1 Introduction

Text-based Formula, or "XF", provides an alternative to the XLink-syntax for XBRL Formula defined by the XBRL Formula specifications [FORMULA]. XF provides the same functionality as XBRL Formula, and formula rules can be freely converted between the XLink and XF syntaxes.

This Working Group Note provides a formal grammar for the XF syntax, expressed in a variant of EBNF notation.

2 XF grammar

@@grammar :: XF @@comments :: /(?s)\(:((?!(\(:|:\))).)*:\)/ @@namechars :: "-" module = {namespace_declaration}* {default}* {parameter}* {filter_declaration|fact_variable|general_variable|function_declaration}* {assertion}* $; separator = ";"; namespace_declaration = "namespace" name "=" quoted_url separator; default = default_severity | "default-language" language separator; default_severity = "default-severity" message_severity separator ; severity = "severity" message_severity separator ; message_severity = "ERROR" | "WARNING" | "INFO"; parameter = "parameter" name "{" [ "required" ] ["select" enclosed_expression ] ["as" qname ] "}" separator ; filter_declaration = "filter" name "{" filter {separator filter}* [ separator ] "}" separator ; filter = [ "not" ] ( concept_filter | general_filter | period_filter | dimension_filter | unit_filter | entity_filter | match_filter | relative_filter | tuple_filter | value_filter | boolean_filter | aspect_cover_filter | concept_relation_filter ) | declared_filter_reference ; concept_filter = ( "covering" | `covering` | "non-covering" ) ( "concept-name" ~ {qname | localname | enclosed_expression}+ | "concept-period-type" ~ ("instant" | "duration") | "concept-balance" ~ ("credit" | "debit" | "none") | "concept-data-type" ~ ("strict" | "non-strict") (qname | enclosed_expression) | "concept-substitution-group" ~ ("strict" | "non-strict") (qname | enclosed_expression) ) ; general_filter = "general" ~ enclosed_expression ; period_filter = ( "period-start" ~ (date_constant | date_time_constant | ("date" enclosed_expression [ "time" enclosed_expression ] )) | "period-end" ~ (date_constant | date_time_constant | ("date" enclosed_expression [ "time" enclosed_expression ] )) | "period-instant" ~ (date_constant | date_time_constant | ("date" enclosed_expression [ "time" enclosed_expression ])) | "period" ~ enclosed_expression | "instant-duration" ~ ("start" | "end") variable_ref ) ; dimension_filter = ( ( "explicit-dimension" ~ (qname | localname | enclosed_expression) { "default-member" | "member" ~ (variable_ref | qname | localname | enclosed_expression) ["linkrole" quoted_anyURI [ "arcrole" quoted_anyURI ] "axis" dimension_axis ] }* ) | ( "typed-dimension" ~ (qname | localname | enclosed_expression) ["test" enclosed_expression ] ) ) ; dimension_axis = "child" | "child-or-self" | "descendant" | "descendant-or-self" ; unit_filter = ( "unit-single-measure" ~ (qname | enclosed_expression) | "unit-general-measures" ~ enclosed_expression ) ; entity_filter = ( "entity-scheme-pattern" ~ regexp_pattern | "entity-scheme" ~ enclosed_expression | "entity-identifier-pattern" ~ regexp_pattern | "entity-identifier" ~ enclosed_expression | "entity" ~ "scheme" enclosed_expression "value" enclosed_expression ) ; match_filter = ( "match-concept" ~ variable_ref | "match-location" ~ variable_ref | "match-entity-identifier" ~ variable_ref | "match-period" ~ variable_ref | "match-unit" ~ variable_ref | "match-dimension" ~ variable_ref "dimension" qname ) [ "match-any" ] ; relative_filter = "relative" ~ variable_ref ; tuple_filter = ( "parent" ~ (qname | enclosed_expression) | "ancestor" ~ (qname | enclosed_expression) | "sibling" ~ variable_ref ) ; (* Note: "location" filter is not supported as it involves path expressions *) value_filter = "nilled" ; (* Note: "precision" filter is not supported *) boolean_filter = ("and" | "or") ~ "{" filter {separator filter}* [ separator ] "}" ; aspect_cover_filter = "aspect-cover" ~ { "all" | "concept" | "entity-identifier" | "location" | "period" | "unit" | "dimensions" | "dimension" (qname | localname | enclosed_expression) | "exclude-dimension" (qname | localname | enclosed_expression) }+ ; concept_relation_filter = "concept-relation" ~ (variable_ref | qname | localname | enclosed_expression) [ "linkrole" (quoted_anyURI|enclosed_expression) ] [ "arcrole" (quoted_anyURI|enclosed_expression) ] [ "axis" relation_axis ] [ "generations" non_negative_integer ] [ "test" enclosed_expression ] ; (* Consider keywords as a short hand for standard arcroles, e.g. presentation => arcrole "http://.../parent-child" *) relation_axis = ( "child-or-self" | "child" | "descendant-or-self" | "descendant" | "parent-or-self" | "parent" | "ancestor-or-self" | "ancestor" | "sibling-or-self" | "sibling-or-descendant" | "sibling" ) ; declared_filter_reference = "filter" ~ variable_ref ; fact_variable = "variable" ~ variable_ref "{" [ "bind-as-sequence" ] [ "nils" ] [ "matches" ] [ "fallback" enclosed_expression ] [ filter { separator filter }* [separator] ] "}" separator ; general_variable = "variable" ~ variable_ref "{" [ "bind-as-sequence" ] "select" enclosed_expression "}" separator ; function_declaration = "function" ~ qname "(" { NCNAME_FRAG "as" qname }* ")" "as" qname [ "{" "return" enclosed_expression separator "}" ] separator ; assertion = "assertion" name "{" { label | message | severity | "aspect-model-non-dimensional" separator | "no-implicit-filtering" separator }* {filter separator}* {fact_variable | general_variable | referenced_parameter }* {precondition}* (value_expression | existence_expression) [ separator ] "}" separator ; label = "label" ["(" language ")"] quoted_string separator ; message = ("satisfied-message" | "unsatisfied-message") ~ ["(" ~ language ")"] quoted_string separator ; referenced_parameter = "parameter" ~ variable_ref "references" qname separator ; precondition = "precondition" enclosed_expression separator ; value_expression = "test" enclosed_expression ; existence_expression = "evaluation-count" enclosed_expression ; enclosed_expression = "{" xPath "}"; name = NCNAME_FRAG ; language = /[A-Za-z]{2}(-[A-Za-z]{2})?/; quoted_anyURI = quoted_url; quoted_url = quoted_string; localname = name; variable_ref = "$" variable_name ; variable_name = name ; non_negative_integer = /[0-9]+/ ; date_time_constant = /\b(-?(?:[1-9][0-9]*)?[0-9]{4})-(1[0-2]|0[1-9])-(3[01]|0[1-9]|[12][0-9])T(24:00:00(\.0+)?|(2[0-3]|[01][0-9]):([0-5][0-9]):([0-5][0-9])(\\.[0-9]+))?(Z)?\b/; date_constant = /\b(-?(?:[1-9][0-9]*)?[0-9]{4})-(1[0-2]|0[1-9])-(3[01]|0[1-9]|[12][0-9])\b/; quoted_string = /("([^\\"]|\\.)*"|'([^\\']|\\.)*')/ ; regexp_pattern = /\/([^\\\/]|\\.)*\// ; #include :: "xpath.ebnf"

3 XPath 2.0 grammar

The XF grammar depends on the XPath 2.0 [XPATH 2.0] grammar, a version of which is included below.

(* Based on https://github.com/XPath-Next/XPath-Next/blob/master/grammars/xpath-2.0.ebnf *) xPath = expr ; expr = exprSingle {"," exprSingle}* ; exprSingle = forExpr | quantifiedExpr | ifExpr | orExpr ; forExpr = simpleForClause "return" exprSingle ; simpleForClause = "for" "$" varName "in" exprSingle {"," "$" varName "in" exprSingle}* ; quantifiedExpr = ("some" | "every") "$" varName "in" exprSingle {"," "$" varName "in" exprSingle}* "satisfies" exprSingle ; ifExpr = "if" "(" expr ")" "then" exprSingle "else" exprSingle ; orExpr = andExpr { "or" andExpr }* ; andExpr = comparisonExpr { "and" comparisonExpr }* ; comparisonExpr = rangeExpr [ (valueComp | nodeComp | generalComp ) rangeExpr ] ; rangeExpr = additiveExpr [ "to" additiveExpr ] ; additiveExpr = multiplicativeExpr { ("+" | "-") multiplicativeExpr }* ; multiplicativeExpr = unionExpr { ("*" | "div" | "idiv" | "mod") unionExpr }* ; unionExpr = intersectExceptExpr { ("union" | "|") intersectExceptExpr }* ; intersectExceptExpr = instanceofExpr { ("intersect" | "except") instanceofExpr }* ; instanceofExpr = treatExpr [ "instance" "of" sequenceType ] ; treatExpr = castableExpr [ "treat" "as" sequenceType ] ; castableExpr = castExpr [ "castable" "as" singleType ] ; castExpr = unaryExpr [ "cast" "as" singleType ] ; unaryExpr = {"-" | "+"}* valueExpr ; valueExpr = pathExpr ; generalComp = "=" | "!=" | "<=" | "<" | ">=" | ">" ; valueComp = "eq" | "ne" | "lt" | "le" | "gt" | "ge" ; nodeComp = "is" | "<<" | ">>" ; pathExpr = ("//" relativePathExpr) | ("/" [ relativePathExpr ] ) | relativePathExpr ; relativePathExpr = stepExpr {("/" | "//") stepExpr}* ; stepExpr = filterExpr | axisStep ; axisStep = (reverseStep | forwardStep) predicateList ; forwardStep = (forwardAxis nodeTest) | abbrevForwardStep ; forwardAxis = ("child" "::") | ("descendant" "::") | ("attribute" "::") | ("self" "::") | ("descendant-or-self" "::") | ("following-sibling" "::") | ("following" "::") | ("namespace" "::") ; abbrevForwardStep = [ "@" ] nodeTest ; reverseStep = (reverseAxis nodeTest) | abbrevReverseStep ; reverseAxis = ("parent" "::") | ("ancestor" "::") | ("preceding-sibling" "::") | ("preceding" "::") | ("ancestor-or-self" "::") ; abbrevReverseStep = ".." ; nodeTest = kindTest | nameTest ; nameTest = qname | wildcard ; wildcard = "*" | (ncname ":" "*") | ("*" ":" ncname) ; filterExpr = primaryExpr predicateList ; predicateList = {predicate}* ; predicate = "[" expr "]" ; primaryExpr = literal | varRef | parenthesizedExpr | contextItemExpr | functionCall ; literal = numericLiteral | stringLiteral ; numericLiteral = integerLiteral | decimalLiteral | doubleLiteral ; varRef = "$" varName ; varName = qname ; parenthesizedExpr = "(" [ expr ] ")" ; contextItemExpr = "." ; functionCall = qname "(" [exprSingle {"," exprSingle}*] ")" ; singleType = atomicType [ "?" ] ; sequenceType = ("empty-sequence" "(" ")") | (itemType [ occurrenceIndicator]) ; occurrenceIndicator = "?" | "*" | "+" ; itemType = kindTest | ("item" "(" ")") | atomicType ; atomicType = qname ; kindTest = documentTest | elementTest | attributeTest | schemaElementTest | schemaAttributeTest | pITest | commentTest | textTest | anyKindTest ; anyKindTest = "node" "(" ")" ; documentTest = "document-node" "(" [elementTest | schemaElementTest] ")" ; textTest = "text" "(" ")" ; commentTest = "comment" "(" ")" ; pITest = "processing-instruction" "(" [ncname | stringLiteral] ")" ; attributeTest = "attribute" "(" [ attribNameOrWildcard ["," typeName] ] ")" ; attribNameOrWildcard = attributeName | "*" ; schemaAttributeTest = "schema-attribute" "(" attributeDeclaration ")" ; attributeDeclaration = attributeName ; elementTest = "element" "(" [elementNameOrWildcard ["," typeName ["?"] ] ] ")" ; elementNameOrWildcard = elementName | "*" ; schemaElementTest = "schema-element" "(" elementDeclaration ")" ; elementDeclaration = elementName ; attributeName = qname ; elementName = qname ; typeName = qname ; integerLiteral = DIGITS ; decimalLiteral = ("." DIGITS) | (DIGITS /\.[0-9]*/) ; doubleLiteral = (("." DIGITS) | (DIGITS /(\.[0-9]*)?/ )) /[eE][+-]?/ DIGITS ; stringLiteral = (/"/ {ESCAPEQUOT | /[^"]/}* /"/) | (/'/ {ESCAPEAPOS | /[^']/}* /'/) ; ESCAPEQUOT = '""' ; ESCAPEAPOS = "''" ; qname = ( NCNAME_FRAG /:/ NCNAME_FRAG ) | NCNAME_FRAG ; ncname = NCNAME_FRAG ; (* Multi-line regexs don't currently work in TatSu NCNAME_FRAG = /(?x) ( [A-Z] | _ | [a-z] | [\u00C0-\u00D6] | [\u00D8-\u00F6] | [\u00F8-\u02FF] | [\u0370-\u037D] | [\u037F-\u1FFF] | [\u200C-\u200D] | [\u2070-\u218F] | [\u2C00-\u2FEF] | [\u3001-\uD7FF] | [\uF900-\uFDCF] | [\uFDF0-\uFFFD] | [\U00010000-\U000EFFFF] ) ( [A-Z] | _ | [a-z] | [\u00C0-\u00D6] | [\u00D8-\u00F6] | [\u00F8-\u02FF] | [\u0370-\u037D] | [\u037F-\u1FFF] | [\u200C-\u200D] | [\u2070-\u218F] | [\u2C00-\u2FEF] | [\u3001-\uD7FF] | [\uF900-\uFDCF] | [\uFDF0-\uFFFD] | [\U00010000-\U000EFFFF] | - | \. | [0-9] | \u00B7 | [\u0300-\u036F] | [\u203F-\u2040] )* /; *) NCNAME_FRAG = /([A-Z]|_|[a-z]|[\u00C0-\u00D6]|[\u00D8-\u00F6]|[\u00F8-\u02FF]|[\u0370-\u037D]|[\u037F-\u1FFF]|[\u200C-\u200D]|[\u2070-\u218F]|[\u2C00-\u2FEF]|[\u3001-\uD7FF]|[\uF900-\uFDCF]|[\uFDF0-\uFFFD]|[\U00010000-\U000EFFFF])([A-Z]|_|[a-z]|[\u00C0-\u00D6]|[\u00D8-\u00F6]|[\u00F8-\u02FF]|[\u0370-\u037D]|[\u037F-\u1FFF]|[\u200C-\u200D]|[\u2070-\u218F]|[\u2C00-\u2FEF]|[\u3001-\uD7FF]|[\uF900-\uFDCF]|[\uFDF0-\uFFFD]|[\U00010000-\U000EFFFF]|-|\.|[0-9]|\u00B7|[\u0300-\u036F]|[\u203F-\u2040])*/; DIGITS = /[0-9]+/ ;