object SimplifierV2
Created by yongkiat on 9/29/16.
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!=(arg0: Any): Boolean
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def
##(): Int
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final
def
==(arg0: Any): Boolean
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- lazy val Fand: ProvableSig
- lazy val Fequiv: ProvableSig
- lazy val Fimply: ProvableSig
- lazy val For: ProvableSig
- lazy val Tand: ProvableSig
- lazy val Tequiv: ProvableSig
- lazy val Timply: ProvableSig
- lazy val Tor: ProvableSig
- def addContext(f: Formula, ctx: IndexedSeq[Formula]): (IndexedSeq[Formula], BelleExpr)
- lazy val andF: ProvableSig
- lazy val andT: ProvableSig
- lazy val arithProps: List[(Term, ProvableSig)]
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asInstanceOf[T0]: T0
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clone(): AnyRef
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- @native() @throws( ... )
- def closeHeuristics(ctx: IndexedSeq[Formula], f: Formula, flip: Boolean = true): Option[ProvableSig]
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final
def
eq(arg0: AnyRef): Boolean
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- lazy val eqGtFalse: ProvableSig
- lazy val eqLtFalse: ProvableSig
- lazy val eqNeqFalse: ProvableSig
- lazy val equalReflex: ProvableSig
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def
equalityRewrites(t: Term, ctx: IndexedSeq[Formula]): ProvableSig
Takes a term t, with an equality context ctx and returns ctx |- t = t' using all equalities of the shape t = n:Number This is probably hopelessly slow...
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def
equals(arg0: Any): Boolean
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- lazy val equivF: ProvableSig
- lazy val equivT: ProvableSig
- lazy val existsFalse: ProvableSig
- lazy val existsTrue: ProvableSig
- lazy val falseReflex: ProvableSig
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def
finalize(): Unit
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- @throws( classOf[java.lang.Throwable] )
- def flattenPlus(t: Term): (Term, BigDecimal)
- def flattenTimes(t: Term): (Term, BigDecimal)
- def flip[A1, A2, B](f: (A1, A2) ⇒ B): (A2, A1) ⇒ B
- lazy val forallFalse: ProvableSig
- lazy val forallTrue: ProvableSig
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def
formulaSimp(f: Formula, ctx: IndexedSeq[Formula] = IndexedSeq()): (Formula, ProvableSig)
Recursive formula simplification under a context using chase, proving ctx |- f <-> f' The recursion always occurs left-to-right
Recursive formula simplification under a context using chase, proving ctx |- f <-> f' The recursion always occurs left-to-right
- f
formula to simplify
- ctx
context in which to simplify
- returns
f',pr where pr proves the equivalence
- lazy val fullSimpTac: DependentTactic
- lazy val geEqTrue: ProvableSig
- lazy val geGtTrue: ProvableSig
- lazy val geLtFalse: ProvableSig
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final
def
getClass(): Class[_]
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- @native()
- lazy val greaterequalReflex: ProvableSig
- def groundTermEval(t: Term): Option[(Term, ProvableSig)]
- lazy val gtEqFalse: ProvableSig
- lazy val gtLeFalse: ProvableSig
- lazy val gtLtFalse: ProvableSig
- lazy val gtNotReflex: ProvableSig
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def
hashCode(): Int
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- lazy val implyF: ProvableSig
- lazy val implyT: ProvableSig
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final
def
isInstanceOf[T0]: Boolean
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- def isNop(p: Program): Boolean
- lazy val leEqTrue: ProvableSig
- lazy val leGtFalse: ProvableSig
- lazy val leLtTrue: ProvableSig
- lazy val lessequalReflex: ProvableSig
- lazy val ltEqFalse: ProvableSig
- lazy val ltGeFalse: ProvableSig
- lazy val ltGtFalse: ProvableSig
- lazy val ltNotReflex: ProvableSig
- def mksubst(s: TactixLibrary.Subst): TactixLibrary.Subst
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final
def
ne(arg0: AnyRef): Boolean
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- lazy val neEqFalse: ProvableSig
- lazy val neGtTrue: ProvableSig
- lazy val neLtTrue: ProvableSig
- lazy val neqNotReflex: ProvableSig
- lazy val neqSym: ProvableSig
- lazy val notF: ProvableSig
- lazy val notT: ProvableSig
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
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- lazy val orF: ProvableSig
- lazy val orT: ProvableSig
- def qeHeuristics(eq: ProvableSig): Option[ProvableSig]
- def reassoc(t: Term): ProvableSig
- def rewriteLoopAux(f: Formula, targets: List[Variable]): (Formula, ProvableSig)
- def rewriteProgramAux(p: Program, targets: List[Variable], rewrites: Map[Variable, Term] = Map()): (Program, Map[Variable, Term])
- def rsimpTac(ipos: IndexedSeq[Integer]): DependentPositionTactic
- lazy val safeFullSimpTac: DependentPositionTactic
- def search(ctx: IndexedSeq[Formula], f: Formula, g: Formula, h: Formula, lem: ProvableSig): Option[ProvableSig]
- lazy val simpTac: DependentPositionTactic
- def splitEquiv(pr: ProvableSig): (ProvableSig, ProvableSig)
- def stripNoOp(p: Program): Program
- lazy val swapImply: ProvableSig
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final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
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def
termSimp(t: Term): (Term, ProvableSig)
Recursive term simplification using chase, proving |- t = t'
Recursive term simplification using chase, proving |- t = t'
- t
The term to be simplifed
- def termSimpWithRewrite(t: Term, ctx: IndexedSeq[Formula]): (Term, ProvableSig)
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def
toString(): String
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- lazy val trueReflex: ProvableSig
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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
,Program
Sequent
- Sequents of formulasProvable
- Proof certificates transformed by rules/axiomsRule
- Proof rules as well asUSubstOne
for (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.kyx
filesDLParser
- Combinator parser reading concrete KeYmaera X syntaxDLArchiveParser
- Combinator parser reading KeYmaera X model and proof archive.kyx
filesedu.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-help
to 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