trait ProofTree extends AnyRef
The central proof tree data structure managing the proof search, consisting of a set of ProofTreeNode. Unlike the stateless edu.cmu.cs.ls.keymaerax.core.Provable representation of the prover kernel, proof trees provide navigation and tactic scheduling infrastructure.
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ProvableSig
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abstract
def
done: Boolean
Lightweight check indicating, if true, that the proof database representation thinks it might be closed (not verified by core yet).
Lightweight check indicating, if true, that the proof database representation thinks it might be closed (not verified by core yet).
- See also
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abstract
def
info: ProofPOJO
The proof info with meta information about this proof, e.g., its name.
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abstract
def
load(withProvables: Boolean = false): ProofTree
Prefetch all nodes in a proof tree from the database.
Prefetch all nodes in a proof tree from the database. Does not include provables by default (expensive to load). The resulting ProofTree is functionally equivalent to this tree but provides fast access.
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abstract
def
locate(id: ProofTreeNodeId): Option[ProofTreeNode]
Locates a node in the proof tree by its ID.
Locates a node in the proof tree by its ID.
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noteIdFromString(String)
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abstract
def
nodeIdFromString(id: String): Option[ProofTreeNodeId]
Converts a string representation to a node ID.
Converts a string representation to a node ID.
- See also
locate(ProofTreeNodeId)
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abstract
def
nodes: List[ProofTreeNode]
All proof nodes anywhere in the proof tree, including root, inner nodes, and leaves.
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abstract
def
openGoals: List[ProofTreeNode]
The proof's open goals, which are the leaves that are not done yet
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abstract
def
proofSubsts: List[SubstitutionPair]
Substitutions from proof steps.
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abstract
def
root: ProofTreeNode
The root node with the desired conclusion of this proof tree
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abstract
def
substs: List[SubstitutionPair]
Substitutions known from the input model.
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abstract
def
tactic: BelleExpr
The global tactic that reproducse this whole proof tree from the conjecture at the root (very expensive)
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abstract
def
tacticString(converter: TraceToTacticConverter): (String, Map[Location, ProofTreeNode])
String representation (including location to node mapping) of the global tactic that reproduces this whole proof tree from the conjecture at the root (very expensive).
String representation (including location to node mapping) of the global tactic that reproduces this whole proof tree from the conjecture at the root (very expensive). Uses
converterto turn the recorded steps into a tactic.
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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.
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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).
- See also
noteIdFromString(String)
locate(ProofTreeNodeId)
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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