class MathematicaInvGenTool extends BaseKeYmaeraMathematicaBridge[Expression] with InvGenTool with Logging
A continuous invariant implementation using Mathematica over the JLink interface.
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- MathematicaInvGenTool
- Logging
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- LoggerHolder
- InvGenTool
- BaseKeYmaeraMathematicaBridge
- KeYmaeraMathematicaBridge
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Instance Constructors
- new MathematicaInvGenTool(link: MathematicaLink)
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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val
DEBUG: Boolean
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- BaseKeYmaeraMathematicaBridge
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val
MEMORY_LIMIT_OFF: Long
Default memory limit: no limit.
Default memory limit: no limit.
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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val
TIMEOUT_OFF: Int
Default timeout for Mathematica requests: no timeout.
Default timeout for Mathematica requests: no timeout.
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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final
def
asInstanceOf[T0]: T0
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def
availableWorkers: Int
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- BaseKeYmaeraMathematicaBridge
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def
clone(): AnyRef
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final
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eq(arg0: AnyRef): Boolean
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equals(arg0: Any): Boolean
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finalize(): Unit
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def
genODECond(ode: ODESystem, assumptions: Seq[Formula], postCond: Formula): (List[Formula], List[Formula])
Returns the sufficient/necessary condition for postCond to be invariant (left of pair) also returns necessary conditions for the safety question to be true at all with those assumptions (right of pair) In either case, all formulas in the returned list must be valid
Returns the sufficient/necessary condition for postCond to be invariant (left of pair) also returns necessary conditions for the safety question to be true at all with those assumptions (right of pair) In either case, all formulas in the returned list must be valid
- Definition Classes
- MathematicaInvGenTool → InvGenTool
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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def
init(): Boolean
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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def
invgen(ode: ODESystem, assumptions: Seq[Formula], postCond: Formula): Seq[Either[Seq[(Formula, String)], Seq[(Formula, String)]]]
Returns a continuous invariant for a safety problem sent to the tool.
Returns a continuous invariant for a safety problem sent to the tool.
- ode
The differential equation for which to generate a continuous invariants.
- assumptions
Assumptions on the initial state of the ODE.
- postCond
What to prove from the invariants.
- returns
A sequence of continuous invariants, each to be proved with a diffcut chain (left=invariant, right=candidate).
- Definition Classes
- MathematicaInvGenTool → InvGenTool
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final
def
isInstanceOf[T0]: Boolean
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- Any
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val
k2m: K2MConverter[Expression]
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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val
link: MathematicaLink
- Definition Classes
- MathematicaInvGenTool → BaseKeYmaeraMathematicaBridge
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lazy val
logger: Logger
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- protected
- Definition Classes
- LazyLogging → LoggerHolder
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final
val
loggerName: String
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- protected
- Definition Classes
- LoggerHolder
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def
lzzCheck(ode: ODESystem, inv: Formula): Boolean
Fast check whether or not
invis worth proving to be an invariant ofode.Fast check whether or not
invis worth proving to be an invariant ofode.- Definition Classes
- MathematicaInvGenTool → InvGenTool
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val
m2k: M2KConverter[Expression]
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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var
mathematicaExecutor: ToolExecutor
- Attributes
- protected
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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def
memoryConstrained(cmd: String): String
- Attributes
- protected
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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def
memoryConstrained(cmd: MExpr): MExpr
- Attributes
- protected
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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var
memoryLimit: Long
Memory limit for Mathematica requests in MB, set to MEMORY_LIMIT_OFF to disable.
Memory limit for Mathematica requests in MB, set to MEMORY_LIMIT_OFF to disable.
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
problemClassification(ode: ODESystem, assumptions: Seq[Formula], postCond: Formula): (Int, String, Map[String, Map[String, String]])
Returns dimension and classification of the problem defined by
odewith assumptionsassumptionsand postconditionpostCond.Returns dimension and classification of the problem defined by
odewith assumptionsassumptionsand postconditionpostCond.- ode
The differential equation system including evolution domain constraint.
- assumptions
Assumptions on the initial state.
- postCond
Postcondition
- returns
The dimension and classification of the problem.
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def
refuteODE(ode: ODESystem, assumptions: Seq[Formula], postCond: Formula): Option[Map[NamedSymbol, Expression]]
Finds counterexamples to an ODE safety conjecture.
Finds counterexamples to an ODE safety conjecture.
- Definition Classes
- MathematicaInvGenTool → InvGenTool
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def
run(cmd: MExpr): (String, Expression)
Runs Mathematica command
cmd, with Mathematica exception checking.Runs Mathematica command
cmd, with Mathematica exception checking.- Definition Classes
- BaseKeYmaeraMathematicaBridge → KeYmaeraMathematicaBridge
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def
runUnchecked(cmd: String): (String, Expression)
Runs Mathematica command
cmdwithout safeguarding by exception checking for Mathematica results.Runs Mathematica command
cmdwithout safeguarding by exception checking for Mathematica results.- Definition Classes
- BaseKeYmaeraMathematicaBridge → KeYmaeraMathematicaBridge
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def
shutdown(): Unit
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
timeConstrained(cmd: String): String
- Attributes
- protected
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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def
timeConstrained(cmd: MExpr): MExpr
- Attributes
- protected
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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var
timeout: Int
Timeout for Mathematica requests in seconds, set to TIMEOUT_OFF to disable.
Timeout for Mathematica requests in seconds, set to TIMEOUT_OFF to disable.
- Definition Classes
- BaseKeYmaeraMathematicaBridge
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def
toString(): String
- Definition Classes
- AnyRef → Any
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final
def
wait(): Unit
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- @throws( ... )
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final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
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final
def
wait(arg0: Long): Unit
- Definition Classes
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- @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