{"title":
 "R1: The signature is a parameter: one located refusal admits Σ_app, and every milestone statement takes it",
 "producer":
 ["GENERATED by tools/Drivers/Semantics.lean (make gen-semantics); do not edit",
  "format: effect4-semantics-report v8",
  "command: make gen-semantics",
  "inputs: tools/ProofGraph/Registry.lean, tools/Tools/Semantics.lean, tools/Drivers/Semantics.lean, tools/Tools/SemanticsDisplay.lean, tools/Tools/SemanticsDocument.lean, tools/Tools/Document.lean, tools/Tools/Document/Json.lean, src/Effect4/Laws/Auto/Semantics.lean, Test/Counterexamples/REGISTER.md, docs/core/decisions.md, lean-toolchain"],
 "format": "effect4-document/1",
 "body":
 [{"lines":
   [[{"text":
      "Open, not triaged: program admission at declared services is reached by tests only: authoring, Built, the session and Run.open admit at the table's own signature ⟨table, []⟩, and code generation's admission check is at nativeSignature table (decisions row 21; the slice plan's steps 3 and 4, docs/research/2026-10-04-claude-lead/sigapp-slice-plan.md)"}],
    [{"text":
      "Open, not triaged: the faces (22 lines) pinned to the built-in signature: Laws/Codegen/Admit, Laws/Codegen/Checked and Laws/Api/ModuleReadable take nativeSignature table (the Σ_app slice; C7, conditional on decisions row 115)"}],
    [{"text":
      "Open, not triaged: meaning, loop and run soundness at service declarations that rebind a code: restored 2026-10-04 at fresh codes only (SoundAnySignature.lean)"}],
    [{"text":
      "Open, waits on a ruling (decisions row 118: waits on a program that needs one): structured service carriers: LawfulSig admits flat carriers only (decisions row 118, open: waits on a program that needs one)"}]],
   "kind": "items"},
  {"title": "Requirement R1: The typing signature is a parameter",
   "kind": "part",
   "key": "about:req:R1",
   "body":
   [{"line":
     [{"text":
       "This page explains requirement R1 in Effect4. It covers what the requirement asks about signature parameterization, why open signatures matter for extensible applications, and how the property is checked."}],
     "kind": "para"},
    {"title": "What the requirement asks",
     "kind": "part",
     "key": "about:req:R1:what-it-asks",
     "body":
     [{"line":
       [{"text":
         "Requirement R1 demands that the language typing signature Σ remains an explicit parameter across all milestone statements and verification layers ("},
        {"code": "docs/core/system-map.md"},
        {"text": " §8)."}],
       "kind": "para"},
      {"line": [{"text": "The specification requires:"}], "kind": "para"},
      {"lines":
       [[{"text": "Program admission checks the application signature via "},
         {"code": "AdmittedSig Σ"},
         {"text": " and "},
         {"code": "admitSig_ok_iff"},
         {"text": "."}],
        [{"text":
          "The typed machine state reads the source's signature dynamically."}],
        [{"text":
          "Core typing theorems and milestone statements take the signature as an explicit hypothesis."}]],
       "kind": "items"},
      {"line":
       [{"text":
         "The runtime must not hard-code operations to a closed built-in set."}],
       "kind": "para"}]},
    {"title": "Why it matters",
     "kind": "part",
     "key": "about:req:R1:why-it-matters",
     "body":
     [{"line":
       [{"text":
         "Real-world Effect applications define custom operations, host integrations, and application services."}],
       "kind": "para"},
      {"line":
       [{"text":
         "If semantic theorems assumed a fixed operation signature, application-defined effects would lack formal verification."}],
       "kind": "para"},
      {"line":
       [{"text":
         "A signature that is a parameter lets an application add operations, and every milestone statement then takes the application's signature."}],
       "kind": "para"}]},
    {"title": "How it is checked",
     "kind": "part",
     "key": "about:req:R1:how-it-is-checked",
     "body":
     [{"line":
       [{"text":
         "The requirement is checked by proving that typing and evaluation hold for an admitted signature:"}],
       "kind": "para"},
      {"lines":
       [[{"text": "Algorithmic soundness and completeness against "},
         {"code": "HasTy"},
         {"text": " ("},
         {"code": "check_sound"},
         {"text": ", "},
         {"code": "check_complete"},
         {"text": ") quantify over any lawful typing signature in "},
         {"code": "src/Effect4/Laws/Program/Typing/CheckSound.lean"},
         {"text": "."}],
        [{"text": "Signature admission equivalence is stated by "},
         {"code": "admitSig_ok_iff"},
         {"text": " ("},
         {"code": "src/Effect4/Program/SigApp.lean"},
         {"text": ")."}],
        [{"text":
          "Operational typing across application signatures is stated by "},
         {"code": "meaning_typed_app"},
         {"text": " and "},
         {"code": "run_typed_app"},
         {"text": " ("},
         {"code": "src/Effect4/Laws/Program/SoundAnySignature.lean"},
         {"text": ")."}]],
       "kind": "items"},
      {"line":
       [{"text":
         "The plan on this page gives each theorem's status and the goals it rests on."}],
       "kind": "para"}]}]},
  {"nodes":
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     "label": "reachable_typed_admitted",
     "key": "Effect4.Program.Typed.reachable_typed_admitted",
     "detail": ""},
    {"status": "modulo",
     "ref": "claim:typed-state-admitted",
     "label": "reachable_typed",
     "key": "Effect4.Program.Typed.reachable_typed",
     "detail": ""},
    {"status": "modulo",
     "ref": "claim:decision-keeps-typed",
     "label": "decision_preserves",
     "key": "Effect4.Program.Typed.decision_preserves",
     "detail": ""},
    {"status": "modulo",
     "ref": "claim:step-deliver-preserves",
     "label": "deliver_preserves",
     "key": "Effect4.Program.Typed.deliver_preserves",
     "detail": ""},
    {"status": "modulo",
     "ref": "claim:step-loop-preserves",
     "label": "loop_preserves",
     "key": "Effect4.Program.Typed.loop_preserves",
     "detail": ""},
    {"status": "goal",
     "ref": "open:Effect4.Program.Typed.Evaluating.countdown_parks_positional",
     "label": "countdown_parks_positional",
     "key": "Effect4.Program.Typed.Evaluating.countdown_parks_positional",
     "detail": ""}],
   "kind": "graph",
   "key": "fig:open:R1",
   "edges":
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     "Effect4.Program.Typed.reachable_typed"],
    ["Effect4.Program.Typed.reachable_typed",
     "Effect4.Program.Typed.decision_preserves"],
    ["Effect4.Program.Typed.decision_preserves",
     "Effect4.Program.Typed.deliver_preserves"],
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     "Effect4.Program.Typed.loop_preserves"],
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    ["Effect4.Program.Typed.loop_preserves",
     "Effect4.Program.Typed.Evaluating.countdown_parks_positional"]],
   "caption":
   "The open part of R1: its planned goals and the theorems proved modulo them. An arrow goes from a node to a node its proof reaches first."},
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   [{"status": "open",
     "label": "No concept",
     "key": "none",
     "detail": "32 nodes, 5 open"},
    {"status": "proved",
     "ref": "concept:initial-algebras-folds",
     "label": "Initial Algebras & Folds",
     "key": "initial-algebras-folds",
     "detail": "6 nodes"},
    {"status": "proved",
     "ref": "concept:translation-simulation",
     "label": "Translation & Simulation",
     "key": "translation-simulation",
     "detail": "1 nodes"},
    {"status": "proved",
     "ref": "concept:store-typing",
     "label": "Store Typing",
     "key": "store-typing",
     "detail": "12 nodes"},
    {"status": "proved",
     "ref": "concept:residual-program-typing",
     "label": "Residual Program Typing",
     "key": "residual-program-typing",
     "detail": "17 nodes"},
    {"status": "proved",
     "ref": "concept:subtyping-algebra",
     "label": "Subtyping Algebra",
     "key": "subtyping-algebra",
     "detail": "44 nodes"},
    {"status": "proved",
     "ref": "concept:exact-codecs",
     "label": "Exact Codecs",
     "key": "exact-codecs",
     "detail": "1 nodes"},
    {"status": "open",
     "ref": "concept:reactive-scheduling",
     "label": "Reactive Scheduling",
     "key": "reactive-scheduling",
     "detail": "2 nodes, 1 open"},
    {"status": "proved",
     "ref": "concept:scope-lifetime-finalization",
     "label": "Scope Lifetime & Finalization",
     "key": "scope-lifetime-finalization",
     "detail": "4 nodes"}],
   "kind": "graph",
   "key": "fig:concepts:R1",
   "edges":
   [["none", "translation-simulation"],
    ["none", "store-typing"],
    ["none", "residual-program-typing"],
    ["none", "subtyping-algebra"],
    ["none", "exact-codecs"],
    ["initial-algebras-folds", "none"],
    ["translation-simulation", "initial-algebras-folds"],
    ["residual-program-typing", "store-typing"],
    ["residual-program-typing", "subtyping-algebra"],
    ["residual-program-typing", "none"],
    ["residual-program-typing", "exact-codecs"],
    ["subtyping-algebra", "none"],
    ["store-typing", "subtyping-algebra"],
    ["store-typing", "none"],
    ["none", "reactive-scheduling"],
    ["none", "initial-algebras-folds"],
    ["none", "scope-lifetime-finalization"],
    ["scope-lifetime-finalization", "store-typing"],
    ["scope-lifetime-finalization", "subtyping-algebra"],
    ["scope-lifetime-finalization", "residual-program-typing"],
    ["scope-lifetime-finalization", "initial-algebras-folds"],
    ["scope-lifetime-finalization", "none"],
    ["residual-program-typing", "initial-algebras-folds"]],
   "caption":
   "R1 by concept: each concept its nodes are placed at, by tag or by module. An arrow goes where a node's proof reaches a node of another concept."},
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      {"code": "lift_sound"},
      {"text": ", "},
      {"code": "subN_trans"},
      {"text": ", "},
      {"code": "causeInputError_upper"},
      {"text": ", "},
      {"code": "matchArgsB_sound"},
      {"text": ", "},
      {"code": "hom_eq_cata_ty"},
      {"text": ", "},
      {"code": "scopeParams_decl"},
      {"text": ", "},
      {"code": "withParams_param"}]],
    [[{"code": "call_arm"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "fits_mono"},
      {"text": ", "},
      {"code": "fits_subN"},
      {"text": ", "},
      {"code": "normalize_idem"},
      {"text": ", "},
      {"code": "order_trans"},
      {"text": ", "},
      {"code": "listOf_upper"},
      {"text": ", "},
      {"code": "fits_normalize"},
      {"text": ", "},
      {"code": "lift_sound"},
      {"text": ", "},
      {"code": "subN_trans"},
      {"text": ", "},
      {"code": "causeInputError_upper"},
      {"text": ", "},
      {"code": "matchArgsB_sound"},
      {"text": ", "},
      {"code": "hom_eq_cata_ty"},
      {"text": ", "},
      {"code": "scopeParams_body"},
      {"text": ", "},
      {"code": "withParams_of_none"}]],
    [[{"code": "Eliminator.lift_least"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "UnionRule.lift_least"}]],
    [[{"code": "mapM_total"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "mapM_cons_eq_some"}]],
    [[{"code": "closeOrder_eq"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "fiber_eliminator"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "subN_fiberOf_iff"},
      {"text": ", "},
      {"code": "normalize_idem"},
      {"text": ", "},
      {"code": "subN_trans"},
      {"text": ", "},
      {"code": "subN_refl"}]],
    [[{"code": "scopeParams_body"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "withParams_defOf"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "exit_eliminator"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "subN_exitOf_iff"},
      {"text": ", "},
      {"code": "normalize_idem"},
      {"text": ", "},
      {"code": "subN_trans"},
      {"text": ", "},
      {"code": "subN_refl"}]],
    [[{"code": "scopeParams_decl"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "withParams_param"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "UnionRule.lift_least"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "subN_trans"},
      {"text": ", "},
      {"code": "mapM_source"},
      {"text": ", "},
      {"code": "joinAll_le"}]],
    [[{"code": "subN_fiberOf_iff"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]],
    [[{"code": "mapM_source"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "mapM_cons_eq_some"}]],
    [[{"code": "joinAll_le"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "joinAll_all"}]],
    [[{"code": "joinAll_all"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"code": "foldl_all"}]],
    [[{"code": "foldl_all"}],
     [{"status": "proved"}],
     [{"text": "—"}],
     [{"text": "—"}]]],
   "kind": "table",
   "headers": ["Node", "Status", "Rests on", "Nearest nodes"]}]}