mathlingua-reference/syntax.txt at main · mathlingua/mathlingua-reference · GitHub

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x_ -> x_ + 1
{x_ : x_ is \real}
{x_ : x_ is \real | f(x_) > 0}


$name :=: real.analysis
\$name.foo
\foo.$name.bar

G is \group via (X, *)

X is? \foo
X is_not? \foo
X "in"? \foo

X member_of \foo

\\type
\\statement
\\expression
\\specification

\\forAll{}:suchThat{}
\\exists{}:suchThat{}
\\existsUnique{}:suchThat{}
\\given{}:then{}
\\if{}:then{}
\\iff{}:then{}


=================================

Root ::= TopLevelItemUnion*


TopLevelItemUnion ::=
    | TitleGroup
    | SectionGroup
    | SubsectionGroup
    | SubsubsectionGroup
    | DescribesGroup
    | DefinesGroup
    | RefinesGroup
    | StatesGroup
    | AxiomGroup
    | TheoremGroup
    | CorollaryGroup
    | LemmaGroup
    | ConjectureGroup
    | PersonGroup
    | ResourceGroup
    | SpecifyGroup


[CommandHeader]
Describes: <FormOrDeclaration>
using?: <IsOrSpec>+
when?: <ClauseUnion>+
extends?: <IsOrViaItemUnion>
specifies?: <IsOrViaItemUnion>+
satisfies?: <ClauseUnion>+
Provides?: <ProvidesItemUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


ProvidesItemUnion ::=
    | SymbolGroup
    | ConnectionGroup


[LabelHeader]?
symbol: <AliasKindUnion>
written?: <WrittenText>+


[LabelHeader]?
connection: <OpenText>*
to: <OpenText>*
using?: <IsOrSpec>+
means: <OpenText>*
signifies?: <OpenText>*
viewable?: <OpenText>*
through?: <OpenText>*


DocumentedItemUnion ::=
    | WrittenGroup
    | CalledGroup
    | WritingGroup
    | OverviewGroup
    | RelatedGroup
    | DiscovererGroup


[LabelHeader]?
written: <WrittenText>+


[LabelHeader]?
called: <CalledText>+
written?: <WrittenText>+


[LabelHeader]?
writing: <WritingAlias>
as: <WritingText>+


[LabelHeader]?
overview: <OpenText>


[LabelHeader]?
related: <OpenText>+


[LabelHeader]?
discoverer: <OpenText>*


JustifiedItemUnion ::=
    | LabelGroup
    | ByGroup


[LabelHeader]?
label: <OpenText>*
by: <OpenText>*
comment: <OpenText>


[LabelHeader]?
by: <OpenText>*
comment: <OpenText>


AliasItemUnion ::=
    | AliasGroup


AliasKindUnion ::=
    | ExpressionAlias
    | SpecOperatorAlias


[LabelHeader]?
alias: <AliasKindUnion>
written?: <WrittenText>+


[CommandHeader]
Defines: <IsOrSpec>
using?: <IsOrSpec>+
when?: <ClauseUnion>+
expresses?: <ClauseUnion>
Provides?: <ProvidesItemUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


[CommandHeader]
Refines: <IsOrRefinedStatementSpec>
using?: <IsOrSpec>+
when?: <ClauseUnion>+
specifies?: <IsOrRefinedStatementSpec>
satisfies?: <ClauseUnion>+
Provides?: <ProvidesItemUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


DISAMBIGUATES


[CommandHeader]
States: <OpenText>*
using?: <IsOrSpec>+
when?: <ClauseUnion>+
that: <ClauseUnion>+
Provides?: <ProvidesItemUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


REPRESENTS


[CommandHeader]?
Theorem: <OpenText>*
given?: <IsOrRefinedStatementSpec>+
where?: <ClauseUnion>+
then: <ClauseUnion>+
iff?: <ClauseUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


[CommandHeader]?
Corollary: <OpenText>*
of: <OpenText>*
given?: <IsOrRefinedStatementSpec>+
where?: <ClauseUnion>+
then: <ClauseUnion>+
iff?: <ClauseUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


[CommandHeader]?
Lemma: <OpenText>*
given?: <IsOrRefinedStatementSpec>+
where?: <ClauseUnion>+
then: <ClauseUnion>+
iff?: <ClauseUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


[CommandHeader]?
Axiom: <OpenText>*
given?: <IsOrRefinedStatementSpec>+
where?: <ClauseUnion>+
then: <ClauseUnion>+
iff?: <ClauseUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


[CommandHeader]?
Conjecture: <OpenText>*
given?: <IsOrRefinedStatementSpec>+
where?: <ClauseUnion>+
then: <ClauseUnion>+
iff?: <ClauseUnion>+
Justified?: <JustifiedItemUnion>+
Documented?: <DocumentedItemUnion>+
Aliases?: <AliasItemUnion>+
References?: <ResourceHeader>+
Metadata?: <MetadataItemUnion>+


Specify: <SpecifyItemUnion>+


[AuthorHeader]
Person: <OpenText>*
name: <OpenText>+
biography: <OpenText>


[ResourceHeader]
Resource: <ResourceItemUnion>+


ResourceItemUnion ::=
    | ResourceTitleGroup
    | ResourceAuthorGroup
    | ResourceOffsetGroup
    | ResourceUrlGroup
    | ResourceHomepageGroup
    | ResourceTypeGroup
    | ResourceEditionGroup
    | ResourceEditorGroup
    | ResourceInstitutionGroup
    | ResourceJournalGroup
    | ResourcePublisherGroup
    | ResourceVolumeGroup
    | ResourceMonthGroup
    | ResourceYearGroup
    | ResourceDescriptionGroup


title: <OpenText>


author: <OpenText>+


offset: <OpenText>


url: <OpenText>


homepage: <OpenText>


type: <OpenText>


edition: <OpenText>


editor: <OpenText>


institution: <OpenText>


journal: <OpenText>


publisher: <OpenText>


volume: <OpenText>


month: <OpenText>


year: <OpenText>


description: <OpenText>


Title: <OpenText>


Section: <OpenText>


Subsection: <OpenText>


Subsubsection: <OpenText>


ClauseUnion ::=
    | NotGroup
    | AllOfGroup
    | AnyOfGroup
    | OneOfGroup
    | ExistsGroup
    | ExistsUniqueGroup
    | ForAllGroup
    | IfGroup
    | IffGroup
    | PiecewiseGroup
    | GivenGroup
    | ExpressionBinding
    | IsOrSpec
    | Expression


[LabelHeader]?
given: <IsOrRefinedStatementSpec>
where?: <ClauseUnion>+
then: <ClauseUnion>+


[LabelHeader]?
not: <ClauseUnion>


[LabelHeader]?
allOf: <ClauseUnion>+


[LabelHeader]?
anyOf: <ClauseUnion>+


[LabelHeader]?
oneOf: <ClauseUnion>+


[LabelHeader]?
exists: <BindingOrSpecUnion>
suchThat: <ClauseUnion>+


[LabelHeader]?
existsUnique: <BindingOrSpecUnion>
suchThat: <ClauseUnion>+


[LabelHeader]?
forAll: <BindingOrSpecUnion>
where?: <ClauseUnion>+
then: <ClauseUnion>+


[LabelHeader]?
if: <ClauseUnion>+
then: <ClauseUnion>+


[LabelHeader]?
iff: <ClauseUnion>+
then: <ClauseUnion>+


[LabelHeader]?
piecewise: <OpenText>*
if: <ClauseUnion>+
then: <ClauseUnion>+
else?: <ClauseUnion>+


SpecifyItemUnion ::=
    | PositiveIntGroup
    | NegativeIntGroup
    | ZeroGroup
    | PositiveDecimalGroup
    | NegativeDecimalGroup


[LabelHeader]?
positive: <OpenText>*
int: <OpenText>*
is: <OpenText>*


[LabelHeader]?
negative: <OpenText>*
int: <OpenText>*
is: <OpenText>*


[LabelHeader]?
positive: <OpenText>*
decimal: <OpenText>*
is: <OpenText>*


[LabelHeader]?
negative: <OpenText>*
decimal: <OpenText>*
is: <OpenText>*


[LabelHeader]?
zero: <OpenText>*
is: <OpenText>*


MetadataItemUnion ::=
    | IdGroup
    | VersionGroup


id: <OpenText>


version: <OpenText>


=================================

// abc
// a_b_c
// x1
// x_1
Name ::= [a-zA-Z0-9]+[a-zA-Z0-9_]*[a-zA-Z0-9]+

// abc?
// x_1?
PlaceholderName ::= <Name> "_"

// abc__
// x_1__
MagneticPlaceholderName ::= <Name> "__"

// *
// *+
// >=
// *_1
// *_name
Operator ::= [!%^&*-+=|<>/]("_" <Name>)?

Identifier ::= <Name> |
               <Operator>