final class Z3 extends Tool with QETacticTool with SimplificationTool with ToolOperationManagement
Z3 quantifier elimination tool for tactics.
- See also
edu.cmu.cs.ls.keymaerax.btactics.Z3ToolProvider to obtain instances of Z3 that are properly initialized and installed/updated.
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- Z3
- ToolOperationManagement
- SimplificationTool
- ToolInterface
- QETacticTool
- Tool
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Instance Constructors
- new Z3()
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
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final
def
asInstanceOf[T0]: T0
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def
cancel(): Boolean
Cancels the current tool operation and returns true on success, false otherwise.
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def
clone(): AnyRef
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final
def
eq(arg0: AnyRef): Boolean
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equals(arg0: Any): Boolean
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def
finalize(): Unit
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def
getAvailableWorkers: Int
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- Z3 → ToolOperationManagement
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final
def
getClass(): Class[_]
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def
getOperationTimeout: Int
Returns the timeout duration.
Returns the timeout duration.
- Definition Classes
- Z3 → ToolOperationManagement
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def
hashCode(): Int
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def
init(config: Map[String, String]): Unit
Initializes the tool with tool-specific configuration parameters.
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def
isInitialized: Boolean
Checks whether this tool has been initialized already.
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final
def
isInstanceOf[T0]: Boolean
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val
name: String
Returns the name of the tool.
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final
def
ne(arg0: AnyRef): Boolean
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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def
qe(g: Goal, continueOnFalse: Boolean): (Goal, Formula)
Returns the result of the first-to-finish (sub-)goal in
g(result of the first-to-finish sub-goal of OneOf, else result of Atom or AllOf).Returns the result of the first-to-finish (sub-)goal in
g(result of the first-to-finish sub-goal of OneOf, else result of Atom or AllOf). WhencontinueOnFalseis set, continues trying other options in case a finished option's result is false.- Definition Classes
- Z3 → QETacticTool
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def
qe(formula: Formula): Lemma
Returns a lemma witnessing equivalence between a quantifier-free formula and the specified formula.
Returns a lemma witnessing equivalence between a quantifier-free formula and the specified formula.
- formula
The formula whose quantifier-free equivalent is sought.
- returns
A lemma showing equivalence between
formulaand a quantifier-free formula, with tool evidence.
- Definition Classes
- Z3 → QETacticTool
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def
restart(): Unit
Check whether the managed tool is still alive and restart it if need be.
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def
setOperationTimeout(timeout: Int): Unit
Sets a maximum duration of this tool's operations (e.g., QE).
Sets a maximum duration of this tool's operations (e.g., QE).
- Definition Classes
- Z3 → ToolOperationManagement
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def
shutdown(): Unit
Shutdown the tool
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def
simplify(expr: Term, assumptions: List[Formula]): Term
<invalid inheritdoc annotation>
<invalid inheritdoc annotation>
- Definition Classes
- Z3 → SimplificationTool
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def
simplify(expr: Formula, assumptions: List[Formula]): Formula
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- Definition Classes
- Z3 → SimplificationTool
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def
simplify(expr: Expression, assumptions: List[Formula]): Expression
Simplifies the given expression
expr, under the list of assumptions.Simplifies the given expression
expr, under the list of assumptions.- expr
The formula or term to simplify.
- assumptions
The list of logical formulas whose conjunction is assumed to hold during the simplification. The assumptions are allowed to contain additional conjunctions.
- returns
A simplified version of
expr.
- Definition Classes
- Z3 → SimplificationTool
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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
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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