{ "content": { "icon": "bi-braces", "id": "grammar", "label": "Grammar", "layout": "grid", "sections": [ { "icon": "bi-braces", "id": "bnf-grammar", "intro": "PAG is defined by a context-free grammar written in Backus–Naur form (BNF), and its rules fall into five categories. The planning and coordination productions are the grammar's own records, each grounded to a reasoning record, and the statement, expression and flowchart rules expand the terminals those records leave open. The scan described in [well-formedness](/pag/guide#well-formedness) reads tokens rather than patterns, although the grammar itself admits a pattern literal in a condition.", "subsections": [ { "blocks": [ { "code": "# Instruction\n ::= \n ::= \"---\" \"---\"\n ::= | ε\n ::= | ε\n ::= \"THIS\" \n ::= \"AGENT\" | \"WORKFLOW\" | \"PROTOCOL\" | \"POLICY\" | \"CHECKLIST\" | \"TEMPLATE\" | \"TASK\" | \"INSTRUCTION\" | \"PROMPT\" | \"COMMAND\" | \"TEST\"\n| \"DEBUG\" | \"VERIFICATION\" | \"DISTILLATION\" | \"AUDIT\" | \"TRANSLATION\" | \"COMPOSITION\"\n ::= \"IS\" | \"ENFORCES\" | \"EXECUTES\" | \"HAS\" | \"PERFORMS\" | \"PROVIDES\" | \"IMPLEMENTS\" | \"DEFINES\" | \"MANAGES\" | \"COORDINATES\" | \"GENERATES\"\n| \"RESOLVES\" | \"FINDS\" | \"FIXES\" | \"VERIFIES\" | \"CLASSIFIES\" | \"DISTILLS\" | \"ABSTRACTS\" | \"ELIMINATES\" | \"AUDITS\" | \"MEASURES\" | \"SCORES\" | \"CORRECTS\" | \"RENDERS\" | \"COMPOSES\" | \"FOLDS\"\n ::= \n ::= + * \n ::= | ε\n ::= | ε\n\n# Meta block\n ::= \"%%\" \"META\" \"%%\" \":\" +\n ::= \"objective\" \":\" \n| \"priority\" \":\" \n| \"trust\" \":\" (\",\" )*\n| \"jurisdiction\" \":\" \"|\" \"external\" \":\" \n| \"recursion_limit\" \":\" \n ::= (\">\" )*\n ::= \"=\" (\"TRUSTED\" | \"UNTRUSTED\" | )\n ::= \n\n# Node\n ::= * \n ::= \"#\" \"NODE\" \"—\" \"[\" \"·\" \"·\" \"·\" \"yields:\" \"]\"\n ::= +\n ::= \n ::= \"epistemic\" | \"conative\" | \"evaluative\"\n ::= \"ontology\" | \"teleology\" | \"analysis\" | \"reasoning\" | \"formalization\" | \"verification\" | \"representation\" | \"termination\"\n ::= \"set-theory\" | \"logic\" | \"graph\" | \"algebra\" | \"analysis\" | \"optimization\" | \"topology\" | \"computation\" | \"probability\" | \"information-theory\" | \"dynamical-systems\"\n ::= \"set\" | \"boolean\" | \"edge-list\" | \"ranking\" | \"procedure\" | \"artifact\" | \n ::= \"@purpose\" \":\" \n| \"@axis_question\" \":\" \n| \"@cue\" \":\" \n| \"@genesis\" \":\" \n| \"@mandatory\"\n ::= \"existence\" | \"difference\" | \"relation\" | \"structure\" | \"transformation\" | \"constraint\" | \"emergence\"\n\n# Contract\n ::= \"CONTRACT\" \":\" \"input\" \":\" \"transform\" \":\" + \"output\" \":\" \n ::= \"NODE\" | | | \n ::= (\"preserves\" \":\" ) | ε\n ::= (\",\" )*\n ::= (\"constraints\" \":\" ) | ε\n ::= (\"freshness\" \":\" \"+\" ) | ε\n ::= \n ::= (\"handoff\" \":\" ) | ε\n ::= (\"#\" \"OUTPUT\" \"CONTRACT\" +) | ε\n ::= \"{\" (\".\" )* \"}\"\n ::= \n\n# Handoff gate\n ::= \"HANDOFF\" \"GATE\" \":\" + \n ::= (\"(\" \")\") | ε\n ::= (\"rule_id\" \":\" \"yields\" \":\" ) | ε\n ::= \"(\" \"evidence\" \":\" \")\" \n ::= \"[check]\" | \"ASSERT\" | \"REQUIRE\"\n ::= \n ::= | ε\n ::= \"over\" \":\" \"measured\" \":\" \"/\" \n ::= \n ::= | \n ::= (\"refuse\" \":\" \"before\" ) | ε\n ::= | \n ::= (\"standing\" \":\" \"moved-set\" ) | ε\n ::= \"result\" \":\" \"pass\" \"->\" (\"|\" \"->\" \"REPAIR\" \"(\" \"owner\" \":\" \")\")+ \"|\" \"unknown\" \"->\" \"BLOCKED\"\n ::= \"pass\" | \"fail\" | \"unknown\"\n ::= \"NODE\" | \"TERMINATE\"\n ::= \n ::= \"NODE\" | \n ::= \"#\" \"REPAIR\" \"EDGE\" \n\n# Invariant block\n ::= \"#\" \"CROSS-NODE\" \"INVARIANTS\" +\n ::= \"INVARIANT\" \":\" \"over\" \":\" \"binds\" \":\" \"objector\" \":\" ( | \"none\")\n ::= \n ::= \n ::= \n ::= \"[check]\" \n\n# Report block\n ::= \"REPORT\" \":\" +\n ::= \"subject\" \":\" \n| \"verdict\" \":\" \n| \"domain\" \":\" \"declared\" \"measured\" \n| \"populations\" \":\" \n| \"inputs\" \":\" \n| \"code\" \":\" \n| \"output\" \":\" \n| \"refusals\" \":\" \n| \"unresolved\" \":\" \n| \"completion\" \":\" \"saturated\" \"complete\" \"verified\" \n ::= \"NODE\" \n ::= (\",\" )*\n ::= (\",\" )*\n ::= \"[\" (\",\" )* \"]\"\n\n# Macro\n ::= \"USE\" \"TEMPLATE\" \n ::= \n\n# Rule\n ::= \"RULE\" \":\" \n ::= \n ::= * +\n ::= \"WHEN\" \":\" +", "kind": "code", "language": "bnf", "title": "BNF grammar" } ], "content": "These rules cover [document structure](/pag/guide#document-structure), the meta block, nodes, contracts, handoff gates, invariant records and the report.", "title": "Planning rules" }, { "blocks": [ { "code": "# Directive\n ::= \n ::= \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n| \n ::= | ε\n ::= \"[\" \"]\"\n ::= \" \" | \"x\" | \">\"\n ::= | ε\n ::= (\"@cue\" \":\" ) | ε\n\n# Action expression\n ::= * \n ::= \n| \"EXECUTE\" | \"READ\" | \"WRITE\" | \"DELETE\" | \"REMOVE\" | \"ANALYZE\"\n| \"CREATE\" | \"FIND\" | \"REPORT\" | \"VALIDATE\" | \"VERIFY\"\n| \"COLLECT\" | \"EXTRACT\" | \"LINK\" | \"DETERMINE\" | \"CLASSIFY\"\n| \"INVESTIGATE\" | \"FILTER\" | \"COMPARE\" | \"CONVERT\" | \"MERGE\" | \"SPLIT\" | \"MARK\"\n| \"SORT\" | \"RANK\" | \"ORDER\" | \"INSERT\" | \"APPEND\"\n| \"ADD\" | \"MOVE\" | \"COPY\" | \"BACKUP\" | \"RESTORE\" | \"LOAD\"\n| \"ITERATE\" | \"ATTEMPT\" | \"ENFORCE\" | \"RENAME\"\n| \"FAIL\" | \"EXIT\" | \"RETURN\" | \"WAIT\" | \"SEND\"\n| \"REDUCE\" | \"PROPAGATE\" | \"FINALIZE\" | \"EVIDENCE\"\n| \"PREDICT\" | \"EXPLAIN\" | \"REFLECT\" | \"ABSTRACT\" | \"GENERALIZE\" | \"DESCRIBE\" | \"FORMALIZE\"\n ::= \"DISCOVER_RESOURCES\" | \"READ_RESOURCE\" | \"SEARCH_CONTENT\" | \"ANALYZE_CONTENT\" | \"EXTRACT_FACTS\" | \"CALCULATE_METRIC\"\n| \"COMPOSE_ARTIFACT\" | \"VALIDATE_ARTIFACT\" | \"PERSIST_ARTIFACT\" | \"EXECUTE_TOOL\" | \"REQUEST_DECISION\" | \"REPORT_RESULT\"\n ::= \"MUST\" | \"NEVER\" | \"ALWAYS\" | \"REQUIRED\" | \"MANDATORY\"\n ::= | | \n ::= \"SYSTEM\" | \"USER\" | \"SERVICE\"\n ::= | | ε\n ::= \"(\" \")\"\n ::= \n ::= (\",\" )*\n ::= | | \n\n# Control flow\n ::= \n| \n| \n| \n| \n| \n| \n ::= \"IF\" \":\" +\n(\"ELSE\" \"IF\" \":\" +)*\n\n ::= (\"ELSE\" \":\" +) | ε\n ::= \"FOR\" \"EACH\" \"IN\" \":\" +\n ::= \"WHILE\" \":\" +\n ::= \"TRY\" \":\" +\n\"CATCH\" \":\" +\n ::= | ε\n ::= \n ::= \"GOTO\" \n ::= \":\"\n ::= \n ::= \"START\" \n| \"LOOP\" \n| \"END\"\n| \"STOP\"\n ::= | ε\n ::= (\"BACKTO\" ) | ε\n\n# Declaration statement\n ::= \"SET\" \"=\" \n| \"DECLARE\" \":\" \n ::= \"string\" | \"number\" | \"boolean\" | \"array\" | \"object\" | \"file\" | \"context\"\n\n# Transform statement\n ::= \n ::= \"BACKUP\" \"TO\" \n| \"COPY\" \"TO\" \n ::= \"PERSIST_ARTIFACT\" \"TO\" \n| \"WRITE\" \n| \"EXECUTE_TOOL\" \"WITH\" \"timeout\" \":\" \n ::= \n ::= \n ::= \"VALIDATE_ARTIFACT\" \"AGAINST\" \n ::= | ε\n ::= \n ::= \"CONTENT\" \n| \"FROM\" \n| \"INTO\" \n| \n ::= \n ::= \n ::= \n\n# Discovery statement\n ::= \n ::= \"DISCOVER_RESOURCES\" \"INTO\" \n| \"SEARCH_CONTENT\" \"FOR\" \"INTO\" \n| \"FIND\" \"IN\" \n ::= \"IF\" \"exists\" \":\" +\n| \"ANALYZE\" \n ::= | ε\n ::= \"IN\" | ε\n ::= \n ::= \n ::= \n ::= ", "kind": "code", "language": "bnf", "title": "BNF grammar" } ], "content": "These rules cover directives, actions, control flow and declarations.", "title": "Statement rules" }, { "blocks": [ { "code": "# Expressions\n ::= \n ::= (\"|>\" )*\n ::= (\"OR\" )*\n ::= (\"AND\" )*\n ::= ((\"===\" | \"!==\") )*\n ::= ((\"<\" | \">\" | \"<=\" | \">=\") )*\n| \"MATCHES\" \n| \"FOR\" \n| \"BETWEEN\" \n ::= ((\"+\" | \"-\") )*\n ::= ((\"*\" | \"/\" | \"%\") )*\n ::= (\"!\" | \"NOT\" | \"-\" | \"+\") \n| \n ::= *\n ::= \"[\" \"]\"\n| \".\" \n| \"(\" \")\"\n ::= \n| \n| \n| \n| \"(\" \")\"\n ::= \"[\" \"]\"\n ::= \"{\" \"}\"\n ::= (\",\" )*\n ::= | ε\n ::= \":\" \n ::= | | \n ::= (\",\" )*\n ::= | ε\n ::= \"(\" \")\"\n ::= | ε\n ::= \n ::= \n ::= \n ::= \n ::= \n ::= | \n ::= \"/\" \"/\" \n ::= | ε\n ::= +\n ::= +\n ::= \"===\" | \"!==\" | \"<\" | \">\" | \"<=\" | \">=\"\n\n# Lexical\n ::= ( | | \"_\" | \"-\")*\n ::= \n ::= \n ::= \n ::= | \n ::= (\"/\" )* \"/\"\n ::= (\"/\" )* \n ::= \n ::= (\".\" ) | ε\n ::= | | \n ::= + \n ::= (\".\" +) | ε\n ::= '\"' * '\"' | \"'\" * \"'\"\n ::= \"true\" | \"false\"\n ::= \"0\" | \"1\" | \"2\" | \"3\" | \"4\" | \"5\" | \"6\" | \"7\" | \"8\" | \"9\"\n ::= \"a\"..\"z\" | \"A\"..\"Z\"\n ::= \n ::= +\n ::= \n ::= | | | \n ::= \"_\" | \"-\" | \".\" | \",\" | \":\" | \";\" | \"!\" | \"?\" | \"@\" | \"#\" | \"$\" | \"%\" | \"^\" | \"&\" | \"*\" | \"(\" | \")\" | \"[\" | \"]\" | \"{\" | \"}\" | \"<\" | \">\" | \"/\" | \"\\\" | \"|\" | \"=\" | \"+\" | \"`\" | \"~\"\n ::= | | \n ::= \" \" | \"\t\" | \"\n\" | \"\r\"\n\n# Iteration statement\n ::= \n ::= \"FOR\" \"EACH\" \"IN\" \n ::= \":\" + \n ::= \"APPEND\" \"TO\" \n| \"CREATE\" \"FROM\" \n| \"EXTRACT\" \"INTO\" \n| \"WRITE\" \"INTO\" \n| \"COLLECT\" \"INTO\" \n| \"SET\" \"=\" \n ::= \"recursion_limit\" \":\" \n ::= | ε\n ::= | ε\n ::= \n ::= | \n ::= \n ::= \n ::= \n ::= \n ::= \n ::= \n ::= \n ::= \n ::= \n\n# Function declaration\n ::= \"FUNCTION\" \"(\" \")\" \":\" +\n ::= | ε\n ::= (\",\" )*\n ::= \n\n# Announcement statement\n ::= \"REPORT\" \n ::= | ", "kind": "code", "language": "bnf", "title": "BNF grammar" } ], "content": "These rules cover expressions, operators, literals and lexical elements.", "title": "Expression rules" }, { "blocks": [ { "code": "# Await\n ::= \"AWAIT\" \n ::= | | \n ::= \"INTO\" | ε\n\n# Parallel\n ::= \"PARALLEL\" \":\" + \"END\"\n\n# Surface\n ::= \"SURFACE\" \":\" +\n ::= \"RECORD\" \"subject\" \":\" * *\n ::= \"ITEM\" \"TO\" \":\" \n ::= \n ::= \"PARENT\" | \"SATISFIED_BY\" | \"BLOCKS\" | \"ANSWERS\" | \"REFUTES\" | \"SUPERSEDES\"\n ::= \"OPEN\" | \"BLOCKED\" | \"ABSORBED\"\n ::= \"WAIT\" \"ON\" \"AS\" \"INTO\" \n ::= \"BARRIER\" \"ON\" \n ::= \"SWAP\" ** \"AGAINST\" ********\n******** ::= \"participant\" | \"bounded\" | ********\n******** ::= ********\n******** ::= ******** \"-\" ********\n******** ::= ******** \"-\" ********\n******** ::= ********\n******** ::= ******** | ********\n******** ::= ********\n**** ::= ********\n******** ::= ********\n\n# State machine\n******** ::= \"STATE_MACHINE\" ******** \":\" ********+ ********+\n******** ::= \"STATE\" ******** ********\n********\n********\n******** ::= \"TRANSITION\" \"FROM\" ******** \"TO\" ********\n\"ON\" ********\n********\n********\n******** ::= \":\" ******** | ε\n******** ::= \"ENTRY\" \":\" ********+ | ε\n******** ::= \"EXIT\" \":\" ********+ | ε\n******** ::= \"GUARD\" \":\" ******** | ε\n******** ::= \":\" ********+ | ε\n******** ::= ********\n******** ::= ********\n******** ::= ********\n******** ::= ********\n\n# DAG\n******** ::= \"DAG\" ******** \":\" ********+\n******** ::= ******** | ********\n******** ::= \"NODE\" ******** ********\n********\n********\n********\n\":\" ********+\n******** ::= \"PARALLEL_GROUP\" \":\" ********\n******** ::= ******** (\",\" ********)*\n******** ::= ******** (\",\" ********)*\n******** ::= ******** (\",\" ********)*\n******** ::= \":\" ******** | ε\n******** ::= \"DEPENDS_ON\" \"[\" ******** \"]\" | ε\n******** ::= \"AFTER\" ******** | ε\n******** ::= \"BEFORE\" ******** | ε\n******** ::= ********\n******** ::= ********\n\n# Priority queue\n******** ::= \"PRIORITY_QUEUE\" ********\n********\n\":\"\n******** ::= ********\n| ********\n| ********\n| ********\n******** ::= \"ENQUEUE\" ******** \"TO\" ********\n********\n******** ::= \"DEQUEUE\" \"FROM\" ********\n********\n******** ::= \"PEEK\" ********\n********\n******** ::= \"HEAPIFY\" ********\n******** ::= ********\n| \"(\" ******** \")\" \"→\" ********\n******** ::= \"COMPARE_BY\" ******** | ε\n******** ::= \"PRIORITY\" \"=\" ******** | ε\n******** ::= \"TO\" ******** | ε\n******** ::= ********\n******** ::= ******** | ********\n******** ::= ********\n\n# Cross reference\n******** ::= ********\n| ********\n| ********\n| ********\n******** ::= \"FROM\" ******** \"COLLECT\" ******** \"TO\" ********\n******** ::= \"FROM\" ******** \"FIND\" ******** \"TO\" ********\n******** ::= \"REFERENCE\" ******** ********\n******** ::= \"LINK\" ******** \"TO\" ********\n******** ::= ******** | ********\n******** ::= ********\n******** ::= ******** ********\n******** ::= \"#\" ******** | ε\n******** ::= ******** | \"*\"\n******** ::= ******** | ********\n******** ::= ********\n******** ::= ********\n******** ::= ********\n******** ::= \"AS\" ******** | ε\n\n# Semantic operation\n******** ::= ******** ******** ******** ********\n******** ::= ******** | ******** | ******** | ********\n******** ::= ******** | ε\n******** ::= \"WITH\" ********\n| \"USING\" ********\n******** ::= ******** (\",\" ********)*\n******** ::= ******** \":\" ********\n| ******** \"=\" ********\n| ********\n******** ::= ********\n******** ::= ********\n| ********\n| ********\n| ********\n| ********\n| ********\n******** ::= ******** | ε\n******** ::= \"->\" ********\n| \"INTO\" ********\n| \"AS\" ********\n******** ::= ******", "kind": "code", "language": "bnf", "title": "BNF grammar" } ], "content": "These rules cover the structure declarations, the [shared surface](/pag/orchestration#shared-surfaces) and the [semantic operations](/pag/guide#tool-invocation).", "title": "Coordination rules" }, { "blocks": [ { "code": "# Flowchart\n ::= \"FLOWCHART\" \":\" \n ::= \"LAYOUT\" | ε\n ::= + \n ::= | ε\n ::= \"ON\" \"ERROR\" \":\" +\n ::= \n| \n| \n| \n| \n ::= \n ::= | \n ::= \"[\" \"]\"\n| \"(\" \")\"\n| \"{\" \"}\"\n| \"<\" \">\"\n| \"((\" \"))\"\n| \"[[\" \"]]\"\n ::= \":\" | ε\n ::= | ε\n ::= \":\" \n ::= +\n| \"EVALUATE\" \n| \"EXECUTE\" \n| \"TRY\" \":\" + \"CATCH\" \":\" +\n ::= \"WITH\" \"STATE\" + | ε\n ::= \":\" \"=\" \n ::= \n ::= \n ::= \n ::= \"→\" | \"↓\" | \"↑\" | \"←\" | \"↔\"\n| \"-->\" | \"--->\" | \"==>\" | \"-.->>\"\n| \"|\"\n ::= \":\" | ε\n ::= \"/\" +\n ::= \n ::= \"→\" \n ::= | \n ::= \n ::= + \"◄\" \n ::= \n ::= \n ::= \"LOOP\" \"→\" \n ::= \n ::= \n ::= \"MAX\" | ε\n ::= \"process\"\n| \"decision\"\n| \"start_end\"\n| \"input_output\"\n| \"subprocess\"\n| \"database\"\n ::= \"vertical\" | \"horizontal\" | \"lr\" | \"rl\" | \"tb\" | \"bt\"\n ::= \n\n# ASCII flowchart\n ::= +\n ::= \n| \n| \n| \n ::= \n ::= \"[\" \"]\"\n| \"(\" \")\"\n| \"{\" \"}\"\n| \"<\" \">\"\n ::= \"|\"\n| \"│\"\n| \"▼\"\n| \"▲\"\n| \"►\"\n| \"◄\"\n ::= \"/\" \"\\\"\n| \"▼\" \"▼\"\n ::= \"\\\" \"/\"\n| \"◄\" \"─\" \"┘\"\n ::= *\n\n# Mermaid flowchart\n ::= \"MERMAID\" \":\" \n ::= \"flowchart\" | \"graph\" | \"sequence\" | \"class\" | \"state\" | \"er\"\n ::= +\n ::= \n| \n| \n| \n ::= \n ::= \n ::= \"[\" \"]\"\n| \"(\" \")\"\n| \"{\" \"}\"\n| \"((\" \"))\"\n| \"[[\" \"]]\"\n| \"[/\" \"/]\"\n| \"[\\\" \"\\]\"\n ::= | ε\n ::= \n ::= \"-->\" | \"--->\" | \"==>\" | \"-.->\" | \"--\"\n ::= \"|\" \"|\" | ε\n ::= \"subgraph\" + \"end\"\n ::= \n ::= \"style\" \n ::= (\",\" )*\n ::= \":\" ", "kind": "code", "language": "bnf", "title": "BNF grammar" } ], "content": "These rules cover flowcharts written in PAG's own form, in ASCII and in Mermaid.", "title": "Flowchart rules" } ], "title": "BNF grammar" } ] }, "description": "PAG is defined by a context-free grammar written in Backus–Naur form (BNF), and its rules fall into five categories.", "id": "pag", "label": "Grammar", "tab": "grammar", "title": "Grammar — PAG — Bane's Lab", "url": "https://banes-lab.com/pag/grammar" }