trait ProofTreeNode extends AnyRef
A Proof Tree Node represents the central element of managing a (possibly large compound) inference during proof search in a ProofTree. Unlike the stateless edu.cmu.cs.ls.keymaerax.core.Provable representation of the prover kernel, proof trees provide navigation and tactic scheduling infrastructure.
Beyond providing proof tree navigation information, this type manages the interface to the kernel's provable. Proof tree nodes consist of a local provable that created this proof node, and which can later be stitched together after completing the entire subproof. The provable function can later perform the computation required to staple the proof together as far as the children have completed it.
The proof treee node also provides infrastructure for letting tactics run to expand this proof tree node.
- See also
ProvableSig
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Abstract Value Members
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abstract
def
children: List[ProofTreeNode]
The node's direct children.
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abstract
def
goal: Option[Sequent]
The node's goal, None if closed.
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abstract
def
goalIdx: Int
The index of the goal (subgoal in local provable) that this node targets.
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abstract
val
id: ProofTreeNodeId
The node ID.
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abstract
def
label: Option[BelleLabel]
The node label.
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abstract
def
localProvable: ProvableSig
The local provable, whose subgoals will be filled in by the node's children.
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abstract
def
maker: Option[String]
The tactic (serialized BelleExpr) that produced this node from its parent.
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abstract
def
makerShortName: Option[String]
The tactic short name.
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abstract
def
numSubgoals: Int
The number of subgoals in the local provable (fast, doesn't actually load the provable).
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abstract
def
parent: Option[ProofTreeNode]
The node's parent, None if root.
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abstract
val
proof: ProofTree
The proof that this proof node is a part of.
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abstract
def
pruneBelow(): Unit
Deletes this node with the entire subtree underneath.
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abstract
def
runTactic(userId: String, interpreter: (List[IOListener]) ⇒ Interpreter, tactic: BelleExpr, shortName: String, executor: BellerophonTacticExecutor = ..., wait: Boolean = false): String
Runs a tactic on this node.
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abstract
def
stepTactic(userId: String, interpreter: Interpreter, tactic: BelleExpr, executor: BellerophonTacticExecutor = ..., wait: Boolean = false): String
Runs a tactic step-by-step, starting on this node.
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abstract
def
tacticInputSuggestions(pos: Position): Map[ArgInfo, Expression]
Returns suggestions for tactic argument inputs, argument info according to UIIndex and DerivationInfo.
Concrete 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
- Definition Classes
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-
def
allAncestors: List[ProofTreeNode]
All direct and indirect ancestors of this node.
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def
allDescendants: List[ProofTreeNode]
All direct and indirect descendants of this node.
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def
applicableTacticsAt(pos: Position, pos2: Option[Position] = None): List[(DerivationInfo, Option[DerivationInfo])]
Returns a list of tactics that are applicable at the specified position in this node's goal.
Returns a list of tactics that are applicable at the specified position in this node's goal. Each entry is the typical form of the tactic and an optional more convenient variant of the tactic.
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final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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final
def
conclusion: Sequent
The tree node's conclusion (might be subject to other nodes being proved).
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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final
def
isInstanceOf[T0]: Boolean
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final
def
isProved: Boolean
Indicates whether or not the proof from this node downwards is done (potentially expensive).
Indicates whether or not the proof from this node downwards is done (potentially expensive).
- See also
ProvableSig.isProved
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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final
def
provable: ProvableSig
Compute the overall provable with the sub-proofs already filled in for the local subgoals (potentially expensive) from children.
Compute the overall provable with the sub-proofs already filled in for the local subgoals (potentially expensive) from children.
- See also
-
def
substs: List[SubstitutionPair]
Uniform substitutions applied at this node.
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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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
- 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