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* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
// RUN: %verify "%s"
/**
* Implements mutable maps in Dafny to guard against inconsistent specifications.
* Only exists to verify feasability; not meant for actual usage.
*/
module {:options "-functionSyntax:4"} MutableMapDafny {
/**
* NOTE: Only here because of #2500; once resolved import "MutableMapTrait.dfy".
*/
trait {:termination false} MutableMapTrait<K(==),V(==)> {
function content(): map<K, V>
reads this
method Put(k: K, v: V)
modifies this
ensures this.content() == old(this.content())[k := v]
ensures k in old(this.content()).Keys ==> this.content().Values + {old(this.content())[k]} == old(this.content()).Values + {v}
ensures k !in old(this.content()).Keys ==> this.content().Values == old(this.content()).Values + {v}
function Keys(): (keys: set<K>)
reads this
ensures keys == this.content().Keys
predicate HasKey(k: K)
reads this
ensures HasKey(k) <==> k in this.content().Keys
function Values(): (values: set<V>)
reads this
ensures values == this.content().Values
function Items(): (items: set<(K,V)>)
reads this
ensures items == this.content().Items
ensures items == set k | k in this.content().Keys :: (k, this.content()[k])
function Select(k: K): (v: V)
reads this
requires this.HasKey(k)
ensures v in this.content().Values
ensures this.content()[k] == v
method Remove(k: K)
modifies this
ensures this.content() == old(this.content()) - {k}
ensures k in old(this.content()).Keys ==> this.content().Values + {old(this.content())[k]} == old(this.content()).Values
function Size(): (size: int)
reads this
ensures size == |this.content().Items|
}
class MutableMapDafny<K(==),V(==)> extends MutableMapTrait<K,V> {
var m: map<K,V>
function content(): map<K, V>
reads this
{
m
}
constructor ()
ensures this.content() == map[]
{
m := map[];
}
method Put(k: K, v: V)
modifies this
ensures this.content() == old(this.content())[k := v]
ensures k in old(this.content()).Keys ==> this.content().Values + {old(this.content())[k]} == old(this.content()).Values + {v}
ensures k !in old(this.content()).Keys ==> this.content().Values == old(this.content()).Values + {v}
{
m := m[k := v];
if k in old(m).Keys {
forall v' | v' in old(m).Values + {v} ensures v' in m.Values + {old(m)[k]} {
if v' == v || v' == old(m)[k] {
assert m[k] == v;
} else {
assert m.Keys == old(m).Keys + {k};
}
}
}
if k !in old(m).Keys {
forall v' | v' in old(m).Values + {v} ensures v' in m.Values {
if v' == v {
assert m[k] == v;
assert m[k] == v';
assert v' in m.Values;
} else {
assert m.Keys == old(m).Keys + {k};
}
}
}
}
function Keys(): (keys: set<K>)
reads this
ensures keys == this.content().Keys
{
m.Keys
}
predicate HasKey(k: K)
reads this
ensures HasKey(k) <==> k in this.content().Keys
{
k in m.Keys
}
function Values(): (values: set<V>)
reads this
ensures values == this.content().Values
{
m.Values
}
function Items(): (items: set<(K,V)>)
reads this
ensures items == this.content().Items
ensures items == set k | k in this.content().Keys :: (k, this.content()[k])
{
var items := set k | k in m.Keys :: (k, m[k]);
assert items == m.Items by {
forall k | k in m.Keys ensures (k, m[k]) in m.Items {
assert (k, m[k]) in m.Items;
}
assert items <= m.Items;
forall x | x in m.Items ensures x in items {
assert (x.0, m[x.0]) in items;
}
assert m.Items <= items;
}
items
}
function Select(k: K): (v: V)
reads this
requires this.HasKey(k)
ensures v in this.content().Values
ensures this.content()[k] == v
{
m[k]
}
method Remove(k: K)
modifies this
ensures this.content() == old(this.content()) - {k}
ensures k in old(this.content()).Keys ==> this.content().Values + {old(this.content())[k]} == old(this.content()).Values
{
m := map k' | k' in m.Keys && k' != k :: m[k'];
if k in old(m).Keys {
var v := old(m)[k];
forall v' | v' in old(m).Values ensures v' in m.Values + {v} {
if v' == v {
} else {
assert exists k' | k' in m.Keys :: old(m)[k'] == v';
}
}
}
}
function Size(): (size: int)
reads this
ensures size == |this.content().Items|
{
|m|
}
}
} |