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Add more specs to List functions using bitvector indexing #1541

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Jul 22, 2024
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Add more specs to List functions using bitvector indexing #1541

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17 changes: 14 additions & 3 deletions frontends/library/stainless/collection/List.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -67,6 +67,7 @@ sealed abstract class List[T] {
@isabelle.fullBody
def apply(index: BigInt): T = {
require(0 <= index && index < size)
decreases(index)
if (index == BigInt(0)) {
head
} else {
Expand All @@ -76,6 +77,7 @@ sealed abstract class List[T] {

def iapply(index: Int): T = {
require(0 <= index && index < isize)
decreases(index)
if (index == 0) {
head
} else {
Expand All @@ -92,15 +94,15 @@ sealed abstract class List[T] {
case Nil() => Cons(t, this)
case Cons(x, xs) => Cons(x, xs :+ (t))
}
} ensuring(res => (res.size == size + 1) && (res.content == content ++ Set(t)) && res == this ++ Cons(t, Nil[T]()))
} ensuring(res => (res.size == size + 1) && (if (isize < Int.MaxValue) res.isize == isize + 1 else res.isize == isize) && (res.content == content ++ Set(t)) && res == this ++ Cons(t, Nil[T]()))

@isabelle.function(term = "List.rev")
def reverse: List[T] = {
this match {
case Nil() => this
case Cons(x,xs) => xs.reverse :+ x
}
} ensuring (res => (res.size == size) && (res.content == content))
} ensuring (res => (res.size == size) && (res.isize == isize) && (res.content == content))

def take(i: BigInt): List[T] = { (this, i) match {
case (Nil(), _) => Nil[T]()
Expand Down Expand Up @@ -412,7 +414,7 @@ sealed abstract class List[T] {
case Cons(x, tail) =>
Cons[T](x, tail.iupdated(i - 1, y))
}
}
}.ensuring(res => res.isize == this.isize && res.iapply(i) == y)

private def insertAtImpl(pos: BigInt, l: List[T]): List[T] = {
require(0 <= pos && pos <= size)
Expand Down Expand Up @@ -672,11 +674,20 @@ object List {

@library
def fill[T](n: BigInt)(x: T) : List[T] = {
decreases(if (n <= BigInt(0)) BigInt(0) else n)
if (n <= 0) Nil[T]()
else Cons[T](x, fill[T](n-1)(x))
} ensuring(res => (res.content == (if (n <= BigInt(0)) Set.empty[T] else Set(x))) &&
res.size == (if (n <= BigInt(0)) BigInt(0) else n))

@library
def ifill[T](n: Int)(x: T) : List[T] = {
decreases(if (n <= 0) 0 else n)
if (n <= 0) Nil[T]()
else Cons[T](x, ifill[T](n - 1)(x))
} ensuring(res => (res.content == (if (n <= 0) Set.empty[T] else Set(x))) &&
res.isize == (if (n <= 0) 0 else n))

/* Range from start (inclusive) to until (exclusive) */
@library
def range(start: BigInt, until: BigInt): List[BigInt] = {
Expand Down
11 changes: 11 additions & 0 deletions frontends/library/stainless/collection/ListSpecs.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -21,6 +21,17 @@ object ListSpecs {
((l :+ t).apply(i) == (if (i < l.size) l(i) else t))
}.holds

def isnocIndex[T](l: List[T], t: T, i: Int): Boolean = {
require(l.isize < Int.MaxValue)
require(0 <= i && i < l.isize + 1)
decreases(l)
l match {
case Nil() => true
case Cons(x, xs) => if (i > 0) isnocIndex[T](xs, t, i - 1) else true
}
((l :+ t).iapply(i) == (if (i < l.isize) l.iapply(i) else t))
}.holds

@isabelle.lemma(about = "stainless.collection.List.apply")
def consIndex[T](h: T, t: List[T], i: BigInt): Boolean = {
require(0 <= i && i < t.size + 1)
Expand Down