object BigDecimalQETool extends Tool with QETool
Proves quantifier- and variable-free arithmetic formulas by exact arithmetic evaluation using java.math.BigDecimal. Ground term evaluation for formulas with concrete number arithmetic.
- Note
Java's BigDecimal is clearer and has less indirection than Scala's BigDecimal.
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!=(arg0: Any): Boolean
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asInstanceOf[T0]: T0
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def
cancel(): Boolean
Cancels the current tool operation and returns true on success, false otherwise.
Cancels the current tool operation and returns true on success, false otherwise.
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- BigDecimalQETool → Tool
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clone(): AnyRef
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eq(arg0: AnyRef): Boolean
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equals(arg0: Any): Boolean
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def
eval(fml: Formula): Boolean
Evaluate a Formula by evaluating its terms in exact java.math.BigDecimal arithmetic.
Evaluate a Formula by evaluating its terms in exact java.math.BigDecimal arithmetic.
- returns
the truth value of the input formula or
- Exceptions thrown
[[IllegalArgumentException]]if terms cannot be evaluated in exact arithmetic or if Formula is not a Boolean combination of numeric comparisons.
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def
eval(t: Term): BigDecimal
Evaluate a Term in exact java.math.BigDecimal arithmetic.
Evaluate a Term in exact java.math.BigDecimal arithmetic.
- returns
the java.math.BigDecimal equal to the input term
- Exceptions thrown
IllegalArgumentExceptionif exact evaluation is not possible, e.g., for Variables or non-exact division- Note
We use java.math.BigDecimal instead of scala.math.BigDecimal in order to avoid one layer of indirection and therefore reduce the trusted code base. Moreover java.math.BigDecimal is more explicit about rounding modes and precision.
- See also
the documentation of java.math.BigDecimal, in particular the paragraph mentioning java.math.MathContext.UNLIMITED:
- Arithmetic methods which take a java.math.MathContext.UNLIMITED or no java.math.MathContext object are exact.
- If the result of division cannot be represented exactly, an ArithmeticException is thrown.
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hashCode(): Int
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def
init(config: Map[String, String]): Unit
Initializes the tool with tool-specific configuration parameters.
Initializes the tool with tool-specific configuration parameters.
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- BigDecimalQETool → Tool
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def
isInitialized: Boolean
Checks whether this tool has been initialized already.
Checks whether this tool has been initialized already.
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- BigDecimalQETool → Tool
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name: String
Returns the name of the tool.
Returns the name of the tool.
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notifyAll(): Unit
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def
quantifierElimination(formula: Formula): Formula
Returns a quantifier-free formula that is equivalent to the specified formula.
Returns a quantifier-free formula that is equivalent to the specified formula.
- formula
The formula whose quantifier-free equivalent is sought.
- returns
An equivalent quantifier-free formula.
- Definition Classes
- BigDecimalQETool → QETool
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final
def
restart(): Unit
Check whether the managed tool is still alive and restart it if need be.
Check whether the managed tool is still alive and restart it if need be.
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- BigDecimalQETool → Tool
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final
def
shutdown(): Unit
Shutdown the tool
Shutdown the tool
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- BigDecimalQETool → Tool
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synchronized[T0](arg0: ⇒ T0): T0
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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