement proof complete
- [ ] Integration testing passed
- [ ] Defect marked CLOSED

=== References

- **Related Defects:** (Other CAPA entries)
- **Proof File:** (docs/src/internal/formal/StarForth_Refinement.thy, line NNN)
- **C File:** (src/vm.c, line NNN)
- **Theory File:** (VM_Core.thy, line NNN)

=== Discussion Notes

*[2025-10-30]:* Initial defect entry. Awaiting team discussion on root cause.

---
----

---

== PHASE 1: VM Core Refinement

[cols="1,2,1,1"]
|===
| **ID** | **Title** | **Severity** | **Status**

|===

=== DEFECT-001: Stack Push Error Handling

[cols="1,3"]
|===
| **ID** | DEFECT-001
| **Phase** | 1 - VM Core
| **Component** | src/vm.c::stack_push()
| **Theory** | VM_Stacks.thy::push :: nat → vm_state → vm_state
| **Status** | OPEN
| **Severity** | HIGH
| **Priority** | P0
| **Date Created** | 2025-10-30
|===

==== Description

**Theory side:** `push` is a pure function that always succeeds.
Precondition: stack not full.
Theory treats error handling through explicit VM error state: `vm_error_flag`.

**Code side:** `stack_push()` checks bounds and sets error flag, but the actual stack modification happens unconditionally.

**Discrepancy:** Does the code guarantee it won't overflow?
Theory assumes stack is finite and bounded.

==== Root Cause Analysis

[x] **Code is incomplete** - Needs formal contract specification
[ ] **Theory is incorrect**
[ ] **Both need revision**

The code correctly prevents overflow but doesn't explicitly formalize this against the theory's precondition.
The theory's `push` definition assumes: "If the precondition holds (stack not full), the operation succeeds." The code needs a formal proof that the bounds check actually maintains the invariant.

==== Impact

**Correctness Impact:** YES - Stack overflow is a critical safety property

**Scope:** All stack operations (push, pop, data/return stack)

**Risk:** CRITICAL - Unhandled overflow could corrupt VM state

==== Corrective Action Plan

**Option A (Recommended): Formalize the contract**

Add explicit precondition proof that shows:

```
IF dsp < STACK_SIZE THEN
  code_push(state) = theory_push(state)
AND
  resulting_dsp = old_dsp + 1
AND
  error_flag = NO_ERROR
```

The C code must formally prove bounds enforcement.

[source,c]
----
/**
 * REFINEMENT: Implements VM_Stacks.thy::push (line 42)
 * Precondition: data_stack_pointer < STACK_MAX
 * Postcondition: push succeeds and error_flag == OK OR push fails and error_flag == STACK_OVERFLOW
 */
void stack_push(vm_state_t *state, uint16_t value) {
    // Precondition check - must prove this prevents overflow
    if (state->dsp >= STACK_MAX - 1) {
        state->error = VM_ERROR_STACK_OVERFLOW;
        return;  // REFINEMENT: Matches theory's error case
    }

    // Actual push - REFINEMENT: Corresponds to theory_push modification
    state->data_stack[++state->dsp] = value;
    state->error = VM_ERROR_NONE;

    // REFINEMENT INVARIANT: 0 <= dsp < STACK_MAX always holds after this
}
----

**Option B: Revise theory to explicit error cases**

Modify theory to make error handling explicit at the HOL level.
(More complex but gives stronger guarantees)

==== Verification Plan

**Step 1:** Write refinement lemma

```isabelle
lemma stack_push_refines:
  assumes "dsp < STACK_MAX - 1"
  shows "code_push(state, value) = theory_push(state, value)"
  by (simp add: stack_push_def, ...)
```

**Step 2:** Write overflow lemma

```isabelle
lemma stack_push_overflow:
  assumes "dsp ≥ STACK_MAX - 1"
  shows "code_push_sets_error(state)"
  by (simp add: stack_push_def, ...)
```

**Step 3:** Integration - prove `code_push ⊑ theory_push` with error handling

**Step 4:** Run: `make verify-defect DEFECT=001`

**Success Criteria:**
- [ ] Isabelle proofs compile without sorry - [ ] Code annotations match theory references - [ ] Test suite passes with new invariants - [ ] No assumptions about bounds outside code

==== Implementation Status

- [ ] Corrective action approved
- [ ] Code changes implemented
- [ ] Theory updated (if needed)
- [ ] Refinement proof started
- [ ] Refinement proof complete
- [ ] Integration testing passed
- [ ] Defect marked CLOSED

==== References

- **C File:** src/vm.c, lines 145-165
- **Theory File:** VM_Stacks.thy, line 42
- **Refinement Theory:** docs/src/internal/formal/StarForth_Refinement.thy (to be created)

==== Discussion Notes

*[2025-10-30]:* Initial defect entry.
Critical path item for Phase 1.
Need team consensus on whether to prove precondition in code or lift error handling to theory level.

---

=== DEFECT-002: Return Stack Misalignment

[cols="1,3"]
|===
| **ID** | DEFECT-002
| **Phase** | 1 - VM Core
| **Component** | src/vm.c::execute_call(), src/vm.c::execute_return()
| **Theory** | VM_Stacks.thy::push_return, pop_return
| **Status** | OPEN
| **Severity** | HIGH
| **Priority** | P0
| **Date Created** | 2025-10-30
|===

==== Description

**Theory side:** Return stack operations are modeled as a simple LIFO stack in HOL.
Theory assumes: Each CALL pushes address, each RET pops address.
Stack is always balanced.

**Code side:** Code has asymmetric behavior:
- CALL increments RSP *before* storing (pre-increment) - RET retrieves *then* decrements RSP (post-decrement)

**Discrepancy:** Do pre vs post increment/decrement semantics match the theory's abstract model?

==== Root Cause Analysis

[x] **Code is incomplete** - Semantics not formally matched to theory
[ ] **Theory is incorrect**
[ ] **Both need revision**

The implementation detail (pre vs post increment) works correctly but must be proven equivalent to the theory's model.
This is a refinement of implementation detail to abstract specification.

==== Impact

**Correctness Impact:** YES - CALL/RET is core VM operation

**Scope:** All subroutine calls and returns

**Risk:** HIGH - Misalignment could cause deep stack corruption that's hard to detect

==== Corrective Action Plan

**Option A (Recommended): Prove semantic equivalence**

Show that the pre/post increment patterns are equivalent to the abstract FIFO model:

```isabelle
lemma call_push_equiv:
  assumes "valid_rsp state"
  shows "execute_code_call state addr =
         theory_push_return_address state addr"
```

Add detailed code comments showing correspondence:

[source,c]
----
/**
 * REFINEMENT: execute_call implements CALL word
 * Theory: VM_Stacks.thy::call_instr (line 156)
 *
 * Implements: push return address to return stack
 * Code pattern: rsp++ then store (pre-increment semantics)
 * Equivalent to theory's abstract push operation
 */
void execute_call(vm_state_t *state, uint16_t address) {
    // Theory: push_return(state, return_addr)
    // Code: pre-increment then store
    state->return_stack[++state->rsp] = state->pc + 1;
    state->pc = address;
}
----

==== Verification Plan

**Step 1:** Formalize pre/post increment semantics in Isabelle

**Step 2:** Prove equivalence to abstract FIFO model

**Step 3:** Verify call/return round-trip maintains stack balance

**Step 4:** Test with complex call chains (recursion, nested calls)

**Success Criteria:**
- [ ] Refinement proof for execute_call complete - [ ] Refinement proof for execute_return complete - [ ] Round-trip property proven (CALL n; ... RET restores state) - [ ] Recursion depth test passes

==== Implementation Status

- [ ] Corrective action approved
- [ ] Code changes implemented
- [ ] Theory updated (if needed)
- [ ] Refinement proof started
- [ ] Refinement proof complete
- [ ] Integration testing passed
- [ ] Defect marked CLOSED

==== References

- **C File:** src/vm.c, lines 280-295
- **Theory File:** VM_Stacks.thy, lines 156-180
- **Related:** DEFECT-001 (stack bounds)

==== Discussion Notes

*[2025-10-30]:* Initial defect.
Depends on DEFECT-001 resolution (bounds checking).

---

=== DEFECT-003: Instruction Dispatch vs Theory Match

[cols="1,3"]
|===
| **ID** | DEFECT-003
| **Phase** | 1 - VM Core
| **Component** | src/vm.c::dispatch_instruction()
| **Theory** | VM_Core.thy::exec_instruction
| **Status** | OPEN
| **Severity** | MEDIUM
| **Priority** | P1
| **Date Created** | 2025-10-30
|===

==== Description

**Theory side:** `exec_instruction` is defined as a case analysis over all instruction types.
Theory explicitly handles each opcode with corresponding state transformation.

**Code side:** Dispatch uses function pointers / switch statement.
Some opcodes call helper functions.
Question: Are all code paths accounted for in theory?
Do all helpers match theory definitions?

==== Root Cause Analysis

[ ] **Code is incomplete** - Some opcodes not in theory?
[ ] **Theory is incomplete** - Not all code paths captured?
[x] **Both need revision** - Systematic mapping needed

Need to enumerate every opcode in code and match against theory definitions.
Some helpers (e.g., arithmetic operations) may need separate refinement proofs.

==== Impact

**Correctness Impact:** MEDIUM - Core execution but typically driven by other proofs

**Scope:** All 200+ Forth words eventually

**Risk:** MEDIUM - Missing opcodes could cause undefined behavior

==== Corrective Action Plan

**Option A (Recommended): Create opcode mapping matrix**

Build explicit enumeration:
- Column A: C opcode constant (e.g., OP_PUSH) - Column B: C function handler - Column C: Isabelle definition - Column D: Refinement status (unproven/in-progress/complete)

Then systematically work through each row.

[source,c]
----
/**
 * REFINEMENT MAPPING TABLE:
 * OP_PUSH (0x01)    -> code_push()      -> VM_Core.push_instr
 * OP_DUP (0x02)     -> code_dup()       -> VM_DataStack_Words.dup_instr
 * OP_DROP (0x03)    -> code_drop()      -> VM_DataStack_Words.drop_instr
 * ...
 * See docs/REFINEMENT_OPCODES.adoc for complete matrix
 */
----

==== Verification Plan

**Step 1:** Create comprehensive opcode matrix (spreadsheet or structured doc)

**Step 2:** For each opcode, list: C function, Isabelle definition, proof status

**Step 3:** Start with subset: PUSH, DUP, DROP, SWAP (basic stack ops)

**Step 4:** Complete others in phases

**Success Criteria:**
- [ ] Opcode matrix complete and verified - [ ] All code functions have Isabelle counterpart (or documented reason for deviation) - [ ] No orphaned code paths

==== Implementation Status

- [ ] Corrective action approved
- [ ] Code changes implemented
- [ ] Theory updated (if needed)
- [ ] Refinement proof started
- [ ] Refinement proof complete
- [ ] Integration testing passed
- [ ] Defect marked CLOSED

==== References

- **C File:** src/vm.c, dispatch function
- **Theory File:** VM_Core.thy, VM_DataStack_Words.thy, VM_ReturnStack_Words.thy, VM_Words.thy

==== Discussion Notes

*[2025-10-30]:* Umbrella defect covering opcode-by-opcode refinement.
Will spawn individual DEFECTs as work progresses.

---

== PHASE 2: Utilities Refinement

[cols="1,2,1,1"]
|===
| **ID** | **Title** | **Severity** | **Status**

| (Pending Phase 1 completion) | - | - | -
|===

---

== PHASE 3: Test Harness Integration

[cols="1,2,1,1"]
|===
| **ID** | **Title** | **Severity** | **Status**

| (Pending Phase 1-2 completion) | - | - | -
|===

---

== PHASE 4: Primitive Dictionary

[cols="1,2,1,1"]
|===
| **ID** | **Title** | **Severity** | **Status**

| (Pending Phase 1-3 completion) | - | - | -
|===

---

== PHASE 5: VM Expansion & Iteration

[cols="1,2,1,1"]
|===
| **ID** | **Title** | **Severity** | **Status**

| (Pending Phase 1-4 completion) | - | - | -
|===

---

== How to Use This Document

=== Adding a New Defect

1. Find the next available DEFECT-NNN ID
2. Copy the DEFECT template section
3. Fill in all required fields
4. Link from the appropriate Phase section
5. Update the summary statistics table
6. Commit with message: `docs: Add DEFECT-NNN: <title>`

=== Tracking Progress

Status values:
- **OPEN** - Defect identified, awaiting action - **IN-PROGRESS** - Corrective action underway - **CLOSED** - Verified resolved - **NOT-APPLICABLE** - Found to be non-issue upon investigation

Update status via:

```bash
make defect-status  # Shows current stats
make verify-defect DEFECT=001  # Details for specific defect
```

=== Code Annotations

Every C function with a theory counterpart should have a header comment:

```c
/**
 * REFINEMENT: <Theory>::<definition> (line NNN)
 * C Function: <function_name>
 * Related CAPAs: DEFECT-001, DEFECT-003
 * Status: [UNPROVEN / IN-PROGRESS / PROVEN]
 */
```

=== Generating Reports

```bash
make refinement-status          # Summary of all defects
make refinement-phase1          # Phase 1 details
make refinement-capa-print      # AsciiDoc → HTML/PDF
```

---

== Legend

[cols="1,3"]
|===
| **Symbol** | **Meaning**

| ✅ | Complete/Verified
| ⚠️ | In Progress/Caution
| ❌ | Incomplete/Blocked
| 📋 | Pending Action
| 🔍 | Under Investigation
|===

---

== Version History

[cols="1,1,2"]
|===
| **Date** | **Version** | **Changes**

| 2025-10-30 | 1.0 | Initial CAPA document created with template and Phase 1 defects
|===

Generated: {docdate}