feat(echo): Option B value shape + product type + echoAdd (structured loss, generalized)#43
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…sidue as projections; capstones over Step* https://claude.ai/code/session_01PgHpCFzwYB7Qy9L6kmR8CE
.claude/worktrees/ holds throwaway git worktrees used by background agents; never commit them. https://claude.ai/code/session_01PgHpCFzwYB7Qy9L6kmR8CE
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Echo-types proof work on
proofs/Tangle.lean— the structured-loss generalization, complete. Four commits, each independently green under pinnedv4.14.0, nosorry/axiom/admit.4296c0a) —echoVal residue resultis the canonical formed echo;echoCloseis a redex reducing into one;lower/residueare the two generic projections; capstones overStepStar.b274995) —Ty.prod+pair/fst/snd, full Progress/Preservation/Determinism/infer.echoAdd(b274995) —addis lossy;echoAdd n₁ n₂ ↝ echoVal (pair n₁ n₂) (n₁+n₂). CapstoneechoAdd_distinguishes:1+3and2+2both lower to4, residues distinct.echoEq(3a5e9a3) —eqis lossy; residue = operand pair, result = bool. CapstoneechoEq_distinguishes:1≟2and3≟4both lower tofalse, residues distinct.So structured loss now spans all three of Tangle's lossy operations (
close,add,eq), each with a recoverable residue and a non-injectivity theorem — the echo-types thesis realized across the language's lossy surface.Verification
lean Tangle.lean→ 0 errors; banned-token grep clean.#print axioms: metatheory uses onlypropext/Quot.sound; all six echo capstones depend on zero axioms.Note
The red
analyze (javascript-typescript)check is an unrelated CodeQL default-setup misconfiguration (analyzes JS/TS on a repo that bans them) — a repo-settings item, not fixable from this branch. The Lean oracle is green on every commit.Next track (separate): TG-1 (
let, full de Bruijn).🤖 Generated with Claude Code