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.

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shifted to separate packages: - opaque: external (i.e., informal, computation) content - informal: partially outdated informal data structures - metadata: metadata annotations to all structural elements or objects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

    The algorithm for proving theorems about MMT content.

    The algorithm for proving theorems about MMT content. This is very premature and experimental.

    See api for an overview of the algorithms.

    The main interfaces are - Prover: object level proving

    Structure level proving does not exist yet.

    The main implementations are - RuleBasedProver for object-level proving

    The latter creates a Searcher for each proving task, which applies search rules to find MMT objects.

    Definition Classes
    api
  • package imperative
    Definition Classes
    proving
  • Alternative
  • ApplicableTactic
  • Atom
  • AtomicShape
  • BackwardInvertible
  • BackwardSearch
  • BoundShape
  • ComplexShape
  • EquivalenceClass
  • EquivalenceRelation
  • Fact
  • Facts
  • ForwardInvertible
  • ForwardSearch
  • Goal
  • InvertibleTactic
  • Prover
  • ProvingUnit
  • RuleBasedProver
  • Searcher
  • Shape
  • ShapeIndexedSet
  • Tactic
  • Wildcard
c

info.kwarc.mmt.api.proving

EquivalenceRelation

class EquivalenceRelation extends AnyRef

a container for relations like ==, !=, and <= on terms which are indexed by shape)

the class approximates the relations based on the available knowledge initially nothing is known, and instances are added over time

knowledge grows monotonously and cannot be removed inconsistency can arise (which can, e.g., be used to terminate a proof)

the class implements - reflexivity, symmetry, and (cached) transitivity of == - irreflexivity and symmetry of != - reflexivity, anti-symmetry wrt ==, and (not cached) transitivity of <= - congruence of <= wrt == - disjointness of == and != (used to detect inconsistency)

Source
EquivalenceRelation.scala
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Instance Constructors

  1. new EquivalenceRelation(levels: Int)

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def belowOrEqual(s: Term, t: Term): Unit

    records the knowledge s <= t

  6. def checkBelowOrEqual(s: Term, t: Term): Option[Boolean]

    checks if s <= t is known to be true or false; possibly inconclusive

  7. def checkEquivalent(s: Term, t: Term): Option[Boolean]

    checks if s == t or s != t is known; possibly inconclusive

  8. def checkStrictlyBelow(s: Term, t: Term): Option[Boolean]

    checks if s < t is known to be true or false; possibly inconclusive

  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  10. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  11. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  12. def equivalent(s: Term, t: Term): Unit

    records the knowledge s == t

  13. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. def getClass(s: Term): Option[EquivalenceClass]

    the equivalence class of s (if any)

  15. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  16. def getOrAddClass(t: Term): EquivalenceClass

    the equivalence class of s (possibly a singleton)

  17. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  18. def inconsistent: Boolean

    true if the available knowledge is inconsistent

  19. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  20. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  21. def notEquivalent(s: Term, t: Term): Unit

    records the knowledge s != t

  22. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  23. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  24. def strictlyBelow(s: Term, t: Term): Unit

    records the knowledge s < t

  25. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  26. def toString(): String
    Definition Classes
    AnyRef → Any
  27. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  28. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  29. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()

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