object BelleParser extends TacticParser with Logging
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Type Members
- case class BelleToken(terminal: BelleTerminal, location: Location) extends BelleItem with Product with Serializable
- case class DefScope[K, V](defs: Map[K, V] = ..., parent: Option[DefScope[K, V]] = None) extends Product with Serializable
- case class ParserState(stack: Stack[BelleItem], input: TokenStream) extends Product with Serializable
- type TacticArg = Either[Any, PositionLocator]
Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- val DOUBLE_COLON: String
- val DOUBLE_QUOTE: String
- val EMPTY_ARGS: String
- val EMPTY_BRANCHES: String
- val EMPTY_TACTIC: String
- val LIST_END: String
- val NEWLINE: String
- val NIL_TACTIC: String
- val SKIP_TACTIC: String
- val SPACE: String
- val TAB: String
- val TODO_TACTIC: String
-
val
allowedUnicodeChars: Set[Char]
Non-unicode characters that are allowed in KeYmaera X input files.
Non-unicode characters that are allowed in KeYmaera X input files. Should correspond to the unicode that's printed in the web UI.
-
def
andThen[A](g: (BelleExpr) ⇒ A): (String) ⇒ A
- Definition Classes
- Function1
- Annotations
- @unspecialized()
-
def
apply(input: String, defs: Declaration): BelleExpr
Parse the input string in the concrete syntax of Bellerophon tactics.
Parse the input string in the concrete syntax of Bellerophon tactics.
- input
the string to parse as a Bellerophon tactic.
- defs
the definitions to elaborate variables/functions/predicates to their expected type.
- Definition Classes
- BelleParser → TacticParser
-
final
def
apply(input: String): BelleExpr
Parse the input string in the concrete syntax of Bellerophon tactics.
Parse the input string in the concrete syntax of Bellerophon tactics.
- input
the string to parse as a Bellerophon tactic.
- Definition Classes
- TacticParser → Function1
- Exceptions thrown
ParseException
ifinput
is not a well-formed Bellerophon tactic.
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )
-
def
compose[A](g: (A) ⇒ String): (A) ⇒ BelleExpr
- Definition Classes
- Function1
- Annotations
- @unspecialized()
-
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
val
expressionParser: Parser
The expression parser for differential dynamic logic
The expression parser for differential dynamic logic
- Definition Classes
- BelleParser → TacticParser
-
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
def
firstUnacceptableCharacter(s: String): Option[(Location, Char)]
Returns the location and value of the first non-ASCII character in a string that is not in allowedUnicodeChars
-
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
lazy val
logger: Logger
- Attributes
- protected
- Definition Classes
- LazyLogging → LoggerHolder
-
final
val
loggerName: String
- Attributes
- protected
- Definition Classes
- LoggerHolder
-
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
parseBackwardsCompatible(t: String, defs: Declaration): BelleExpr
Parses
t
backwards-compatible with definitionsdefs
expanded in tactic arguments depending on whethert
expands symbols or uses substitutions explicitly or not. -
def
parsePositionLocator(s: String, location: Location, shape: Option[Expression], sub: PosInExpr, exact: Boolean, defs: Declaration): PositionLocator
Parses a position locator string.
-
def
parsePositionLocator(s: String, location: Location, shape: Option[Expression], exact: Boolean, defs: Declaration): PositionLocator
Parses a string of the form int.int.int.int to a Bellerophon position.
Parses a string of the form int.int.int.int to a Bellerophon position. Public because this is a useful utility function.
- See also
parseArgumentToken
-
def
parseTokenStream(toks: TokenStream, tacticDefs: DefScope[String, DefTactic], g: Option[Generator[GenProduct]], defs: Declaration, expandAll: Boolean): BelleExpr
Parses the token stream
toks
.Parses the token stream
toks
. Expands tactic abbreviations according totacticDefs
, function and predicate symbols according todefs
, and passes the invariant generatorg
on to tactics requiring a generator. -
def
parseWithInvGen(s: String, g: Option[Generator[GenProduct]] = None, defs: Declaration = Declaration(Map.empty), expandAll: Boolean = false): BelleExpr
Parses the string
s
as a Bellerophon tactic.Parses the string
s
as a Bellerophon tactic. Uses optional invariant generatorg
and definitionsdefs
to expand function and predicate symbols. - def parseWithTacticDefs(s: String, defs: Map[String, BelleExpr]): BelleExpr
-
val
printer: (BelleExpr) ⇒ String
A pretty-printer that can write the output that this parser reads
A pretty-printer that can write the output that this parser reads
- Definition Classes
- BelleParser → TacticParser
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
tacticExpandsDefsExplicitly(s: String): Boolean
Detects whether a tactic string uses
expand "..."
orexpandAllDefs
. -
val
tacticParser: (String) ⇒ BelleExpr
Parse the input string in the concrete syntax as a Bellerophon tactic
Parse the input string in the concrete syntax as a Bellerophon tactic
- Definition Classes
- BelleParser → TacticParser
-
def
tacticSubstsDefsExplicitly(s: String): Boolean
Detects whether a tactic string uses
US(...)
. -
def
toString(): String
- Definition Classes
- Function1 → AnyRef → Any
-
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
,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