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test(bst): add BST as an example (#320)
* test(bst): add BST as an example This adds binary search trees as an example from my internship's staging repository. It adds a bunch of unit tests for them. Signed-off-by: Ryan Lahfa <[email protected]> * Regenerate the Lean files * Fix a typing issue in InterpreterBorrows.convert_value_to_abstractions The type of the sub-values in the loans converted to abstractions was incorrect. * Update the BST example --------- Signed-off-by: Ryan Lahfa <[email protected]> Co-authored-by: Ryan Lahfa <[email protected]> Co-authored-by: Son HO <[email protected]>
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-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS | ||
-- [bst]: function definitions | ||
import Base | ||
import Bst.Types | ||
open Primitives | ||
set_option linter.dupNamespace false | ||
set_option linter.hashCommand false | ||
set_option linter.unusedVariables false | ||
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namespace bst | ||
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/- [bst::{bst::TreeSet<T>}::new]: | ||
Source: 'src/bst.rs', lines 28:4-30:5 -/ | ||
def TreeSet.new {T : Type} (OrdInst : Ord T) : Result (TreeSet T) := | ||
Result.ok { root := none } | ||
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/- [bst::{bst::TreeSet<T>}::find]: loop 0: | ||
Source: 'src/bst.rs', lines 35:8-44:5 -/ | ||
divergent def TreeSet.find_loop | ||
{T : Type} (OrdInst : Ord T) (value : T) (current_tree : Option (Node T)) : | ||
Result Bool | ||
:= | ||
match current_tree with | ||
| none => Result.ok false | ||
| some current_node => | ||
do | ||
let o ← OrdInst.cmp current_node.value value | ||
match o with | ||
| Ordering.Less => TreeSet.find_loop OrdInst value current_node.right | ||
| Ordering.Equal => Result.ok true | ||
| Ordering.Greater => TreeSet.find_loop OrdInst value current_node.left | ||
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/- [bst::{bst::TreeSet<T>}::find]: | ||
Source: 'src/bst.rs', lines 32:4-44:5 -/ | ||
def TreeSet.find | ||
{T : Type} (OrdInst : Ord T) (self : TreeSet T) (value : T) : Result Bool := | ||
TreeSet.find_loop OrdInst value self.root | ||
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/- [bst::{bst::TreeSet<T>}::insert]: loop 0: | ||
Source: 'src/bst.rs', lines 48:8-63:5 -/ | ||
divergent def TreeSet.insert_loop | ||
{T : Type} (OrdInst : Ord T) (value : T) (current_tree : Option (Node T)) : | ||
Result (Bool × (Option (Node T))) | ||
:= | ||
match current_tree with | ||
| none => let n := Node.mk value none none | ||
Result.ok (true, some n) | ||
| some current_node => | ||
do | ||
let o ← OrdInst.cmp current_node.value value | ||
match o with | ||
| Ordering.Less => | ||
do | ||
let (b, current_tree1) ← | ||
TreeSet.insert_loop OrdInst value current_node.right | ||
Result.ok (b, some (Node.mk current_node.value current_node.left | ||
current_tree1)) | ||
| Ordering.Equal => Result.ok (false, some current_node) | ||
| Ordering.Greater => | ||
do | ||
let (b, current_tree1) ← | ||
TreeSet.insert_loop OrdInst value current_node.left | ||
Result.ok (b, some (Node.mk current_node.value current_tree1 | ||
current_node.right)) | ||
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/- [bst::{bst::TreeSet<T>}::insert]: | ||
Source: 'src/bst.rs', lines 45:4-63:5 -/ | ||
def TreeSet.insert | ||
{T : Type} (OrdInst : Ord T) (self : TreeSet T) (value : T) : | ||
Result (Bool × (TreeSet T)) | ||
:= | ||
do | ||
let (b, ts) ← TreeSet.insert_loop OrdInst value self.root | ||
Result.ok (b, { root := ts }) | ||
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end bst |
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-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS | ||
-- [bst]: type definitions | ||
import Base | ||
open Primitives | ||
set_option linter.dupNamespace false | ||
set_option linter.hashCommand false | ||
set_option linter.unusedVariables false | ||
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namespace bst | ||
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/- [bst::Ordering] | ||
Source: 'src/bst.rs', lines 5:0-9:1 -/ | ||
inductive Ordering := | ||
| Less : Ordering | ||
| Equal : Ordering | ||
| Greater : Ordering | ||
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/- Trait declaration: [bst::Ord] | ||
Source: 'src/bst.rs', lines 11:0-13:1 -/ | ||
structure Ord (Self : Type) where | ||
cmp : Self → Self → Result Ordering | ||
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/- [bst::Node] | ||
Source: 'src/bst.rs', lines 15:0-19:1 -/ | ||
inductive Node (T : Type) := | ||
| mk : T → Option (Node T) → Option (Node T) → Node T | ||
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@[reducible] | ||
def Node.value {T : Type} (x : Node T) := | ||
match x with | Node.mk x1 _ _ => x1 | ||
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@[reducible] | ||
def Node.left {T : Type} (x : Node T) := | ||
match x with | Node.mk _ x1 _ => x1 | ||
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@[reducible] | ||
def Node.right {T : Type} (x : Node T) := | ||
match x with | Node.mk _ _ x1 => x1 | ||
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@[simp] | ||
theorem Node.value._simpLemma_ {T : Type} (value : T) (left : Option (Node T)) | ||
(right : Option (Node T)) : (Node.mk value left right).value = value := | ||
by rfl | ||
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@[simp] | ||
theorem Node.left._simpLemma_ {T : Type} (value : T) (left : Option (Node T)) | ||
(right : Option (Node T)) : (Node.mk value left right).left = left := by rfl | ||
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@[simp] | ||
theorem Node.right._simpLemma_ {T : Type} (value : T) (left : Option (Node T)) | ||
(right : Option (Node T)) : (Node.mk value left right).right = right := | ||
by rfl | ||
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/- [bst::TreeSet] | ||
Source: 'src/bst.rs', lines 23:0-25:1 -/ | ||
structure TreeSet (T : Type) where | ||
root : Option (Node T) | ||
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end bst |
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[package] | ||
name = "bst" | ||
version = "0.1.0" | ||
edition = "2021" | ||
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[lib] | ||
name = "bst" | ||
path = "src/bst.rs" |
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.PHONY: all | ||
all: tests | ||
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.PHONY: test | ||
test: | ||
cargo test | ||
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.PHONY: clean | ||
clean: | ||
cargo clean |
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[!lean] skip | ||
[lean] aeneas-args=-split-files -no-gen-lib-entry |
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[toolchain] | ||
channel = "nightly-2023-06-02" | ||
components = [ "rustc-dev", "llvm-tools-preview" ] |
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//! Adapted from https://github.com/RaitoBezarius/avl-verification | ||
#![feature(register_tool)] | ||
#![register_tool(aeneas)] | ||
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pub enum Ordering { | ||
Less, | ||
Equal, | ||
Greater, | ||
} | ||
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trait Ord { | ||
fn cmp(&self, other: &Self) -> Ordering; | ||
} | ||
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struct Node<T> { | ||
value: T, | ||
left: Tree<T>, | ||
right: Tree<T>, | ||
} | ||
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type Tree<T> = Option<Box<Node<T>>>; | ||
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struct TreeSet<T> { | ||
root: Tree<T>, | ||
} | ||
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impl<T: Ord> TreeSet<T> { | ||
pub fn new() -> Self { | ||
Self { root: None } | ||
} | ||
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pub fn find(&self, value: T) -> bool { | ||
let mut current_tree = &self.root; | ||
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while let Some(current_node) = current_tree { | ||
match current_node.value.cmp(&value) { | ||
Ordering::Less => current_tree = ¤t_node.right, | ||
Ordering::Equal => return true, | ||
Ordering::Greater => current_tree = ¤t_node.left, | ||
} | ||
} | ||
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false | ||
} | ||
pub fn insert(&mut self, value: T) -> bool { | ||
let mut current_tree = &mut self.root; | ||
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while let Some(current_node) = current_tree { | ||
match current_node.value.cmp(&value) { | ||
Ordering::Less => current_tree = &mut current_node.right, | ||
Ordering::Equal => return false, | ||
Ordering::Greater => current_tree = &mut current_node.left, | ||
} | ||
} | ||
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*current_tree = Some(Box::new(Node { | ||
value, | ||
left: None, | ||
right: None, | ||
})); | ||
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true | ||
} | ||
} | ||
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#[cfg(test)] | ||
mod tests { | ||
use super::*; | ||
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impl Ord for i32 { | ||
fn cmp(&self, other: &Self) -> Ordering { | ||
if *self < *other { | ||
Ordering::Less | ||
} else if *self == *other { | ||
Ordering::Equal | ||
} else { | ||
Ordering::Greater | ||
} | ||
} | ||
} | ||
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trait Bounded { | ||
type Value; | ||
fn max_value() -> Self::Value; | ||
fn min_value() -> Self::Value; | ||
} | ||
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impl Bounded for i32 { | ||
type Value = i32; | ||
fn min_value() -> i32 { | ||
i32::MIN | ||
} | ||
fn max_value() -> i32 { | ||
i32::MAX | ||
} | ||
} | ||
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impl<T: Bounded<Value = T> + Ord + Copy> Node<T> { | ||
fn check_bst_inv(&self, min: T, max: T) -> bool { | ||
matches!(self.value.cmp(&min), Ordering::Greater) | ||
&& matches!(self.value.cmp(&max), Ordering::Less) | ||
&& self | ||
.left | ||
.as_ref() | ||
.map_or(true, |left| left.check_bst_inv(min, self.value)) | ||
&& self | ||
.right | ||
.as_ref() | ||
.map_or(true, |right| right.check_bst_inv(self.value, max)) | ||
} | ||
} | ||
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impl<T: Bounded<Value = T> + Ord + Copy> TreeSet<T> { | ||
fn check_bst_inv(&self) -> bool { | ||
self.root | ||
.as_ref() | ||
.map_or(true, |r| r.check_bst_inv(T::min_value(), T::max_value())) | ||
} | ||
} | ||
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#[test] | ||
fn unbalanced_right() { | ||
let mut t: TreeSet<i32> = TreeSet::new(); | ||
for i in 0..100 { | ||
t.insert(i); | ||
t.check_bst_inv(); | ||
} | ||
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assert!( | ||
t.find(50), | ||
"Unexpectedly failed to find the 50 value in the tree" | ||
); | ||
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assert!(!t.find(-50), "Unexpectedly find the -50 value in the tree"); | ||
} | ||
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#[test] | ||
fn unbalanced_left() { | ||
let mut t: TreeSet<i32> = TreeSet::new(); | ||
for i in -100..0 { | ||
t.insert(i); | ||
t.check_bst_inv(); | ||
} | ||
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assert!( | ||
t.find(-50), | ||
"Unexpectedly failed to find the -50 value in the tree" | ||
); | ||
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assert!(!t.find(50), "Unexpectedly find the 50 value in the tree"); | ||
} | ||
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#[test] | ||
fn right_left_unbalanced() { | ||
let mut t: TreeSet<i32> = TreeSet::new(); | ||
for i in 0..100 { | ||
t.insert(i); | ||
t.check_bst_inv(); | ||
} | ||
for i in -100..0 { | ||
t.insert(i); | ||
t.check_bst_inv(); | ||
} | ||
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assert!( | ||
t.find(-50), | ||
"Unexpectedly failed to find the -50 value in the tree" | ||
); | ||
assert!( | ||
t.find(50), | ||
"Unexpectedly failed to find the 50 value in the tree" | ||
); | ||
} | ||
} |