case class Snapshot(m: Map[String, Subscript]) extends Product with Serializable
- Alphabetic
- By Inheritance
- Snapshot
- Serializable
- Serializable
- Product
- Equals
- AnyRef
- Any
- Hide All
- Show All
- Public
- All
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
++(other: Snapshot): Snapshot
Take the union of two snapshots.
Take the union of two snapshots. When both snapshots mention the same variable, the greater subscript is kept.
-
def
<=(other: Snapshot): Boolean
- returns
whether every key has same or higher subscript in other snapshot
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
addPattern(pat: Expression): Snapshot
Augment snapshot with all variables freshly bound in the pattern.
-
def
addSet(vars: Set[Variable]): Snapshot
Add a set of bound variables to a snapshot.
Add a set of bound variables to a snapshot. This (or increment) should be called wherever variables are assigned. If the variables have been bound before, their subscripts are increased according to SSA.
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
val
asMap: Map[String, Subscript]
Entry (x -> None) means we saw base variable "x", whereas no "x" entry means we never saw any version of "x".
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
- def contains(s: String): Boolean
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def filter(p: ((String, Subscript)) ⇒ Boolean): Snapshot
-
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
def
get(s: String): Subscript
Look up "x" and don't distinguish the "never saw x" case.
Look up "x" and don't distinguish the "never saw x" case. This can be more convenient, and is adequate so long as we wish for SSA numbering to start at x_0 rather than x.
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
getOpt(s: String): Option[Subscript]
Look up "x" but distinguish the "never saw x" case (None) vs "only saw x with no index" case (Some(None))
-
def
increment(x: Variable): (Variable, Snapshot)
Add a variable to a snapshot.
Add a variable to a snapshot. This (or addSet) should be called wherever a single variable is assigned. If x is already in the snapshot, its subscript is incremented.
- returns
the variable with its new index and the updated snapshot.
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def keySet: Set[String]
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
def
revisit(x: Variable): Snapshot
Input should be in SSA form already.
Input should be in SSA form already. Call this on every variable to reconstruct Snapshot from output of SSA.
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
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