class Executionsteps extends scala.slick.driver.JdbcProfile.SimpleQL.Table[ExecutionstepsRow]
Table description of table executionSteps. Objects of this class serve as prototypes for rows in queries.
Linear Supertypes
Ordering
- Alphabetic
- By Inheritance
Inherited
- Executionsteps
- Table
- AbstractTable
- Rep
- AnyRef
- Any
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Visibility
- Public
- All
Instance Constructors
- new Executionsteps(_tableTag: scala.slick.driver.JdbcProfile.SimpleQL.Tag)
Type Members
-
final
type
TableElementType = ExecutionstepsRow
- Definition Classes
- Table → AbstractTable
Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
*: ProvenShape[ExecutionstepsRow]
- Definition Classes
- Executionsteps → AbstractTable
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final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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def
?: MappedProjection[Option[ExecutionstepsRow], (Option[Int], Option[Int], Option[Int], Option[Int], Option[String], Option[Int], Option[Int], Option[Int], Option[Int], Option[String], Option[String], Option[String], Option[Int], Option[Int])]
Maps whole row to an option.
Maps whole row to an option. Useful for outer joins.
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val
O: scala.slick.driver.JdbcProfile.columnOptions.type
- Definition Classes
- Table
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val
_Id: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column _id DBType(INTEGER), PrimaryKey
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
val
branchorder: scala.slick.driver.JdbcProfile.SimpleQL.Column[Int]
Database column branchOrder DBType(INT)
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val
childrenrecorded: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column childrenRecorded DBType(BOOLEAN)
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def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
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
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def
encodeRef(path: List[Symbol]): AbstractTable[ExecutionstepsRow]
- Definition Classes
- AbstractTable → Rep
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
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val
executableid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column executableId DBType(INTEGER)
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lazy val
executablesFk: ForeignKeyQuery[Executables, ExecutablesRow]
Foreign key referencing Executables (database name executables_FK_1)
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lazy val
executionstepsFk: ForeignKeyQuery[Executionsteps, ExecutionstepsRow]
Foreign key referencing Executionsteps (database name executionSteps_FK_2)
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def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
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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
-
val
inputprovableid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column inputProvableId DBType(INTEGER)
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
lazy val
lemmasFk: ForeignKeyQuery[Lemmas, LemmasRow]
Foreign key referencing Lemmas (database name lemmas_FK_3)
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val
localprovableid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column localProvableId DBType(INTEGER)
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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()
-
val
numopensubgoals: scala.slick.driver.JdbcProfile.SimpleQL.Column[Int]
Database column numOpenSubGoals DBType(INTEGER)
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val
numsubgoals: scala.slick.driver.JdbcProfile.SimpleQL.Column[Int]
Database column numSubGoals DBType(INTEGER)
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val
previousstep: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column previousStep DBType(INTEGER)
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def
primaryKey[T](name: String, sourceColumns: T)(implicit shape: Shape[_ <: FlatShapeLevel, T, _, _]): PrimaryKey
- Definition Classes
- AbstractTable
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final
def
primaryKeys: Iterable[PrimaryKey]
- Definition Classes
- AbstractTable
-
val
proofid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column proofId DBType(INTEGER)
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lazy val
proofsFk: ForeignKeyQuery[Proofs, ProofsRow]
Foreign key referencing Proofs (database name proofs_FK_4)
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val
resultprovableid: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[Int]]
Database column resultProvableId DBType(INTEGER)
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val
rulename: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column ruleName DBType(STRING)
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val
schemaName: Option[String]
- Definition Classes
- AbstractTable
-
val
status: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column status DBType(TEXT)
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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
-
def
toNode: Node
- Definition Classes
- AbstractTable → Rep
-
def
toString(): String
- Definition Classes
- AnyRef → Any
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val
userexecuted: scala.slick.driver.JdbcProfile.SimpleQL.Column[Option[String]]
Database column userExecuted DBType(BOOLEAN)
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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( ... )
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 structuresExpression- Differential dynamic logic expressions:Term,Formula,ProgramSequent- Sequents of formulasProvable- Proof certificates transformed by rules/axiomsRule- Proof rules as well asUSubstOnefor (one-pass) uniform substitutions and renaming.StaticSemantics- Static semantics with free and bound variable analysisKeYmaeraXParser.edu.cmu.cs.ls.keymaerax.parser- Parser and pretty printer with concrete syntax and notation for differential dynamic logic.KeYmaeraXPrettyPrinter- Pretty printer producing concrete KeYmaera X syntaxKeYmaeraXParser- Parser reading concrete KeYmaera X syntaxKeYmaeraXArchiveParser- Parser reading KeYmaera X model and proof archive.kyxfilesDLParser- Combinator parser reading concrete KeYmaera X syntaxDLArchiveParser- Combinator parser reading KeYmaera X model and proof archive.kyxfilesedu.cmu.cs.ls.keymaerax.infrastruct- Prover infrastructure outside the kernelUnificationMatch- Unification algorithmRenUSubst- 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 functionalityExpressionTraversal- Generic traversal functionality for expressionsedu.cmu.cs.ls.keymaerax.bellerophon- Bellerophon tactic language and tactic interpreterBelleExpr- Tactic language expressionsSequentialInterpreter- Sequential tactic interpreter for Bellerophon tacticsedu.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 logicSequentCalculus- Sequent Calculus for propositional and first-order logicHybridProgramCalculus- Hybrid Program Calculus for differential dynamic logicDifferentialEquationCalculus- Differential Equation Calculus for differential dynamic logicUnifyUSCalculus- 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 conclusionsedu.cmu.cs.ls.keymaerax.lemma- Lemma mechanismLemma- 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 solversMathematicaQETool- 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-helpto obtain usage informationedu.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