object DependencyAnalysis
Dependency Analysis For a set of output variables, determine the set of input variables across a hybrid program that could affect their values
- Alphabetic
- By Inheritance
- DependencyAnalysis
- AnyRef
- Any
- Hide All
- Show All
- Public
- All
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def analyseModal(p: Program, s: Sequent, ignoreTest: Boolean = false): Map[BaseVariable, (Set[BaseVariable], Set[Function])]
- def analyseModalVars(p: Program, ls: Set[BaseVariable], ignoreTest: Boolean = false): Map[BaseVariable, (Set[BaseVariable], Set[Function])]
-
def
analyseODE(p: ODESystem, s: Set[BaseVariable], ignoreTest: Boolean, checkLinear: Boolean = true): (Set[BaseVariable], Set[Function])
Dependency Analysis for ODEs
Dependency Analysis for ODEs
- p
the ODE system to analyse
- s
the set of variables concerned with
- ignoreTest
whether to check the domain constraint
- checkLinear
whether to account for linearity
- returns
the sets of variables and function symbols that s depends on in the ODE
- def analyseODEVars(p: ODESystem, ignoreTest: Boolean = false, checkLinear: Boolean = true): Map[BaseVariable, Set[BaseVariable]]
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
- def bfsSCC[A](adjlist: Map[A, Set[A]]): List[List[Set[A]]]
- def breadthClosure[A](cur: Set[A], adjlist: Map[A, Set[A]]): (List[Set[A]], Set[A])
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
- def collapseODE(p: DifferentialProgram): Map[BaseVariable, Term]
- def degVar(t: Term, vs: Set[BaseVariable]): Int
- def dependencies(p: Program, s: Set[BaseVariable], ignoreTest: Boolean = false): (Set[BaseVariable], Set[Function])
- def dfs[A](adjlist: Map[A, Set[A]]): List[A]
- def dfs_aux[A](v: A, adjlist: Map[A, Set[A]], done: Set[A]): (List[A], Set[A])
-
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 freeVars(s: Sequent): Set[BaseVariable]
- def freeVars(t: Expression): Set[BaseVariable]
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- def inducedOrd(edges: Map[BaseVariable, Set[BaseVariable]]): Ordering[Variable]
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isLinearODE(vs: Map[BaseVariable, Term]): Boolean
-
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 odevars(p: ODESystem): Set[BaseVariable]
- def scc[A](adjlist: Map[A, Set[A]]): List[Set[A]]
- def signature(t: Expression): Set[Function]
- def stripImp(f: Formula): Option[Program]
- def stripSeq(s: Sequent): Option[Program]
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
toString(): String
- Definition Classes
- AnyRef → Any
- def transClose[A](adjlist: Map[A, Set[A]]): Map[A, Set[A]]
- def transitiveAnalysis(vs: Map[BaseVariable, (Set[BaseVariable], Set[Function])], s: Set[BaseVariable], f: Set[Function]): (Set[BaseVariable], Set[Function])
- def transpose[A](adjlist: Map[A, Set[A]]): Map[A, Set[A]]
- def varSetToBaseVarSet(s: Set[Variable]): Set[BaseVariable]
-
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
,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