{"title": "R9: Never goes wrong: M7a–c on M7Fragment (the empty host table, answer-free tapes)", "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, waits on a ruling (decisions row 117: the frame contract, designed first): part two: a saved frame transports missingService across a change in the requirement row (decisions row 117)"}]], "kind": "items"}, {"title": "Requirement R9: Well-typed programs never go wrong", "kind": "part", "key": "about:req:R9", "body": [{"line": [{"text": "This page explains requirement R9 in Effect4. It covers what the requirement asks for type safety and defect exclusion, why non-halting matters, and how the property is checked."}], "kind": "para"}, {"title": "What the requirement asks", "kind": "part", "key": "about:req:R9:what-it-asks", "body": [{"line": [{"text": "Requirement R9 formalizes type safety by proving that every typed program execution satisfies "}, {"code": "ExitOk"}, {"text": " and never halts ("}, {"code": "docs/core/system-map.md"}, {"text": " §8, DB-16):"}], "kind": "para"}, {"lines": [[{"text": "Exit correctness: "}, {"code": "ExitOk w ty ex := FitsExit w ty ex ∧ NoShapeDefect ty ex"}, {"text": " holds at every typed exit position."}], [{"text": "Shape defect exclusion: "}, {"code": "NoShapeDefect"}, {"text": " excludes reserved malformed code defects such as "}, {"code": "badName"}, {"text": " and "}, {"code": "notImplemented"}, {"text": " (decisions row 107)."}], [{"text": "Non-halting: the small-step transition system never encounters a stuck configuration ("}, {"code": "machineTyped_not_halted"}, {"text": ")."}]], "kind": "items"}, {"line": [{"text": "The property is scoped to "}, {"code": "M7Fragment"}, {"text": ": a lawful source, an empty row table, an admitted closed program, and an answer-free tape."}], "kind": "para"}]}, {"title": "Why it matters", "kind": "part", "key": "about:req:R9:why-it-matters", "body": [{"line": [{"text": "Type systems aim to prove that well-typed programs cannot go wrong (Milner 1978)."}], "kind": "para"}, {"line": [{"text": "In untyped JavaScript, unhandled shapes, missing services, and internal runtime bugs cause unexpected crashes."}], "kind": "para"}, {"line": [{"text": "Requirement R9 asks that a checked program end in a value or a typed cause, and never halt the machine."}], "kind": "para"}]}, {"title": "How it is checked", "kind": "part", "key": "about:req:R9:how-it-is-checked", "body": [{"line": [{"text": "The requirement is checked by assembling the milestone proofs M5, M6, and M7:"}], "kind": "para"}, {"lines": [[{"text": "The route theorem "}, {"code": "m7_of_ledger"}, {"text": " states that load typing (M5) and the preservation of "}, {"code": "ConfigTyped"}, {"text": " by each command (M6) imply milestone M7 ("}, {"code": "src/Effect4/Laws/Program/Typed/Assembly.lean"}, {"text": ")."}], [{"text": "The theorem "}, {"code": "machineTyped_not_halted"}, {"text": ", in the same file, states that a typed machine is never halted."}], [{"text": "Milestone results are stated by "}, {"code": "m7_proved"}, {"text": " in "}, {"code": "src/Effect4/Laws/Program/Typed/Commands/Clauses/All.lean"}, {"text": "."}], [{"text": "Source program admission connecting checked programs to M7 is stated by "}, {"code": "m7_admitted"}, {"text": " ("}, {"code": "src/Effect4/Laws/Program/Typed/AdmittedSource.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": [{"status": "modulo", "ref": "claim:m7-admitted", "label": "m7_admitted", "key": "Effect4.Program.Typed.m7_admitted", "detail": ""}, {"status": "modulo", "ref": "claim:m7-never-halts", "label": "m7_proved", "key": "Effect4.Program.Typed.m7_proved", "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:R9", "edges": [["Effect4.Program.Typed.m7_admitted", "Effect4.Program.Typed.m7_proved"], ["Effect4.Program.Typed.m7_proved", "Effect4.Program.Typed.decision_preserves"], ["Effect4.Program.Typed.decision_preserves", "Effect4.Program.Typed.deliver_preserves"], ["Effect4.Program.Typed.decision_preserves", "Effect4.Program.Typed.loop_preserves"], ["Effect4.Program.Typed.deliver_preserves", "Effect4.Program.Typed.Evaluating.countdown_parks_positional"], ["Effect4.Program.Typed.loop_preserves", "Effect4.Program.Typed.Evaluating.countdown_parks_positional"]], "caption": "The open part of R9: its planned goals and the theorems proved modulo them. 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