Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
5 changed files
with
217 additions
and
26 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,166 @@ | ||
| import leon.lang._ | ||
| import leon.lang.synthesis._ | ||
|
|
||
| object HOFDecomp1 { | ||
| abstract class Tree[T] { | ||
| def map[B](f: T => B): Tree[B] = { | ||
| this match { | ||
| case Node(v, l, r) => Node(f(v), l.map(f), r.map(f)) | ||
| case Leaf() => Leaf() | ||
| } | ||
| } | ||
|
|
||
| def fold[B](z: B)(f: (T, B, B) => B): B = { | ||
| this match { | ||
| case Node(v, l, r) => f(v, l.fold(z)(f), r.fold(z)(f)) | ||
| case Leaf() => z | ||
| } | ||
| } | ||
| } | ||
|
|
||
| case class Node[T](v: T, l: Tree[T], r: Tree[T]) extends Tree[T] | ||
| case class Leaf[T]() extends Tree[T] | ||
|
|
||
| abstract class List[T] { | ||
| def filter(f: T => Boolean): List[T] = { | ||
| this match { | ||
| case Cons(h, t) => | ||
| if (f(h)) { | ||
| Cons(h, t.filter(f)) | ||
| } else { | ||
| t.filter(f) | ||
| } | ||
|
|
||
| case Nil() => Nil() | ||
| } | ||
| } | ||
|
|
||
| def map[B](f: T => B): List[B] = { | ||
| this match { | ||
| case Cons(h, t) => Cons(f(h), t.map(f)) | ||
| case Nil() => Nil[B]() | ||
| } | ||
| } | ||
|
|
||
| def foldr[B](z: B)(f: (B, T) => B): B = { | ||
| this match { | ||
| case Cons(h, t) => f(t.foldr(z)(f), h) | ||
| case Nil() => z | ||
| } | ||
| } | ||
|
|
||
| def foldl[B](z: B)(f: (B, T) => B): B = { | ||
| this match { | ||
| case Cons(h, t) => t.foldl(f(z, h))(f) | ||
| case Nil() => z | ||
| } | ||
| } | ||
|
|
||
| def ++(l: List[T]): List[T] = { | ||
| this match { | ||
| case Cons(h, t) => Cons(h, t ++ l) | ||
| case Nil() => l | ||
| } | ||
| } | ||
| } | ||
|
|
||
| case class Cons[T](h: T, t: List[T]) extends List[T] | ||
| case class Nil[T]() extends List[T] | ||
|
|
||
| def countLeaves(in: Tree[Int]): Int = { | ||
| // in.fold(1){ (v,l,r) => l+r } | ||
| ???[Int] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Leaf() => 1 | ||
| case Node(13, Leaf(), Leaf()) => 2 | ||
| case Node(13, Leaf(), Node(13, Leaf(), Leaf())) => 3 | ||
| case Node(13, Node(13, Leaf(), Leaf()), Node(13, Leaf(), Node(13, Leaf(), Leaf()))) => 5 | ||
| } | ||
| } | ||
|
|
||
| def countNodes(in: Tree[Int]): Int = { | ||
| // in.fold(0){ (v,l,r) => 1+l+r } | ||
| ???[Int] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Leaf() => 0 | ||
| case Node(13, Leaf(), Leaf()) => 1 | ||
| case Node(13, Leaf(), Node(13, Leaf(), Leaf())) => 2 | ||
| case Node(13, Node(13, Leaf(), Leaf()), Node(13, Leaf(), Node(13, Leaf(), Leaf()))) => 4 | ||
| } | ||
| } | ||
|
|
||
| def flatten(in: Tree[Int]): List[Int] = { | ||
| // in.fold(Nil) { (v, l, r) => Cons(v, Nil) ++ l ++ r } | ||
| ???[List[Int]] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Leaf() => Nil[Int]() | ||
| case Node(13, Leaf(), Leaf()) => Cons(13, Nil()) | ||
| case Node(12, Leaf(), Node(13, Leaf(), Leaf())) => Cons(12, Cons(13, Nil())) | ||
| case Node(12, Node(13, Leaf(), Leaf()), Leaf()) => Cons(12, Cons(13, Nil())) | ||
| case Node(12, Node(13, Leaf(), Leaf()), Node(12, Leaf(), Node(13, Leaf(), Leaf()))) => Cons(12, Cons(13, Cons(12, Cons(13, Nil())))) | ||
| } | ||
| } | ||
|
|
||
| def max(a: Int, b: Int): Int = { | ||
| if (a > b) a else b | ||
| } | ||
|
|
||
| def height(in: Tree[Int]): Int = { | ||
| // in.fold(0) { (v, l, r) => 1+max(l, r) } | ||
| ???[Int] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Leaf() => 0 | ||
| case Node(13, Leaf(), Leaf()) => 1 | ||
| case Node(13, Leaf(), Node(13, Leaf(), Leaf())) => 2 | ||
| case Node(13, Node(13, Leaf(), Leaf()), Leaf()) => 2 | ||
| case Node(13, Node(13, Leaf(), Leaf()), Node(13, Leaf(), Node(13, Leaf(), Leaf()))) => 3 | ||
| } | ||
| } | ||
|
|
||
| def incr(in: Tree[Int]): Tree[Int] = { | ||
| // in.map{ _ + 1 } | ||
| ???[Tree[Int]] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Leaf() => Leaf() | ||
| case Node(13, Leaf(), Leaf()) => Node(14, Leaf(), Leaf()) | ||
| case Node(-4, Leaf(), Node(13, Leaf(), Leaf())) => Node(-3, Leaf(), Node(14, Leaf(), Leaf())) | ||
| case Node(10, Node(11, Leaf(), Leaf()), Leaf()) => Node(11, Node(12, Leaf(), Leaf()), Leaf()) | ||
| } | ||
| } | ||
|
|
||
| def maxt(in: Tree[Int]): Int = { | ||
| require(in != Leaf[Int]()) | ||
| // in.fold(in.v) { (v, l, r) => max(v, max(l, r)) } | ||
| ???[Int] | ||
| } ensuring { | ||
| out => (in, out) passes { | ||
| case Node(13, Leaf(), Leaf()) => 13 | ||
| case Node(11, Leaf(), Leaf()) => 11 | ||
| case Node(-4, Leaf(), Node(13, Leaf(), Leaf())) => 13 | ||
| case Node(16, Leaf(), Node(11, Leaf(), Leaf())) => 16 | ||
| case Node(9, Node(11, Leaf(), Leaf()), Leaf()) => 11 | ||
| case Node(12, Node(13, Leaf(), Leaf()), Leaf()) => 13 | ||
| case Node(12, Node(13, Leaf(), Leaf()), Node(11, Leaf(), Leaf())) => 13 | ||
| } | ||
| } | ||
|
|
||
| def member(in: Tree[Int], v: Int): Boolean = { | ||
| // in.fold(false) { (v2, l, r) => v == v2 || l || r } | ||
| ???[Boolean] | ||
| } ensuring { | ||
| out => ((in, v), out) passes { | ||
| case (Leaf(), 10) => false | ||
| case (Node(10, Leaf(), Leaf()), 10) => true | ||
| case (Node(11, Leaf(), Leaf()), 10) => false | ||
| case (Node(11, Node(10, Leaf(), Leaf()), Leaf()), 10) => true | ||
| case (Node(11, Leaf(), Node(10, Leaf(), Leaf())), 10) => true | ||
| case (Node(11, Node(12, Leaf(), Leaf()), Leaf()), 10) => false | ||
| case (Node(11, Leaf(), Node(12, Leaf(), Leaf())), 10) => false | ||
| } | ||
| } | ||
| } |