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R0054-27503 · q-20261015-advance-20261118-r06-regular-expression-0003
Use alphabet=[a, b, c] and typed regular-expression AST={"type":"concat","children":[{"type":"symbol","value":"c"},{"type":"symbol","value":"a"},{"type":"symbol","value":"b"}]}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Give (alphabet, canonical_typed_AST, AST_qualified, qualification_statement).
G001 — Use alphabet=[a, b, c] and typed regular-expression AST={"type":"concat","children":[{"type":"symbol","value":"c"},{"type":"symbol","value":"a"},{"type":"symbol","value":"b"}]}. Words are arrays of alphabet symbols; distinguish empty language from the language containing the empty word. Give (alphabet, canonical_typed_AST, AST_qualified, qualification_statement).Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
source roles = [regex-ast-qualification]
After
derived = [[alphabet, canonical_typed_AST, AST_qualified, qualification_statement]]
Conditions: none
List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [root.children[0], [a, b, c], {'type': 'symbol', 'value': 'c'}]After
derived = [{'type': 'symbol', 'value': 'c'}, {type:"symbol",value:"c"}]Conditions: none
For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate.
Rule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S001
Before
source roles = [root.children[1], [a, b, c], {'type': 'symbol', 'value': 'a'}]After
derived = [{'type': 'symbol', 'value': 'a'}, {type:"symbol",value:"a"}]Conditions: none
For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate.
Rule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S002
Before
source roles = [root.children[2], [a, b, c], {'type': 'symbol', 'value': 'b'}]After
derived = [{'type': 'symbol', 'value': 'b'}, {type:"symbol",value:"b"}]Conditions: none
For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate.
Rule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S003
Before
source roles = [root, [a, b, c], {'type': 'concat', 'children': [{'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}]After
derived = [{'type': 'concat', 'children': [{'type': 'symbol', 'value': 'c'}, {'type': 'symbol', 'value': 'a'}, {'type': 'symbol', 'value': 'b'}]}, {children:[{type:"symbol",value:"c"},{type:"symbol",value:"a"},{type:"symbol",value:"b"}],type:"concat"}]Conditions: none
For EACH node qualify type,exact keys and symbol membership.A union checks raw arity>=2 BEFORE extensional deduplication,so its canonical form may have one child.Concatenation retains order and star retains its child.Do not revalidate canonical output as raw input with a new arity gate.
Rule: Regex_EACH_typed_node_exact_keys_symbol_scope_union_set_concat_order · Uses: G001, S004
S005 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S004 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S003 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.([a, b, c], {children:[{type:"symbol",value:"c"},{type:"symbol",value:"a"},{type:"symbol",value:"b"}],type:"concat"}, Yes, typed_AST_symbols_in_alphabet)The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: cbbdcb72b7fa9cce7cee4816406aaa1cc908bd7c0330a58a0bead543cecb2c6ecandidate record SHA-256: 046862fb62c026133538a3c5c9ab12b1180937cd01879cea8533e709b53429f5semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437Lean: NOT_RUN · human review: NOT_PERFORMED