object BelleInterpreter extends Interpreter
Provides the interpreter for running tactics.
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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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def
apply(expr: BelleExpr, v: BelleValue): BelleValue
Returns the result of applying tactic
exprto the proof valuev(usually a provable).Returns the result of applying tactic
exprto the proof valuev(usually a provable).- Definition Classes
- BelleInterpreter → Interpreter
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def
applySubDerivation(original: ProvableSig, n: Int, subderivation: ProvableSig, subst: USubst): (Boolean, ProvableSig)
Replaces the nth subgoal of
originalwith the remaining subgoals ofsubderivation.Replaces the nth subgoal of
originalwith the remaining subgoals ofsubderivation.- original
A Provable whose nth subgoal is equal to the conclusion of
subderivation(modulo substitution).- n
The numerical index of the subgoal of original to rewrite (Seqs are zero-indexed)
- subderivation
The provable to replace the original subgoal.
- returns
A tuple of: * Indicator whether
originalandsubderivationwere merged. * A new provable that is identical tooriginal, except that the nth subgoal is replaced with the remaining subgoals ofsubderivation.
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final
def
asInstanceOf[T0]: T0
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def
assertConclusionsMatchModuloConstification(parent: ProvableSig, sub: ProvableSig, subst: USubst): Unit
Assert that the conclusion of provable
submatches the conclusion of provableparenteither verbatim or modulo constification renaming that is assumed to be applied in the future.Assert that the conclusion of provable
submatches the conclusion of provableparenteither verbatim or modulo constification renaming that is assumed to be applied in the future.- Attributes
- protected
- Definition Classes
- Interpreter
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def
assertSubMatchesModuloConstification(parent: ProvableSig, sub: ProvableSig, n: Int, subst: USubst): Unit
Assert that the conclusion of provable
submatches the subgoalnof provableparenteither verbatim or modulo constification renaming that is assumed to be applied in the future.Assert that the conclusion of provable
submatches the subgoalnof provableparenteither verbatim or modulo constification renaming that is assumed to be applied in the future. Constification renaming requiresparentto have exactly one single subgoal.- Attributes
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- Interpreter
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def
clone(): AnyRef
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def
collectSubst(goal: Sequent, have: Sequent, haveIsProved: Boolean, defs: Declaration): USubst
Collects substitutions (of
defs) that are needed to makehavefitgoal.Collects substitutions (of
defs) that are needed to makehavefitgoal.- Attributes
- protected
- Definition Classes
- Interpreter
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def
collectSubst(goal: ProvableSig, i: Int, sub: ProvableSig): USubst
Collects substitutions (of
defs) that are needed to makesubfit thei-th subgoal ofgoal.Collects substitutions (of
defs) that are needed to makesubfit thei-th subgoal ofgoal.- Attributes
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- Definition Classes
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
exhaustiveSubst(p: ProvableSig, s: USubst): ProvableSig
Applies substitutions
sto provablepexhaustively.Applies substitutions
sto provablepexhaustively.- Attributes
- protected
- Definition Classes
- Interpreter
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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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def
interpreter: Interpreter
Returns the interpreter.
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def
isDead: Boolean
Indicates whether the interpreter is still operational.
Indicates whether the interpreter is still operational. A killed interpreter refuses to run tactics.
- Definition Classes
- BelleInterpreter → Interpreter
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
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def
kill(): Unit
Stops the interpreter and kills all its tactic executions.
Stops the interpreter and kills all its tactic executions.
- Definition Classes
- BelleInterpreter → Interpreter
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def
listeners: Seq[IOListener]
Registered listeners.
Registered listeners.
- Definition Classes
- BelleInterpreter → Interpreter
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
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lazy val
nilNames: List[String]
Names of nil tactics.
Names of nil tactics.
- Attributes
- protected
- Definition Classes
- Interpreter
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final
def
notify(): Unit
- Definition Classes
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- Annotations
- @native()
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final
def
notifyAll(): Unit
- Definition Classes
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- Annotations
- @native()
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def
progress(prev: BelleValue, curr: BelleValue): Boolean
Compares provables ignoring labels.
Compares provables ignoring labels.
- Attributes
- protected
- Definition Classes
- Interpreter
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def
setInterpreter(i: Interpreter): Unit
Sets a new interpreter (kills the old one).
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def
start(): Unit
Starts the interpreter.
Starts the interpreter.
- Definition Classes
- BelleInterpreter → Interpreter
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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