creusot_std/logic/ra/
fmap.rs

1#[cfg(creusot)]
2use crate::logic::such_that;
3use crate::{
4    logic::{
5        FMap,
6        ra::{RA, UnitRA, update::LocalUpdate},
7    },
8    prelude::*,
9};
10
11impl<K, V: RA> RA for FMap<K, V> {
12    #[logic(open)]
13    fn op(self, other: Self) -> Option<Self> {
14        pearlite! {
15            if (forall<k: K> self.get(k).op(other.get(k)) != None) {
16                Some(self.total_op(other))
17            } else {
18                None
19            }
20        }
21    }
22
23    #[logic(open)]
24    #[ensures(match result {
25        Some(c) => factor.op(c) == Some(self),
26        None => forall<c: Self> factor.op(c) != Some(self),
27    })]
28    fn factor(self, factor: Self) -> Option<Self> {
29        pearlite! {
30            if (forall<k: K> factor.get(k).incl(self.get(k))) {
31                let res = self.filter_map(|(k, vo): (K, V)|
32                    match Some(vo).factor(factor.get(k)) {
33                        Some(r) => r,
34                        None => None,
35                });
36                proof_assert!(
37                    match factor.op(res) {
38                        None => false,
39                        Some(o) => o.ext_eq(self)
40                    }
41                );
42                Some(res)
43            } else {
44                None
45            }
46        }
47    }
48
49    #[logic(open, inline)]
50    #[ensures(result == (self == other))]
51    fn eq(self, other: Self) -> bool {
52        pearlite! {
53            let _ = Self::ext_eq;
54            forall<k: K> self.get(k).eq(other.get(k))
55        }
56    }
57
58    #[logic(law)]
59    #[ensures(a.op(b) == b.op(a))]
60    fn commutative(a: Self, b: Self) {
61        proof_assert!(match (a.op(b), b.op(a)) {
62            (Some(ab), Some(ba)) => ab.ext_eq(ba),
63            (None, None) => true,
64            _ => false,
65        })
66    }
67
68    #[logic]
69    #[ensures(a.op(b).and_then_logic(|ab: Self| ab.op(c)) == b.op(c).and_then_logic(|bc| a.op(bc)))]
70    fn associative(a: Self, b: Self, c: Self) {
71        match (a.op(b), b.op(c)) {
72            (Some(ab), Some(bc)) => match (ab.op(c), a.op(bc)) {
73                (Some(x), Some(y)) => proof_assert!(x.ext_eq(y)),
74                _ => (),
75            },
76            _ => (),
77        }
78    }
79
80    #[logic(open)]
81    fn core(self) -> Option<Self> {
82        Some(self.filter_map(|(_, v): (K, V)| v.core()))
83    }
84
85    #[logic]
86    #[requires(self.core() != None)]
87    #[ensures({
88        let c = self.core().unwrap_logic();
89        c.op(c) == Some(c)
90    })]
91    #[ensures(self.core().unwrap_logic().op(self) == Some(self))]
92    fn core_idemp(self) {
93        self.core_total_idemp()
94    }
95
96    #[logic]
97    #[requires(i.op(i) == Some(i))]
98    #[requires(i.op(self) == Some(self))]
99    #[ensures(match self.core() {
100        Some(c) => i.incl(c),
101        None => false,
102    })]
103    fn core_is_maximal_idemp(self, i: Self) {
104        let _ = V::core_is_maximal_idemp;
105    }
106
107    #[logic(open)]
108    #[ensures(result == (forall<x, y> self.op(x) != None ==>
109        self.op(x) == self.op(y) ==> x == y))]
110    fn cancelable(self) -> bool {
111        proof_assert!(
112            (forall<x, y> self.op(x) != None ==> self.op(x) == self.op(y) ==> x == y) ==>
113            forall<k> match self.get(k) {
114                None => true,
115                Some(v) => forall<x, y> Some(v).op(x) != None ==> Some(v).op(x) == Some(v).op(y) ==> {
116                    let fx = match x {
117                        None => FMap::empty(),
118                        Some(x) => FMap::singleton(k, x),
119                    };
120                    let fy = match y {
121                        None => FMap::empty(),
122                        Some(y) => FMap::singleton(k, y),
123                    };
124                    let opx = self.op(fx).unwrap_logic();
125                    let opy = self.op(fy).unwrap_logic();
126                    opx.ext_eq(opy) && (opx == opy ==> fx == fy)
127                }
128            }
129        );
130        proof_assert!((forall<k> self.get(k).cancelable()) ==>
131            forall<x, y> self.op(x) != None ==> self.op(x) == self.op(y) ==>
132            x.ext_eq(y)
133        );
134        pearlite! { forall<k> self.get(k).cancelable() }
135    }
136}
137
138impl<K, V: RA> UnitRA for FMap<K, V> {
139    #[logic(open)]
140    #[ensures(forall<x: Self> #[trigger(x.op(result))] x.op(result) == Some(x))]
141    fn unit() -> Self {
142        proof_assert!(forall<x: Self> x.op(Self::empty()).unwrap_logic().ext_eq(x));
143        Self::empty()
144    }
145
146    #[logic(open)]
147    #[ensures(self.core() == Some(result))]
148    fn core_total(self) -> Self {
149        self.filter_map(|(_, v): (K, V)| v.core())
150    }
151
152    #[logic]
153    #[ensures(self.core_total().op(self.core_total()) == Some(self.core_total()))]
154    #[ensures(self.core_total().op(self) == Some(self))]
155    fn core_total_idemp(self) {
156        let _ = V::core_idemp;
157        let c = self.core_total();
158        proof_assert!(c.op(c).unwrap_logic().ext_eq(c));
159        proof_assert!(c.op(self).unwrap_logic().ext_eq(self));
160    }
161}
162
163impl<K, V: RA> FMap<K, V> {
164    #[logic]
165    #[requires(forall<k: K> self.get(k).op(other.get(k)) != None)]
166    #[ensures(forall<k: K> Some(result.get(k)) == self.get(k).op(other.get(k)))]
167    pub fn total_op(self, other: Self) -> Self {
168        self.merge(other, |(x, y): (V, V)| match x.op(y) {
169            Some(r) => r,
170            _ => such_that(|_| true),
171        })
172    }
173}
174
175/// Add a key-value to an authority/fragment pair of [`FMap`]s.
176///
177/// It requires that the key is not in the map yet.
178pub struct FMapInsertLocalUpdate<K, V>(pub Snapshot<K>, pub Snapshot<V>);
179
180impl<K, V: RA> LocalUpdate<FMap<K, V>> for FMapInsertLocalUpdate<K, V> {
181    #[logic(open, inline)]
182    fn premise(self, from_auth: FMap<K, V>, _: FMap<K, V>) -> bool {
183        from_auth.get(*self.0) == None
184    }
185
186    #[logic(open, inline)]
187    fn update(self, from_auth: FMap<K, V>, from_frag: FMap<K, V>) -> (FMap<K, V>, FMap<K, V>) {
188        (from_auth.insert(*self.0, *self.1), from_frag.insert(*self.0, *self.1))
189    }
190
191    #[logic]
192    #[allow(unused)]
193    #[requires(self.premise(from_auth, from_frag))]
194    #[requires(Some(from_frag).op(frame) == Some(Some(from_auth)))]
195    #[ensures({
196        let (to_auth, to_frag) = self.update(from_auth, from_frag);
197        Some(to_frag).op(frame) == Some(Some(to_auth))
198    })]
199    fn frame_preserving(
200        self,
201        from_auth: FMap<K, V>,
202        from_frag: FMap<K, V>,
203        frame: Option<FMap<K, V>>,
204    ) {
205        let (to_auth, to_frag) = self.update(from_auth, from_frag);
206        proof_assert!(match Some(to_frag).op(frame) {
207            Some(Some(x)) => to_auth.ext_eq(x),
208            _ => false,
209        });
210    }
211}
creusot_std/logic/ra/fmap.rs

creusot_std/logic/ra/
fmap.rs
