feat(formal): grow P-2 to the STLC with functions + the substitution lemma

[hyperpolymath]

What

P-2, Wave 1: the STLC with functions. Adds what the first-order P2_Progress.v lacked — functions, binders, and the substitution lemma. Full progress + preservation for the simply-typed lambda calculus (base type TUnit + →), call-by-value, named (nat) variables.

Axiom-free and funext-free

The substitution lemma's abstraction case normally wants context equality (update_shadow/update_permute), which needs functional_extensionality — an axiom. This development avoids it entirely: contexts are compared only on a term's free variables (free_in_context + context_invariance), so it uses no functional_extensionality and Print Assumptions stays "Closed under the global context". No Admitted.

Contents

free_in_context · context_invariance · subst_preserves_typing (the substitution lemma) · canonical forms · progress (induction on typing) · preservation (induction on the step relation). Discharges the Siblings_Stated P2 statements at the closed-term (empty-context) instantiation, as P2_Progress.v does.

Scope (honest)

Simply-typed only — the QTT/affine quantities (the substructural context-splitting discipline, the heart of "AffineScript is affine") are the remaining increment on top of this.

Track status

10 files, 16 closure reports, zero axioms. P2_Progress.v stays as the first-order seed; P2_Stlc.v is the grown STLC (the K1/K1Let, P3Sound/P3Graph pattern). justfile/_CoqProject build it; .hypatia-ignore extends the Coq-.v-isn't-V-lang carve-out; README + PROOF-NEEDS.adoc P-2 row updated.

just -f formal/justfile check

🤖 Generated with Claude Code

https://claude.ai/code/session_01KPG9mEQXFyA3k7NWAzMNMr

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Generated by Claude Code

[github-actions]

🔍 Hypatia Security Scan

Findings: 41 issues detected

Severity	Count
🔴 Critical	2
🟠 High	23
🟡 Medium	16

⚠️ Action Required: Critical security issues found!

View findings

[
  {
    "reason": "Action denoland/setup-deno@v2 needs attention",
    "type": "unpinned_action",
    "file": "publish-jsr.yml",
    "action": "pin_sha",
    "rule_module": "workflow_audit",
    "severity": "medium"
  },
  {
    "reason": "Issue in instant-sync.yml",
    "type": "secret_action_without_presence_gate",
    "file": "instant-sync.yml",
    "action": "peter-evans/repository-dispatch",
    "rule_module": "workflow_audit",
    "severity": "high"
  },
  {
    "reason": "Shell execution -- validate input before passing to shell (1 occurrences, CWE-78)",
    "type": "js_exec_sync",
    "file": "/home/runner/work/affinescript/affinescript/packages/affinescript-cli/mod.js",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "high"
  },
  {
    "reason": "Shell execution -- validate input before passing to shell (2 occurrences, CWE-78)",
    "type": "js_exec_sync",
    "file": "/home/runner/work/affinescript/affinescript/packages/affine-vscode/mod.js",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "high"
  },
  {
    "reason": "Shell execution -- validate input before passing to shell (1 occurrences, CWE-78)",
    "type": "js_exec_sync",
    "file": "/home/runner/work/affinescript/affinescript/affinescript-vite/src/affine-plugin-improved.js",
    "action": "flag",
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    "severity": "high"
  },
  {
    "reason": "expect() in hot path (32 occurrences, CWE-754)",
    "type": "expect_in_hot_path",
    "file": "/home/runner/work/affinescript/affinescript/affinescriptiser/src/codegen/wasm_gen.rs",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "medium"
  },
  {
    "reason": "expect() in hot path (29 occurrences, CWE-754)",
    "type": "expect_in_hot_path",
    "file": "/home/runner/work/affinescript/affinescript/affinescriptiser/src/codegen/affine_gen.rs",
    "action": "flag",
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    "severity": "medium"
  },
  {
    "reason": "unsafe block -- requires SAFETY comment (2 occurrences, CWE-676)",
    "type": "unsafe_block",
    "file": "/home/runner/work/affinescript/affinescript/runtime/src/panic.rs",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "medium"
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  {
    "reason": "unsafe block -- requires SAFETY comment (1 occurrences, CWE-676)",
    "type": "unsafe_block",
    "file": "/home/runner/work/affinescript/affinescript/runtime/src/alloc.rs",
    "action": "flag",
    "rule_module": "code_safety",
    "severity": "medium"
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  {
    "reason": "unsafe block -- requires SAFETY comment (3 occurrences, CWE-676)",
    "type": "unsafe_block",
    "file": "/home/runner/work/affinescript/affinescript/runtime/src/ffi.rs",
    "action": "flag",
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]

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