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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 cli

Definition Classes: keymaerax

object KeYmaeraXProofChecker extends Serializable

Proof checker command-line interface implementation.

Definition Classes: cli

ProofStatistics

edu.cmu.cs.ls.keymaerax.cli.KeYmaeraXProofChecker

ProofStatistics

Companion object ProofStatistics

case class ProofStatistics(name: String, tacticName: String, status: String, witness: Option[ProvableSig], timeout: Long, duration: Long, qeDuration: Long, rcfDuration: Long, proofSteps: Int, tacticSize: Int) extends Product with Serializable

Collects proof statistics.

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Serializable, Serializable, Product, Equals, AnyRef, Any

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new ProofStatistics(name: String, tacticName: String, status: String, witness: Option[ProvableSig], timeout: Long, duration: Long, qeDuration: Long, rcfDuration: Long, proofSteps: Int, tacticSize: Int)

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
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final def ##(): Int

Definition Classes
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final def ==(arg0: Any): Boolean

Definition Classes
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final def asInstanceOf[T0]: T0

Definition Classes
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def clone(): AnyRef

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protected[java.lang]
Definition Classes
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@native() @throws( ... )
val duration: Long
final def eq(arg0: AnyRef): Boolean

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def finalize(): Unit

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protected[java.lang]
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@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

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@native()
final def isInstanceOf[T0]: Boolean

Definition Classes
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val name: String
final def ne(arg0: AnyRef): Boolean

Definition Classes
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final def notify(): Unit

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

Definition Classes
AnyRef
Annotations
@native()
val proofSteps: Int
val qeDuration: Long
val rcfDuration: Long
val status: String
def summary: String
Prints a statistics summary string.
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
val tacticName: String
val tacticSize: Int
val timeout: Long
def toCsv: String
Prints in CSV format.
def toString(): String
Short single-line summary.
Short single-line summary.

Definition Classes
ProofStatistics → AnyRef → Any
final def wait(): Unit

Definition Classes
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@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
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@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
AnyRef
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@native() @throws( ... )
val witness: Option[ProvableSig]

Packages

KeYmaera X: An aXiomatic Tactical Theorem Prover

Package Structure

Entry Points

References

ProofStatistics

Companion object ProofStatistics

case class ProofStatistics(name: String, tacticName: String, status: String, witness: Option[ProvableSig], timeout: Long, duration: Long, qeDuration: Long, rcfDuration: Long, proofSteps: Int, tacticSize: Int) extends Product with Serializable

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Packages

KeYmaera X: An aXiomatic Tactical Theorem Prover

Package Structure

Entry Points

References

ProofStatistics 

Companion object ProofStatistics

case class ProofStatistics(name: String, tacticName: String, status: String, witness: Option[ProvableSig], timeout: Long, duration: Long, qeDuration: Long, rcfDuration: Long, proofSteps: Int, tacticSize: Int) extends Product with Serializable

Instance Constructors

Value Members

Inherited from Serializable

Inherited from Serializable

Inherited from Product

Inherited from Equals

Inherited from AnyRef

Inherited from Any

Ungrouped

ProofStatistics