package axioms
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Type Members
- trait Axiom extends AnyRef
- trait AxiomFactory extends AnyRef
- case class DomainClosureAxioms(types: List[TBase] = Nil) extends AxiomFactory with Product with Serializable
- type FormulaSelector = (Sequent[(String, Formula)]) => ThrowsError[Formula]
- case class GeneralInductionAxioms(vsel: VariableSelector = allVariablesSelector( _ )( _ ), fsel: FormulaSelector = firstFormulaSelector( _ )) extends AxiomFactory with Product with Serializable
- case class IndependentInductionAxioms(vsel: VariableSelector = allVariablesSelector( _ )( _ ), fsel: FormulaSelector = firstFormulaSelector( _ )) extends AxiomFactory with Product with Serializable
Generates independent induction axioms.
Generates independent induction axioms.
- vsel
The variables for which induction axioms are generated.
- fsel
The formula of a sequent for which axioms are generated.
- case class SequentialInductionAxioms(vsel: VariableSelector = allVariablesSelector( _ )( _ ), fsel: FormulaSelector = firstFormulaSelector( _ )) extends AxiomFactory with Product with Serializable
Generates sequential induction axioms.
Generates sequential induction axioms.
- vsel
The variables for which an induction axiom is generated.
- fsel
The formula of a sequent for which induction axioms are generated.
- case class StandardInductionAxioms(variableSelector: VariableSelector = allVariablesSelector( _ )( _ ), formulaSelector: FormulaSelector = firstFormulaSelector( _ )) extends AxiomFactory with Product with Serializable
- case class TipDomainClosureAxioms(types: List[InductiveType] = Nil) extends AxiomFactory with Product with Serializable
- case class UserDefinedInductionAxioms(axioms: List[String]) extends AxiomFactory with Product with Serializable
- type VariableSelector = (Formula, Context) => List[Var]
Value Members
- def allVariablesSelector(formula: Formula)(implicit ctx: Context): List[Var]
Selects variables of inductive types.
Selects variables of inductive types.
- formula
The formula from which the variables are selected.
- ctx
The context which fixes constants, types, etc.
- returns
A list of all free inductive variables and all universally quantified inductive variables that are bound in the universal quantifier prefix of the given formula.
- def firstFormulaSelector(sequent: Sequent[(String, Formula)]): ThrowsError[Formula]
Selects the first formula in the succedent of a sequent.
Selects the first formula in the succedent of a sequent.
- sequent
The sequent from which the formula is selected.
- returns
The formula at the first position of the sequent's succedent.
- def inductionAxiom(inductionVariable: Var, formula: Formula, constructors: Seq[Const])(implicit ctx: Context): Formula
Constructs a standard induction axiom.
Constructs a standard induction axiom.
- inductionVariable
The variable on which the induction is carried out.
- formula
The formula for which the induction axiom is to be generated
- constructors
The constructors of the induction variable.
- ctx
The context which fixes constants, types, etc.
- returns
An induction axiom representing an induction on the specified variable and formula with one induction case for each of the constructors.
- def inductionCase(inductionVariable: Var, formula: Formula, constructor: Const): Formula
Constructs a formula representing an inductive case.
Constructs a formula representing an inductive case.
- inductionVariable
The variable on which the induction is carried out.
- formula
The induction formula.
- constructor
The constructor associated with the induction case.
- returns
A formula representing the inductive case for the given constructor for an induction on the specified formula and variable.
- def inductionCaseConclusion(freeVariable: Var, constructor: Const, formula: Expr): (List[Var], List[Var], Expr)
- def inductionCaseConclusion(freeVariable: Var, constructor: Const, formula: Formula): (List[Var], List[Var], Formula)
Constructs the conclusion of an inductive case.
Constructs the conclusion of an inductive case.
- freeVariable
The free variable which is to be replaced by the given constructor.
- constructor
The constructor to be inserted at all occurrences of the specified freeVariable.
- formula
The formula in which the substitution is to be carried out.
- returns
A three tuple whose first component contains a list of all newly introduced free variables that are of the same type as the type to which the constructor belongs, the second component contains a list of all newly introduced variables that are of a different type than the constructor's type, the third component contains the result of the substitution.
- object StandardInductionAxioms extends Serializable
- case object UntrustedFunctionalInductionAxioms extends AxiomFactory with Product with Serializable
This is the API documentation for GAPT.
The main package is gapt.