case class DifferentialProgramConst(name: String, space: Space = AnyArg) extends AtomicDifferentialProgram with SpaceDependent with NamedSymbol with Product with Serializable
Uninterpreted differential program constant, limited to the given state space. The semantics of arity 0 DifferentialProgramConst symbol is looked up by the state, with the additional promise that taboos are neither free nor bound, so the run does not depend on the value of taboos nor does the value of taboos change when space=Except(taboos).
- space
The part of the state space that the interpretation/replacement of this symbol is limited to have free or bound.
AnyArg isthe default allowing full read/write access to the state.Taboo(x)meansxcan neither be free nor bound.
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- DifferentialProgramConst
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- AtomicDifferentialProgram
- DifferentialProgram
- AtomicProgram
- Atomic
- Program
- Expression
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Instance Constructors
-
new
DifferentialProgramConst(name: String, space: Space = AnyArg)
- space
The part of the state space that the interpretation/replacement of this symbol is limited to have free or bound.
AnyArg isthe default allowing full read/write access to the state.Taboo(x)meansxcan neither be free nor bound.
Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
def
<(that: NamedSymbol): Boolean
- Definition Classes
- Ordered
-
def
<=(that: NamedSymbol): Boolean
- Definition Classes
- Ordered
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
>(that: NamedSymbol): Boolean
- Definition Classes
- Ordered
-
def
>=(that: NamedSymbol): Boolean
- Definition Classes
- Ordered
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
asString: String
Get name with index of this NamedSymbol.
Get name with index of this NamedSymbol.
- Definition Classes
- DifferentialProgramConst → NamedSymbol
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
def
compare(other: NamedSymbol): Int
Compare named symbols lexicographically: by name, index, category.
Compare named symbols lexicographically: by name, index, category.
- returns
0 for equal symbols <0 if this is lexicographically before
other>0 if this is lexicographically afterother
- Definition Classes
- NamedSymbol → Ordered
- Note
not used in the core, so not soundness-critical, but breaks tactics if wrong.
-
def
compareTo(that: NamedSymbol): Int
- Definition Classes
- Ordered → Comparable
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
finalize(): scala.Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
def
fullString: String
Full string with names and full types
Full string with names and full types
- Definition Classes
- NamedSymbol
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
final
val
index: Option[Int]
- Definition Classes
- SpaceDependent
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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final
val
kind: Kind
What kind of an expression this is, e.g., TermKind, FormulaKind, ProgramKind.
What kind of an expression this is, e.g., TermKind, FormulaKind, ProgramKind.
- Definition Classes
- DifferentialProgram → Program → Expression
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val
name: String
- Definition Classes
- DifferentialProgramConst → NamedSymbol
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final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
final
def
notify(): scala.Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
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final
def
notifyAll(): scala.Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
def
prettyString: String
Pretty-printed string representing this expression
Pretty-printed string representing this expression
- Definition Classes
- Expression
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final
val
sort: Sort
The sort of this expression, e.g., Real, Bool.
- Definition Classes
- Program → Expression
-
val
space: Space
The space that this expression lives on.
The space that this expression lives on.
- Definition Classes
- DifferentialProgramConst → SpaceDependent
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
toString(): String
- Definition Classes
- NamedSymbol → Expression → AnyRef → Any
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final
def
wait(): scala.Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): scala.Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): scala.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