:test whether bsimp(bders(r, s)) == ders_simp(r,s)
This does not hold. As illustrated by the output of the example where string is abaa and regex is (a* + ab)*
this property still holds when s = aba
but after the derivative of the last character a, the result is negative.
However this seems easily fixable as the difference is relatively small, it might be possible to find where the difference happens
and by taking that difference into accound we have some function f s.t.
f(bsimp(r,s)) = ders_simp(r,s)
and mkeps(f(r)) = mkeps(r)
This will complete the correctness proof.
Even if finding such f is hard, it would still provide insights for the real difference between simp(der(simp(der(simp(der...... and simp(ders
import Element.elem
abstract class Element{
def contents: Array[String]
def height: Int = contents.length
def width: Int = contents(0).length
def above(that: Element): Element = {
//new ArrayElement(this.contents ++ that.contents)
val this1 = this widen that.width
val that1 = that widen this.width
elem(this1.contents ++ that1.contents)
}
def left_align(that: Element): Element = {
if (this.width == that.width){
this above that
}
else if (this.width < that.width) {
(this beside elem(' ', that.width - this.width, this.height)) above that
}
else {
this above (that beside elem(' ', this.width - that.width, that.height))
}
}
def up_align(that: Element): Element = {
if (this.height == that.height){
this beside that
}
else if (this.height < that.height) {
(this above elem(' ', this.width, that.height - this.height)) beside that
}
else {
this beside (that above elem(' ', that.width, this.height - that.height))
}
}
def beside(that: Element): Element = {
val this1 = this heighten that.height
val that1 = that heighten this.height
elem(
for ((line1, line2) <- this1.contents zip that1.contents)
yield line1 + line2)
}
def widen(w: Int): Element =
if(w <= width) this
else {
val left = Element.elem(' ', (w - width) / 2, height)
var right = Element.elem(' ', w - width - left.width, height)
left beside this beside right
}
def heighten(h: Int): Element =
if (h <= height) this
else {
val top = Element.elem(' ', width, (h - height) / 2)
val bot = Element.elem(' ', width, h - height - top.height)
top above this above bot
}
override def toString = contents mkString "\n"
}
object Element {
private class ArrayElement(
val contents: Array[String]
) extends Element
private class LineElement(s: String) extends Element {
val contents = Array(s)
override def width = s.length
override def height = 1
}
private class UniformElement(
ch: Char,
override val width: Int,
override val height: Int
) extends Element {
private val line = ch.toString * width
def contents = Array.fill(height)(line)
}
def elem(contents: Array[String]): Element =
new ArrayElement(contents)
def elem(chr: Char, width: Int, height: Int): Element =
new UniformElement(chr, width, height)
def elem(line: String): Element =
new LineElement(line)
}