case class DbProofTree(db: DBAbstraction, proofId: String) extends ProofTreeBase with Product with Serializable
Builds proof trees from database-recorded step executions, starting at the specified root step (None: proof root).
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Instance Constructors
- new DbProofTree(db: DBAbstraction, proofId: String)
Value Members
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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==(arg0: Any): Boolean
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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- val db: DBAbstraction
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def
done: Boolean
Indicates whether or not the proof might be closed.
Indicates whether or not the proof might be closed.
- Definition Classes
- DbProofTree → ProofTree
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final
def
eq(arg0: AnyRef): Boolean
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def
finalize(): Unit
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final
def
getClass(): Class[_]
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def
info: ProofPOJO
The proof info.
The proof info.
- Definition Classes
- DbProofTree → ProofTree
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
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def
isProved: Boolean
Verify that the proof is closed by constructing a proved provable.
Verify that the proof is closed by constructing a proved provable.
- Definition Classes
- ProofTree
- See also
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def
load(withProvables: Boolean = false): ProofTree
Returns a loaded proof tree to avoid ripple loading.
Returns a loaded proof tree to avoid ripple loading.
- Definition Classes
- DbProofTree → ProofTree
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def
locate(id: ProofTreeNodeId): Option[ProofTreeNode]
Locates a node in the proof tree relative to its parent.
Locates a node in the proof tree relative to its parent.
- Definition Classes
- DbProofTree → ProofTree
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def
locate(id: String): Option[ProofTreeNode]
Locates a node in the proof tree by its ID (string representation).
Locates a node in the proof tree by its ID (string representation).
- Definition Classes
- ProofTree
- See also
noteIdFromString(String)
locate(ProofTreeNodeId)
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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def
nodeIdFromString(id: String): Option[ProofTreeNodeId]
Converts a string representation to a node ID.
Converts a string representation to a node ID.
- Definition Classes
- DbProofTree → ProofTree
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def
nodes: List[ProofTreeNode]
All proof nodes, in order of step execution.
All proof nodes, in order of step execution.
- Definition Classes
- DbProofTree → ProofTree
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
openGoals: List[ProofTreeNode]
The proof's open goals
The proof's open goals
- Definition Classes
- DbProofTree → ProofTree
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val
proofId: String
- Definition Classes
- DbProofTree → ProofTreeBase
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def
proofSubsts: List[SubstitutionPair]
Substitutions from proof steps.
Substitutions from proof steps.
- Definition Classes
- DbProofTree → ProofTree
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def
root: ProofTreeNode
Locates the tree root.
Locates the tree root.
- Definition Classes
- DbProofTree → ProofTree
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def
substs: List[SubstitutionPair]
The known substitutions.
The known substitutions.
- Definition Classes
- DbProofTree → ProofTree
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
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def
tactic: BelleExpr
The global tactic that reproducse this whole proof tree from the conjecture at the root (very expensive)
The global tactic that reproducse this whole proof tree from the conjecture at the root (very expensive)
- Definition Classes
- DbProofTree → ProofTree
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def
tacticString(converter: TraceToTacticConverter): (String, Map[Location, ProofTreeNode])
The tactic to produce this tree from its root conclusion.
The tactic to produce this tree from its root conclusion.
- Definition Classes
- DbProofTree → ProofTree
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def
toString(): String
- Definition Classes
- ProofTree → AnyRef → Any
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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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