gapt-examples
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gapt-examples/gapt.examples/gapt.examples.sequence/UniformAssociativity3ExampleProof

UniformAssociativity3ExampleProof

gapt.examples.sequence.UniformAssociativity3ExampleProof
object UniformAssociativity3ExampleProof extends ProofSequence

Attributes

Graph
Supertypes
class Object
trait Matchable
class Any
Self type

Members list

Value members

Concrete methods

def addAllAxioms(proof: LKProof): LKProof
def apply(n: Int): LKProof
def ax2_ax(): FOLFormula
def ax2_ax(x: FOLTerm): FOLFormula
def ax2_ax(x: FOLTerm, y: FOLTerm): FOLFormula
def cs_ax(): FOLFormula
def cs_ax(x: FOLTerm): FOLFormula
def cs_ax(x: FOLTerm, y: FOLTerm): FOLFormula
def f1(sym: String, arg: FOLTerm): FOLTerm
def f2(sym: String, arg1: FOLTerm, arg2: FOLTerm): FOLTerm
def f2(arg1: FOLTerm, sym: String, arg2: FOLTerm): FOLTerm
def gen_proof_step(i: Int, n: Int): LKProof

Returns proof Pi (currently including line above and below Pi), with numerals n, i, i+1: (n + n) + i+1 = n + (n + i+1), Ax |- ... Pi (n + n) + i = n + (n + i), Ax |- ...

Returns proof Pi (currently including line above and below Pi), with numerals n, i, i+1: (n + n) + i+1 = n + (n + i+1), Ax |- ... Pi (n + n) + i = n + (n + i), Ax |- ...

Attributes

def induction_start(n: Int, p0: LKProof): LKProof

Close off proof ending in (n + n) + 0 = n + (n + 0) |- ...

Close off proof ending in (n + n) + 0 = n + (n + 0) |- ...

Attributes

def refl_ax(): FOLFormula
def refl_ax(x: FOLTerm): FOLFormula
def refl_ax(x: FOLTerm, y: FOLTerm): FOLFormula
def reflect(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

Takes a proof s2 with end-sequent of the form (x=y), ... |- ... and return one with end-sequent of the form (y=x), ... |- ...

Takes a proof s2 with end-sequent of the form (x=y), ... |- ... and return one with end-sequent of the form (y=x), ... |- ...

Attributes

def show_by_ax2(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof
def show_by_cs(x: FOLTerm, y: FOLTerm, p: LKProof): LKProof

Inherited methods

def name: String

Attributes

Inherited from:
ProofSequence

Concrete fields

val Ax1: FOLFormula
val Cs: FOLFormula
val Symm: FOLFormula
val Trans: FOLFormula
val p: String
val s: String
val x: FOLVar
val x1: FOLVar
val x2: FOLVar
val y: FOLVar
val y1: FOLVar
val y2: FOLVar
val z: FOLVar
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