creusot_std/logic/ra/
option.rs

1#[cfg(creusot)]
2use crate::logic::such_that;
3use crate::{
4    logic::ra::{
5        RA, UnitRA,
6        update::{LocalUpdate, Update},
7    },
8    prelude::*,
9};
10
11impl<T: RA> RA for Option<T> {
12    #[logic(open)]
13    fn op(self, other: Self) -> Option<Self> {
14        match (self, other) {
15            (None, _) => Some(other),
16            (_, None) => Some(self),
17            (Some(x), Some(y)) => x.op(y).map_logic(|z| Some(z)),
18        }
19    }
20
21    #[logic(open)]
22    #[ensures(match result {
23        Some(c) => factor.op(c) == Some(self),
24        None => forall<c: Self> factor.op(c) != Some(self),
25    })]
26    fn factor(self, factor: Self) -> Option<Self> {
27        match (self, factor) {
28            (x, None) => Some(x),
29            (None, _) => None,
30            (Some(x), Some(y)) => match x.factor(y) {
31                Some(z) => Some(Some(z)),
32                None => {
33                    if x == y {
34                        Some(None)
35                    } else {
36                        None
37                    }
38                }
39            },
40        }
41    }
42
43    #[logic(open, inline)]
44    #[ensures(result == (self == other))]
45    fn eq(self, other: Self) -> bool {
46        match (self, other) {
47            (Some(s), Some(o)) => s.eq(o),
48            (None, None) => true,
49            _ => false,
50        }
51    }
52
53    #[logic(law)]
54    #[ensures(a.op(b) == b.op(a))]
55    fn commutative(a: Self, b: Self) {
56        let _ = <T as RA>::commutative;
57    }
58
59    #[logic]
60    #[ensures(a.op(b).and_then_logic(|ab: Self| ab.op(c)) == b.op(c).and_then_logic(|bc| a.op(bc)))]
61    fn associative(a: Self, b: Self, c: Self) {}
62
63    #[logic(open)]
64    fn core(self) -> Option<Self> {
65        match self {
66            None => Some(None),
67            Some(x) => Some(x.core()),
68        }
69    }
70
71    #[logic]
72    #[requires(self.core() != None)]
73    #[ensures({
74        let c = self.core().unwrap_logic();
75        c.op(c) == Some(c)
76    })]
77    #[ensures(self.core().unwrap_logic().op(self) == Some(self))]
78    fn core_idemp(self) {
79        self.core_total_idemp()
80    }
81
82    #[logic]
83    #[requires(i.op(i) == Some(i))]
84    #[requires(i.op(self) == Some(self))]
85    #[ensures(match self.core() {
86        Some(c) => i.incl(c),
87        None => false,
88    })]
89    fn core_is_maximal_idemp(self, i: Self) {
90        match (self, i) {
91            (Some(x), Some(i)) => x.core_is_maximal_idemp(i),
92            _ => (),
93        }
94    }
95
96    #[logic(open)]
97    #[ensures(result == (forall<x, y> self.op(x) != None ==>
98        self.op(x) == self.op(y) ==> x == y))]
99    fn cancelable(self) -> bool {
100        match self {
101            None => true,
102            Some(this) => {
103                proof_assert! {
104                    let _ = T::core_is_maximal_idemp;
105                    let _ = T::core_idemp;
106                    ((forall<x, y> self.op(x) != None ==> self.op(x) == self.op(y) ==> x == y) ==>
107                        self.op(this.core()) == self.op(None)) &&
108                    this.cancelable() ==> this.core() == None ==>
109                        forall<x, y> self.op(x) != None ==> self.op(x) == self.op(y) ==>
110                        match (x, y) {
111                            (Some(x), Some(y)) => this.op(x) != None && this.op(x) == this.op(y),
112                            (Some(_), None) => false,
113                            (None, Some(y)) => y.op(this) == Some(this),
114                            (None, None) => true,
115                        }
116                };
117                this.cancelable() && this.core() == None
118            }
119        }
120    }
121}
122
123impl<T: RA> UnitRA for Option<T> {
124    #[logic(open)]
125    #[ensures(forall<x: Self> #[trigger(x.op(result))] x.op(result) == Some(x))]
126    fn unit() -> Self {
127        None
128    }
129
130    #[logic(open)]
131    #[ensures(self.core() == Some(result))]
132    fn core_total(self) -> Self {
133        match self {
134            None => None,
135            Some(x) => x.core(),
136        }
137    }
138
139    #[logic]
140    #[ensures(self.core_total().op(self.core_total()) == Some(self.core_total()))]
141    #[ensures(self.core_total().op(self) == Some(self))]
142    fn core_total_idemp(self) {
143        let _ = T::core_idemp;
144    }
145}
146
147/// Apply an [update](Update) to the inner value of an [`Option`] resource.
148///
149/// This requires the resource to be in the `Some` state.
150///
151/// # Example
152///
153/// ```
154/// use creusot_std::{
155///     ghost::resource::Resource,
156///     logic::ra::{
157///         excl::{Excl, ExclUpdate},
158///         option::OptionUpdate,
159///     },
160///     prelude::*,
161/// };
162///
163/// let mut res = Resource::alloc(snapshot!(Some(Excl(1))));
164/// ghost! { res.update(OptionUpdate(ExclUpdate(snapshot!(2)))) };
165/// proof_assert!(res@ == Some(Excl(2)));
166/// ```
167pub struct OptionUpdate<U>(pub U);
168
169impl<R: RA, U: Update<R>> Update<Option<R>> for OptionUpdate<U> {
170    type Choice = U::Choice;
171
172    #[logic(open, inline)]
173    fn premise(self, from: Option<R>) -> bool {
174        match from {
175            Some(from) => self.0.premise(from),
176            None => false,
177        }
178    }
179
180    #[logic(open, inline)]
181    #[requires(self.premise(from))]
182    fn update(self, from: Option<R>, ch: U::Choice) -> Option<R> {
183        match from {
184            Some(from) => Some(self.0.update(from, ch)),
185            None => None, /* Dummy */
186        }
187    }
188
189    #[logic]
190    #[requires(self.premise(from))]
191    #[requires(from.op(frame) != None)]
192    #[ensures(self.update(from, result).op(frame) != None)]
193    fn frame_preserving(self, from: Option<R>, frame: Option<R>) -> U::Choice {
194        match frame {
195            Some(frame) => self.0.frame_preserving(from.unwrap_logic(), frame),
196            None => such_that(|_| true),
197        }
198    }
199}
200
201/// Apply an [update](LocalUpdate) to the inner value of an authority/fragment
202/// pair of [`Option`]s.
203///
204/// This requires that both the authority and the fragment are not `None`.
205pub struct OptionLocalUpdate<U>(pub U);
206
207impl<R: RA, U: LocalUpdate<R>> LocalUpdate<Option<R>> for OptionLocalUpdate<U> {
208    #[logic(open, inline)]
209    fn premise(self, from_auth: Option<R>, from_frag: Option<R>) -> bool {
210        match (from_auth, from_frag) {
211            (Some(from_auth), Some(from_frag)) => self.0.premise(from_auth, from_frag),
212            _ => false,
213        }
214    }
215
216    #[logic(open, inline)]
217    fn update(self, from_auth: Option<R>, from_frag: Option<R>) -> (Option<R>, Option<R>) {
218        match (from_auth, from_frag) {
219            (Some(from_auth), Some(from_frag)) => {
220                let (to_auth, to_frag) = self.0.update(from_auth, from_frag);
221                (Some(to_auth), Some(to_frag))
222            }
223            _ => (None, None), // Dummy
224        }
225    }
226
227    #[logic]
228    #[requires(self.premise(from_auth, from_frag))]
229    #[requires(Some(from_frag).op(frame) == Some(Some(from_auth)))]
230    #[ensures({
231        let (to_auth, to_frag) = self.update(from_auth, from_frag);
232        Some(to_frag).op(frame) == Some(Some(to_auth))
233    })]
234    fn frame_preserving(
235        self,
236        from_auth: Option<R>,
237        from_frag: Option<R>,
238        frame: Option<Option<R>>,
239    ) {
240        let frame = match frame {
241            None => None,
242            Some(f) => f,
243        };
244        self.0.frame_preserving(from_auth.unwrap_logic(), from_frag.unwrap_logic(), frame)
245    }
246}
creusot_std/logic/ra/option.rs

creusot_std/logic/ra/
option.rs
