object friedman
- Source
- transformation.scala
- Alphabetic
- By Inheritance
- friedman
- 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
- final def ==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
- def apply(proof: NDProof, a: Formula): NDProof
Applies the Friedman proof transformation for a formula A to a given intuitionistic natural deduction proof.
Applies the Friedman proof transformation for a formula A to a given intuitionistic natural deduction proof.
The conclusion of the resulting proof is the Friedman translation fr applied to the original conclusion.
- proof
A proof in ND for a sequent Γ :- A, without applications of the excluded middle rule
- a
The formula that we instantiate the Friedman translation with
- returns
A proof in ND for the sequent fr(Γ, a) :- fr(A, a)
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- def clone(): AnyRef
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.CloneNotSupportedException]) @native()
- final def eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
- def equals(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef → Any
- def finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.Throwable])
- def fr(formula: Expr, a: Formula): Formula
Applies the Friedman translation fr for a given formula a to a formula.
Applies the Friedman translation fr for a given formula a to a formula.
This function replaces every atom occurring in the formula by a disjunction formed by the atom and the formula a. The case of the negation is explained by treating ¬A as an abbreviation for A→⊥ The Bottom and Top cases are explained by observing that ⊥∨A and ⊤∨A or equivalent to A and ⊤ respectively.
- formula
input formula for the function fr
- a
formula that is disjunctively added to the atoms of the input formula
- returns
result of applying fr for a to the input formula
- def frAux(formula: Formula, a: Formula): NDProof
Creates a proof of the sequent
a :- fr(formula, a)
. - final def getClass(): Class[_ <: AnyRef]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- def hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- 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()
- final def synchronized[T0](arg0: => T0): T0
- Definition Classes
- AnyRef
- def toString(): String
- Definition Classes
- AnyRef → Any
- final def wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException])
- final def wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws(classOf[java.lang.InterruptedException]) @native()
This is the API documentation for GAPT.
The main package is gapt.