object KeYmaeraX
Command-line interface launcher for KeYmaera X, the aXiomatic Tactical Theorem Prover for Hybrid Systems and Hybrid Games.
- edu.cmu.cs.ls.keymaerax.core
- KeYmaera X kernel, proof certificates, main data structures
- edu.cmu.cs.ls.keymaerax.btactics
- Tactic language library
- edu.cmu.cs.ls.keymaerax.bellerophon
- Bellerophon tactic language and tactic interpreter
- See also
Andre Platzer. A complete uniform substitution calculus for differential dynamic logic. Journal of Automated Reasoning, 59(2), pp. 219-266, 2017.
Andre Platzer. A uniform substitution calculus for differential dynamic logic. In Amy P. Felty and Aart Middeldorp, editors, International Conference on Automated Deduction, CADE'15, Berlin, Germany, Proceedings, LNCS. Springer, 2015. arXiv 1503.01981
Andre Platzer. Logical Foundations of Cyber-Physical Systems. Springer, 2018.
Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Volp and Andre 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, LNCS. Springer, 2015.
Andre Platzer. Differential game logic. ACM Trans. Comput. Log. 17(1), 2015. arXiv 1408.1980
Andre Platzer. Logics of dynamical systems. ACM/IEEE Symposium on Logic in Computer Science, LICS 2012, June 25–28, 2012, Dubrovnik, Croatia, pages 13-24. IEEE 2012
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Type Members
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class
KeYmaeraXSecurityManager extends SecurityManager
Implements the security policy for the KeYmaera X web server.
Implements the security policy for the KeYmaera X web server.
Preferably we would heavily restrict uses of reflection (to prevent, for example, creating fake Provables), but we know of no way to do so except relying on extremely fragile methods such as crawling the call stack. The same goes for restricting read access to files.
Instead we settle for preventing people from installing less-restrictive security managers and restricting all writes to be inside the .keymaerax directory.
Value Members
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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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- var LAUNCH: Boolean
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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- protected[java.lang]
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- @native() @throws( ... )
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def
convertTactics(options: OptionMap, usage: String): Unit
Executes all entries in
options('in)
to convert their tactics intooptions('conversion)
format.Executes all entries in
options('in)
to convert their tactics intooptions('conversion)
format. Prints the result tooptions('out)
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final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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- protected[java.lang]
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- @throws( classOf[java.lang.Throwable] )
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final
def
getClass(): Class[_]
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- @native()
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def
hashCode(): Int
- Definition Classes
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- Annotations
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def
help: String
KeYmaera X -help string.
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
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def
launchUI(args: Array[String]): Unit
Launch the web user interface
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def
main(args: Array[String]): Unit
main function to start KeYmaera X from command line.
main function to start KeYmaera X from command line. Other entry points exist but this one is best for command line interfaces.
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def
modelplex(options: OptionMap): Unit
ModelPlex monitor synthesis for the given input files
ModelPlex monitor synthesis for the given input files
KeYmaeraXPrettyPrinter(ModelPlex(vars)(KeYmaeraXProblemParser(input))
- options
in describes input file name, vars describes the list of variables, out describes the output file name.
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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def
nextOption(map: OptionMap, list: List[String]): OptionMap
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- @tailrec()
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final
def
notify(): Unit
- Definition Classes
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final
def
notifyAll(): Unit
- Definition Classes
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- Annotations
- @native()
- def printNode(node: Sequent): Unit
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def
printOpenGoals(node: ProvableSig): Unit
Print brief information about all open goals in the proof tree under node
- def repl(options: OptionMap): Unit
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def
stats: String
Statistics about size of prover kernel.
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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val
usage: String
Usage -help information.
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final
def
wait(): Unit
- Definition Classes
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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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object
Modes
Names of actions that full KeYmaera X supports.
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
,Program
Sequent
- Sequents of formulasProvable
- Proof certificates transformed by rules/axiomsRule
- Proof rules as well asUSubstOne
for (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.kyx
filesDLParser
- Combinator parser reading concrete KeYmaera X syntaxDLArchiveParser
- Combinator parser reading KeYmaera X model and proof archive.kyx
filesedu.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-help
to 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