Packages

package root

Definition Classes: root

package info

Definition Classes: root

package kwarc

Definition Classes: info

package mmt

Definition Classes: kwarc

package api

This is the main package of the MMT API.

It holds subpackages for all data structures, data containers, and the central algorithms and services.

Classes directly defined in the package

Some minor classes that are used throughout MMT are defined in this package, in particular:

MMT URIs in the class Path and Namespace
processing and content errors in the class Error

The package also contains root classes for certain types that are subclassed throughout the package. Most importantly:

StructuralElement: structure-level (= named) parts in the data structures for the MMT language: documents, theories, constants, ...
MMTTask: tasks for a single object: parsing, checking, ...
Rule: object-level part of the MMT language that is written in Scala

Subpackages

Data structures for the MMT language

The data structures for the MMT languages are defined in 4 packages corresponding to the 4 levels: - documents: Documents and all other NarrativeElements - modules: Modules (= the toplevel declarations), in particular Theorys and Views - symbols: all Declarations inside modules, in particular Constants - objects: all anonymous Objects (e.g., formulas, functions, etc.), in particular Contexts and Terms

The former 3 levels are jointly called 'structural' levels. All elements subclass StructuralElement, have an MMT URI, and carry an MMT URI referring to their parent in the MMT abstract syntax tree.

Structural elements are extensible (via DerivedModules and DerivedDeclarations), and the package patterns defines declaration patterns as a built-in extension.

All structural elements are mutable and implement the ContainerElement interface for changing their children. Objects, by contrast, are represented as immutable inductive types.(except for carrying metadata.Metadata and objects.ClientProperties). The boundary between structural elements and objects is mediated by ComponentContainers: these are mutable, owned by structural elements, and maintain objects.

A few auxiliary data structures shifted to separate packages: - opaque: external (i.e., informal, computation) content - informal: partially outdated informal data structures - metadata: metadata annotations to all structural elements or objects

The MMT main class and its internal state

The package frontend contains the class Controller, which owns all state relevant for running MMT. Typically, each application creates a single instance of this class. The package also defines several other essential classes, most importantly MMT's extension (=plug-in, add-on) interfaces via the Extension class.

The package libraries maintains the instances of MMT language data structures, in particular the Library class. Controller owns a Library, which stores all structural elements that have been loaded into memory.

User interfaces

The package frontend also contains the main executable classes, in particular the Shell class.

The package gui collects all classes for building graphical user interfaces. This includes auxiliary classes for use in IDE plugins.

The package web collects all classes for the HTTP interface of MMT.

Physical storage of the MMT language files

The package archives defines MMT Archives (= projects) as well as classes for building and working with archives. The latter include in particular the BuildManager and BuildTarget. Build targets include Importers and [Exporter]]s that translate between MMT and other formats.

The package backend defines classes for maintaining archives and translating between the MMT URIs of structural elements and their physical storage locations.

The central algorithms for processing MMT content

The processing model of MMT consists of several major algorithms. - parser: read strings into MMT data structures - checking: check and refine MMT data structures - uom: pure computation on MMT data structures - proving: theorem proving on MMT data structures (in very early state)) - execution: imperative computation (in very, very early state) - presentation: rendering MMT data structures in user-facing formats (including HTML+presentation MathML)

All algorithms are defined in Extensions coupled with default implementations. Moreover, all algorithms are split into two separate levels, one for structural elements and objects. See LeveledExtension.

The package notations maintains the common code for parsing and presentation.

The package valuebases maintains mathematical databases as a part of MMT.

Other algorithms on the MMT data structures

The package ontology contains a relational, semantic web-style ontology and query engine for it.

The package moc contains change management.

The package refactoring contains refactoring principles.

General purpose utility functions

The package utils defines general purpose APIs for files, URIs, HTML building, etc.

Definition Classes: mmt

package uom

The algorithm for immutably computing with MMT content, i.e., simplification (strings to MMT data structures).

Simplification

The algorithm for immutably computing with MMT content, i.e., simplification (strings to MMT data structures). See api for an overview of the algorithms.

The main interfaces are - Simplifier: the main interface for parser (combining a structure and an object simplifier) - StructureSimplifier: simplifying structural elements - ObjectSimplifier: simplifying objects

The main implementations are - ElaborationBasedSimplifier for structural elements - RuleBasedSimplifier for objects

Structure simplification is extensible using derived elements. Object simplification is extensible using rules.

Literals and semantic objects

This package also contains the classes for using Scala objects as MMT literals.

SemanticType defines types as sets of Scala objects. SemanticValue defines a distinguished element of such a type. SemanitcOperator defines functions on such types as Scala functions.

Literals and operations on them are injected into the MMT language by declaring RealizedValue, RealizedType and RealizedOperator rules, which tie a syntactic type/operator (i.e., an MMT term) to a semantic counterpart.

StandardLiterals defines semantic types for the most important types.

RealizedTheory represents an MMT theory programmed in Scala, usually as a Scala class.

Scala companion objects for MMT theories

TheoryScala and ConstantScala are auxiliary classes that are useful when implementing MMT rules or other logic-specific algorithms.

Definition Classes: api

AbbrevRule

Arithmetic

Atomic

BinaryConstantScala

ByStructureSimplifier

CannotSimplify

ComplexRat

ComplificationRule

ConstantScala

DefinitionExpander

DefinitionsExpanded

DocumentScala

ElaboratedElement

ElaborationBasedSimplifier

ExtendedSimplificationEnvironment

FlexaryConstantScala

FouraryConstantScala

FunctionN

GenericScalaExporter

IntModulo

IntegerLiteral

IntegerRepresented

Integrator

InvFunctionN

InverseOperator

Invertible

KnownArg

ListType

MatchingSimplificationRule

OMLiteral

ObjectSimplifier

OpenMath

OpenMathScalaExporter

Product

Quotient

RList

RProduct

RQuotient

RSemanticType

RSubtype

RTuple

RealizationInScala

RealizedOperator

RealizedTheory

RealizedType

RealizedValue

Recurse

RecurseOnly

RepresentedRealizedType

RewriteRule

RuleBasedSimplifier

Scala

SemOpType

SemanticOperator

SemanticType

SemanticValue

Simplifiability

SimplificationEnvironment

SimplificationRule

SimplificationUnit

Simplifier

SimplifierRule

SimplifierState

Simplify

StandardBool

StandardDouble

StandardInt

StandardNat

StandardPositive

StandardRat

StandardString

StringOperations

StructureSimplifier

Subtype

SynOpType

TermLiteral

TermTransformationRule

TermTransformer

TernaryConstantScala

TheoryScala

TrivialSimplificationEnvironment

TupleType

URILiteral

UUIDLiteral

UnapplyArg

UnaryConstantScala

UnknownArg

ViewScala

info.kwarc.mmt.api.uom

Quotient

abstract class Quotient extends SemanticType

Source: StandardLiterals.scala

Linear Supertypes

SemanticType, SemanticObject, AnyRef, Any

Known Subclasses

IntModulo, RQuotient, StandardRat

Ordering

Alphabetic
By Inheritance

Inherited

Quotient
SemanticType
SemanticObject
AnyRef
Any

Hide All
Show All

Visibility

Public
All

Instance Constructors

new Quotient(of: SemanticType)

Abstract Value Members

abstract def by(u: Any): Any

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def =>:(args: List[SemanticType]): SemOpType

Definition Classes
SemanticType
def =>:(arg: SemanticType): SemOpType
enables the notation (a,b) =>: c for function types
enables the notation (a,b) =>: c for function types

Definition Classes
SemanticType
final def asInstanceOf[T0]: T0

Definition Classes
Any
def asString: String
string representation of this type (should be toString, but we want to force people to implement this)
string representation of this type (should be toString, but we want to force people to implement this)

Definition Classes
Quotient → SemanticType
def clone(): AnyRef

Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws( ... ) @native()
def embed(into: SemanticType): Option[Unary]
returns a canonical embedding from this type into some other type only the identity of this type by default, override as needed
returns a canonical embedding from this type into some other type only the identity of this type by default, override as needed

Definition Classes
SemanticType
def enumerate: Option[Iterator[Any]]
for a finite quotient of an infinite type, hasNext will eventually run forever
for a finite quotient of an infinite type, hasNext will eventually run forever
returns
a fresh iterator over values of this type

Definition Classes
Quotient → SemanticType
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def escapedLiteral(begin: String, end: String): Some[AsymmetricEscapeLexer]
convenience method to construct a lexer for this type
convenience method to construct a lexer for this type

Definition Classes
SemanticType
def finalize(): Unit

Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
def fromString(s: String): Any
converts strings into values; pre: s == toString(u) for some u with valid(u) == true
converts strings into values; pre: s == toString(u) for some u with valid(u) == true

Definition Classes
Quotient → SemanticType
final def getClass(): Class[_]

Definition Classes
AnyRef → Any
Annotations
@native()
def hashCode(): Int

Definition Classes
AnyRef → Any
Annotations
@native()
def id: Unary
the identify function of this type
the identify function of this type

Definition Classes
SemanticType
def init: Unit
errors in Java initializers are hard to debug; therefore, objects should put initialization code here, which will be called by MMT empty by default, may throw errors
errors in Java initializers are hard to debug; therefore, objects should put initialization code here, which will be called by MMT empty by default, may throw errors

Definition Classes
SemanticObject
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def lex: Option[LexFunction]
returns
a LexerExtension that is to be used when this type is in scope

Definition Classes
Quotient → SemanticType
lazy val mpath: MPath
the MMT URI of this object, derived from its Scala name: scala://package?name
the MMT URI of this object, derived from its Scala name: scala://package?name

Definition Classes
SemanticObject
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def normalform(u: Any): Any
the equivalence relation (given as a normal form conversion) on the semantic type used to obtain quotient types pre: valid(u) == true identity by default
the equivalence relation (given as a normal form conversion) on the semantic type used to obtain quotient types pre: valid(u) == true identity by default

Definition Classes
Quotient → SemanticType
final def notify(): Unit

Definition Classes
AnyRef
Annotations
@native()
final def notifyAll(): Unit

Definition Classes
AnyRef
Annotations
@native()
val of: SemanticType
def quotedLiteral(key: String): Some[AsymmetricEscapeLexer]
convenience method to construct a lexer for this type
convenience method to construct a lexer for this type

Definition Classes
SemanticType
def repr: Unary
the projection of an element to its representative
def subtype(of: SemanticType): Boolean
subtype relation only reflexivity by default, override as needed invariant: if true, embed must return identity
subtype relation only reflexivity by default, override as needed invariant: if true, embed must return identity

Definition Classes
SemanticType
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(u: Any): String
converts values into strings; pre: valid(u) == true
converts values into strings; pre: valid(u) == true

Definition Classes
Quotient → SemanticType
def toString(): String

Definition Classes
SemanticType → AnyRef → Any
def valid(u: Any): Boolean
the predicate on the semantic type used to obtain subtypes
the predicate on the semantic type used to obtain subtypes
true by default

Definition Classes
Quotient → SemanticType
final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... ) @native()

Packages

Classes directly defined in the package

Subpackages

Data structures for the MMT language

The MMT main class and its internal state

User interfaces

Physical storage of the MMT language files

The central algorithms for processing MMT content

Other algorithms on the MMT data structures

General purpose utility functions

Simplification

Literals and semantic objects

Scala companion objects for MMT theories

Quotient

abstract class Quotient extends SemanticType

Instance Constructors

Abstract Value Members

Concrete Value Members

Inherited from SemanticType

Inherited from SemanticObject

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

Classes directly defined in the package

Subpackages

Data structures for the MMT language

The MMT main class and its internal state

User interfaces

Physical storage of the MMT language files

The central algorithms for processing MMT content

Other algorithms on the MMT data structures

General purpose utility functions

Simplification

Literals and semantic objects

Scala companion objects for MMT theories

Quotient 

abstract class Quotient extends SemanticType

Instance Constructors

Abstract Value Members

Concrete Value Members

Inherited from SemanticType

Inherited from SemanticObject

Inherited from AnyRef

Inherited from Any

Ungrouped

Quotient