{"title": "R2: Extension is conservative: C1–C8 over DI-47's relation on Σ_app", "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: C2 for host rows outside the fragment StraightRows: operational; on the fragment it is meaningUnder_append (decisions row 313)"}], [{"text": "Open, not triaged: C4 for TypedProg (the generic judgment is proved both ways)"}], [{"text": "Open, not triaged: C5: the world projection with its back condition (its red controls are proved)"}], [{"text": "Open, not triaged: C7: conditional on decisions row 115"}], [{"text": "Open, not triaged: C8: per form"}]], "kind": "items"}, {"title": "Requirement R2: Conservative extension", "kind": "part", "key": "about:req:R2", "body": [{"line": [{"text": "This page explains requirement R2 in Effect4. It covers what conservative extension requires across eight obligations, why typing signature independence matters, and how the property is checked."}], "kind": "para"}, {"title": "What the requirement asks", "kind": "part", "key": "about:req:R2:what-it-asks", "body": [{"line": [{"text": "Requirement R2 requires that extending an application signature is conservative across eight named obligations (DB-01, "}, {"code": "docs/core/system-map.md"}, {"text": " §8):"}], "kind": "para"}, {"lines": [[{"text": "C1 syntax: extending a signature leaves existing program representations unchanged."}], [{"text": "C2 meaning: extending operations leaves existing program denotations unchanged."}], [{"text": "C3 checker: extending a signature admits exactly the same existing programs."}], [{"text": "C4 protocol typing: existing programs keep their protocol certificates."}], [{"text": "C5 world: extending allocated operations projects onto earlier world states."}], [{"text": "C6 local lawfulness: appending rows keeps signature validity intact."}], [{"text": "C7 representation: target representations remain compatible."}], [{"text": "C8 forms: higher-level form expansions remain stable under extension."}]], "kind": "items"}, {"line": [{"text": "Extending a signature must never alter the typing, semantics, or admission of existing programs."}], "kind": "para"}]}, {"title": "Why it matters", "kind": "part", "key": "about:req:R2:why-it-matters", "body": [{"line": [{"text": "Software composition relies on stability under modular extension."}], "kind": "para"}, {"line": [{"text": "If adding a new library, operation row, or service changed how existing programs run, modular verification would collapse."}], "kind": "para"}, {"line": [{"text": "Conservative extension lets separate modules compose without changing what the earlier ones mean."}], "kind": "para"}]}, {"title": "How it is checked", "kind": "part", "key": "about:req:R2:how-it-is-checked", "body": [{"line": [{"text": "The requirement is checked by proving conservative extension theorems for syntax, checking, meaning, and sums:"}], "kind": "para"}, {"lines": [[{"text": "Checker extension and restriction are stated by "}, {"code": "check_ext"}, {"text": " and "}, {"code": "check_restrict"}, {"text": " in "}, {"code": "src/Effect4/Laws/Program/Signature.lean"}, {"text": "."}], [{"text": "Signature lawfulness under appending is stated by "}, {"code": "lawful_append"}, {"text": " in the same file."}], [{"text": "Denotational meaning under row extension is stated on "}, {"code": "StraightRows"}, {"text": " by "}, {"code": "meaningUnder_append"}, {"text": " ("}, {"code": "src/Effect4/Laws/Program/DenoteRowsAppend.lean"}, {"text": ")."}], [{"text": "That a signature sum is a coproduct of free monads is stated by "}, {"code": "sum_is_coproduct"}, {"text": " ("}, {"code": "src/Effect4/Laws/Effects/Sum.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": "proved", "ref": "concept:translation-simulation", "label": "Translation & Simulation", "key": "translation-simulation", "detail": "2 nodes"}, {"status": "proved", "ref": "concept:initial-algebras-folds", "label": "Initial Algebras & Folds", "key": "initial-algebras-folds", "detail": "7 nodes"}, {"status": "proved", "label": "No concept", "key": "none", "detail": "9 nodes"}], "kind": "graph", "key": "fig:concepts:R2", "edges": [["translation-simulation", "none"], ["initial-algebras-folds", "none"]], "caption": "R2 by concept: each concept its nodes are placed at, by tag or by module. 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