Packages

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KeYmaera X is a theorem prover for differential dynamic logic (dL), a logic for specifying and verifying properties of hybrid systems with mixed discrete and continuous dynamics.

KeYmaera X: An aXiomatic Tactical Theorem Prover

KeYmaera X is a theorem prover for differential dynamic logic (dL), a logic for specifying and verifying properties of hybrid systems with mixed discrete and continuous dynamics. Reasoning about complicated hybrid systems requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute tactics in parallel, and interface with partial proofs via an extensible user interface.

http://keymaeraX.org/

Concrete syntax for input language Differential Dynamic Logic

Package Structure

Main documentation entry points for KeYmaera X API:

edu.cmu.cs.ls.keymaerax.core - KeYmaera X kernel, proof certificates, main data structures
- Expression - Differential dynamic logic expressions: Term, Formula, Program
- Sequent - Sequents of formulas
- Provable - Proof certificates transformed by rules/axioms
- Rule - Proof rules as well as USubstOne for (one-pass) uniform substitutions and renaming.
- StaticSemantics - Static semantics with free and bound variable analysis
- Instead of constructing dL expressions from constructors, it is easier to use the KeYmaeraXParser.
edu.cmu.cs.ls.keymaerax.parser - Parser and pretty printer with concrete syntax and notation for differential dynamic logic.
- Concrete syntax for input language Differential Dynamic Logic
- KeYmaeraXPrettyPrinter - Pretty printer producing concrete KeYmaera X syntax
- KeYmaeraXParser - Parser reading concrete KeYmaera X syntax
- KeYmaeraXArchiveParser - Parser reading KeYmaera X model and proof archive .kyx files
- DLParser - Combinator parser reading concrete KeYmaera X syntax
- DLArchiveParser - Combinator parser reading KeYmaera X model and proof archive .kyx files
edu.cmu.cs.ls.keymaerax.infrastruct - Prover infrastructure outside the kernel
- UnificationMatch - Unification algorithm
- RenUSubst - Renaming Uniform Substitution quickly combining kernel's renaming and substitution.
- Context - Representation for contexts of formulas in which they occur.
- Augmentors - Augmenting formula and expression data structures with additional functionality
- ExpressionTraversal - Generic traversal functionality for expressions
edu.cmu.cs.ls.keymaerax.bellerophon - Bellerophon tactic language and tactic interpreter
- BelleExpr - Tactic language expressions
- SequentialInterpreter - Sequential tactic interpreter for Bellerophon tactics
edu.cmu.cs.ls.keymaerax.btactics - Bellerophon tactic library for conducting proofs.
- TactixLibrary - Main KeYmaera X tactic library including many proof tactics.
- HilbertCalculus - Hilbert Calculus for differential dynamic logic
- SequentCalculus - Sequent Calculus for propositional and first-order logic
- HybridProgramCalculus - Hybrid Program Calculus for differential dynamic logic
- DifferentialEquationCalculus - Differential Equation Calculus for differential dynamic logic
- UnifyUSCalculus - Unification-based uniform substitution calculus underlying the other calculi
- [edu.cmu.cs.ls.keymaerax.btactics.UnifyUSCalculus.ForwardTactic ForwardTactic] - Forward tactic framework for conducting proofs from premises to conclusions
edu.cmu.cs.ls.keymaerax.lemma - Lemma mechanism
- Lemma - Lemmas are Provables stored under a name, e.g., in files.
- LemmaDB - Lemma database stored in files or database etc.
edu.cmu.cs.ls.keymaerax.tools.qe - Real arithmetic back-end solvers
- MathematicaQETool - Mathematica interface for real arithmetic.
- Z3QETool - Z3 interface for real arithmetic.
edu.cmu.cs.ls.keymaerax.tools.ext - Extended back-ends for noncritical ODE solving, counterexamples, algebra, simplifiers, etc.
- Mathematica - Mathematica interface for ODE solving, algebra, simplification, invariant generation, etc.
- Z3 - Z3 interface for real arithmetic including simplifiers.

Entry Points

Additional entry points and usage points for KeYmaera X API:

edu.cmu.cs.ls.keymaerax.launcher.KeYmaeraX - Command-line launcher for KeYmaera X supports command-line argument -help to obtain usage information
edu.cmu.cs.ls.keymaerax.btactics.AxIndex - Axiom indexing data structures with keys and recursors for canonical proof strategies.
edu.cmu.cs.ls.keymaerax.btactics.DerivationInfo - Meta-information on all derivation steps (axioms, derived axioms, proof rules, tactics) with user-interface info.
edu.cmu.cs.ls.keymaerax.bellerophon.UIIndex - Index determining which canonical reasoning steps to display on the KeYmaera X User Interface.
edu.cmu.cs.ls.keymaerax.btactics.Ax - Registry for derived axioms and axiomatic proof rules that are proved from the core.

References

Full references on KeYmaera X are provided at http://keymaeraX.org/. The main references are the following:

1. André Platzer. A complete uniform substitution calculus for differential dynamic logic. Journal of Automated Reasoning, 59(2), pp. 219-265, 2017.

2. Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Völp and André Platzer. KeYmaera X: An axiomatic tactical theorem prover for hybrid systems. In Amy P. Felty and Aart Middeldorp, editors, International Conference on Automated Deduction, CADE'15, Berlin, Germany, Proceedings, volume 9195 of LNCS, pp. 527-538. Springer, 2015.

3. André Platzer. Logical Foundations of Cyber-Physical Systems. Springer, 2018. Videos

Definition Classes: root

package edu

Definition Classes: root

package cmu

Definition Classes: edu

package cs

Definition Classes: cmu

package ls

Definition Classes: cs

package keymaerax

Definition Classes: ls

package hydra

HyDRA Hybrid Distributed Reasoning Architecture server with a REST-API and database.

HyDRA Hybrid Distributed Reasoning Architecture server with a REST-API and database. HyDRA provides a simplified high-level programming interface to the KeYmaeara X prover. It provides components for proof tree simplification, tactic search, and custom tactic scheduling policies, as well as for storing and accessing proofs in files or databases. These components can be accessed remotely through a REST-API.

Definition Classes: keymaerax
To do: Stub. Describe for real.

trait Tables extends AnyRef

Slick data model trait for extension, choice of backend or usage in the cake pattern.

Slick data model trait for extension, choice of backend or usage in the cake pattern. (Make sure to initialize this late.)

Definition Classes: hydra

Agendaitems

AgendaitemsRow

Config

ConfigRow

Executables

ExecutablesRow

Executionsteps

ExecutionstepsRow

Lemmas

LemmasRow

Models

ModelsRow

Proofs

ProofsRow

Users

UsersRow

edu.cmu.cs.ls.keymaerax.hydra.Tables

Proofs

class Proofs extends scala.slick.driver.JdbcProfile.SimpleQL.Table[ProofsRow]

Table description of table proofs. Objects of this class serve as prototypes for rows in queries.

Linear Supertypes

scala.slick.driver.JdbcProfile.Table[ProofsRow], AbstractTable[ProofsRow], Rep[ProofsRow], AnyRef, Any

Ordering

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By Inheritance

Inherited

Proofs
Table
AbstractTable
Rep
AnyRef
Any

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Visibility

Public
All

Instance Constructors

new Proofs(_tableTag: scala.slick.driver.JdbcProfile.SimpleQL.Tag)

Type Members

final type TableElementType = ProofsRow

Definition Classes
Table → AbstractTable

Value Members

final def !=(arg0: Any): Boolean

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

Definition Classes
AnyRef → Any
def *: ProvenShape[ProofsRow]

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

Definition Classes
AnyRef → Any
val O: scala.slick.driver.JdbcProfile.columnOptions.type

Definition Classes
Table
val _Id: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column _id DBType(INTEGER), PrimaryKey
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@native() @throws( ... )
val closed: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column closed DBType(INTEGER)
def collectFieldSymbols(n: Node): Iterable[FieldSymbol]

Attributes
protected[this]
Definition Classes
AbstractTable
def column[C](n: String, options: ColumnOption[C]*)(implicit tm: TypedType[C]): Column[C]

Definition Classes
Table
def create_*: Iterable[FieldSymbol]

Definition Classes
AbstractTable
val date: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column date DBType(TEXT)
val description: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column description DBType(TEXT)
def encodeRef(path: List[Symbol]): AbstractTable[ProofsRow]

Definition Classes
AbstractTable → Rep
final def eq(arg0: AnyRef): Boolean

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

Definition Classes
AnyRef → Any
def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
def foreignKey[P, PU, TT <: AbstractTable[_], U](name: String, sourceColumns: P, targetTableQuery: TableQuery[TT])(targetColumns: (TT) ⇒ P, onUpdate: ForeignKeyAction, onDelete: ForeignKeyAction)(implicit unpack: Shape[_ <: FlatShapeLevel, TT, U, _], unpackp: Shape[_ <: FlatShapeLevel, P, PU, _]): ForeignKeyQuery[TT, U]

Definition Classes
AbstractTable
final def foreignKeys: Iterable[ForeignKey]

Definition Classes
AbstractTable
final def getClass(): Class[_]

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

Definition Classes
AnyRef → Any
Annotations
@native()
def index[T](name: String, on: T, unique: Boolean)(implicit shape: Shape[_ <: FlatShapeLevel, T, _, _]): Index

Definition Classes
AbstractTable
def indexes: Iterable[Index]

Definition Classes
AbstractTable
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
val istemporary: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column isTemporary DBType(INTEGER)
val lemmaid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column lemmaId DBType(INTEGER)
val modelid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column modelId DBType(INTEGER)
lazy val modelsFk: ForeignKeyQuery[Models, ModelsRow]
Foreign key referencing Models (database name models_FK_1)
val name: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column name DBType(TEXT)
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

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

Definition Classes
AnyRef
Annotations
@native()
def primaryKey[T](name: String, sourceColumns: T)(implicit shape: Shape[_ <: FlatShapeLevel, T, _, _]): PrimaryKey

Definition Classes
AbstractTable
final def primaryKeys: Iterable[PrimaryKey]

Definition Classes
AbstractTable
val schemaName: Option[String]

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

Definition Classes
AnyRef
def tableConstraints: Iterator[Constraint]

Definition Classes
AbstractTable
def tableIdentitySymbol: TableIdentitySymbol

Definition Classes
Table → AbstractTable
val tableName: String

Definition Classes
AbstractTable
lazy val tableNode: TableNode

Definition Classes
AbstractTable
def tableProvider: RelationalDriver

Definition Classes
Table
val tableTag: Tag

Definition Classes
AbstractTable
val tactic: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column tactic DBType(TEXT)
def toNode: Node

Definition Classes
AbstractTable → Rep
def toString(): String

Definition Classes
AnyRef → Any
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
@native() @throws( ... )

Packages

KeYmaera X: An aXiomatic Tactical Theorem Prover

Package Structure

Entry Points

References

Proofs

class Proofs extends scala.slick.driver.JdbcProfile.SimpleQL.Table[ProofsRow]

Instance Constructors

Type Members

Value Members

Inherited from scala.slick.driver.JdbcProfile.Table[ProofsRow]

Inherited from AbstractTable[ProofsRow]

Inherited from Rep[ProofsRow]

Inherited from AnyRef

Inherited from Any

Ungrouped

Packages

KeYmaera X: An aXiomatic Tactical Theorem Prover

Package Structure

Entry Points

References

Proofs 

class Proofs extends scala.slick.driver.JdbcProfile.SimpleQL.Table[ProofsRow]

Instance Constructors

Type Members

Value Members

Inherited from scala.slick.driver.JdbcProfile.Table[ProofsRow]

Inherited from AbstractTable[ProofsRow]

Inherited from Rep[ProofsRow]

Inherited from AnyRef

Inherited from Any

Ungrouped

Proofs