vstd/std_specs/
vec.rs

1use super::super::prelude::*;
2use verus_builtin::*;
3
4use alloc::vec::{IntoIter, Vec};
5use core::alloc::Allocator;
6use core::clone::Clone;
7use core::marker::PhantomData;
8use core::option::Option;
9use core::option::Option::None;
10
11use verus as verus_;
12verus_! {
13
14#[verifier::external_type_specification]
15#[verifier::external_body]
16#[verifier::accept_recursive_types(T)]
17#[verifier::reject_recursive_types(A)]
18pub struct ExVec<T, A: Allocator>(Vec<T, A>);
19
20pub trait VecAdditionalSpecFns<T>: View<V = Seq<T>> {
21    spec fn spec_index(&self, i: int) -> T
22        recommends
23            0 <= i < self.view().len(),
24    ;
25}
26
27impl<T, A: Allocator> VecAdditionalSpecFns<T> for Vec<T, A> {
28    #[verifier::inline]
29    open spec fn spec_index(&self, i: int) -> T {
30        self.view().index(i)
31    }
32}
33
34// TODO this should really be an 'assume_specification' function
35// but it's difficult to handle vec.index right now because
36// it uses more trait polymorphism than we can handle right now.
37//
38// So this is a bit of a hack, but I'm just manually redirecting
39// `vec[i]` to this function here from rust_to_vir_expr.
40//
41// It's not ideal, but I think it's better than the alternative, which would
42// be to have users call some function with a nonstandard name to perform indexing.
43/// This is a specification for the indexing operator `vec[i]`
44#[verifier::external_body]
45#[cfg_attr(verus_keep_ghost, rustc_diagnostic_item = "verus::vstd::std_specs::vec::vec_index")]
46pub fn vec_index<T, A: Allocator>(vec: &Vec<T, A>, i: usize) -> (element: &T)
47    requires
48        i < vec.view().len(),
49    ensures
50        *element == vec.view().index(i as int),
51    no_unwind
52{
53    &vec[i]
54}
55
56////// Len (with autospec)
57pub uninterp spec fn spec_vec_len<T, A: Allocator>(v: &Vec<T, A>) -> usize;
58
59// This axiom is slightly better than defining spec_vec_len to just be `v@.len() as usize`
60// (the axiom also shows that v@.len() is in-bounds for usize)
61pub broadcast proof fn axiom_spec_len<A>(v: &Vec<A>)
62    ensures
63        #[trigger] spec_vec_len(v) == v@.len(),
64{
65    admit();
66}
67
68#[verifier::when_used_as_spec(spec_vec_len)]
69pub assume_specification<T, A: Allocator>[ Vec::<T, A>::len ](vec: &Vec<T, A>) -> (len: usize)
70    ensures
71        len == spec_vec_len(vec),
72    no_unwind
73;
74
75////// Other functions
76pub assume_specification<T>[ Vec::<T>::new ]() -> (v: Vec<T>)
77    ensures
78        v@ == Seq::<T>::empty(),
79;
80
81pub assume_specification<T>[ Vec::<T>::with_capacity ](capacity: usize) -> (v: Vec<T>)
82    ensures
83        v@ == Seq::<T>::empty(),
84;
85
86pub assume_specification<T, A: Allocator>[ Vec::<T, A>::reserve ](
87    vec: &mut Vec<T, A>,
88    additional: usize,
89)
90    ensures
91        vec@ == old(vec)@,
92;
93
94pub assume_specification<T, A: Allocator>[ Vec::<T, A>::push ](vec: &mut Vec<T, A>, value: T)
95    ensures
96        vec@ == old(vec)@.push(value),
97;
98
99pub assume_specification<T, A: Allocator>[ Vec::<T, A>::pop ](vec: &mut Vec<T, A>) -> (value:
100    Option<T>)
101    ensures
102        old(vec)@.len() > 0 ==> value == Some(old(vec)@[old(vec)@.len() - 1]) && vec@ == old(
103            vec,
104        )@.subrange(0, old(vec)@.len() - 1),
105        old(vec)@.len() == 0 ==> value == None::<T> && vec@ == old(vec)@,
106;
107
108pub assume_specification<T, A: Allocator>[ Vec::<T, A>::append ](
109    vec: &mut Vec<T, A>,
110    other: &mut Vec<T, A>,
111)
112    ensures
113        vec@ == old(vec)@ + old(other)@,
114        other@ == Seq::<T>::empty(),
115;
116
117pub assume_specification<T: core::clone::Clone, A: Allocator>[ Vec::<T, A>::extend_from_slice ](
118    vec: &mut Vec<T, A>,
119    other: &[T],
120)
121    ensures
122        vec@.len() == old(vec)@.len() + other@.len(),
123        forall|i: int|
124            #![trigger vec@[i]]
125            0 <= i < vec@.len() ==> if i < old(vec)@.len() {
126                vec@[i] == old(vec)@[i]
127            } else {
128                cloned::<T>(other@[i - old(vec)@.len()], vec@[i])
129            },
130;
131
132/*
133// TODO find a way to support this
134// This is difficult because of the SliceIndex trait
135use std::ops::Index;
136
137pub assume_specification<T, A: Allocator>[Vec::<T,A>::index](vec: &Vec<T>, i: usize) -> (r: &T)
138    requires
139        i < vec.len(),
140    ensures
141        *r == vec[i as int];
142*/
143
144pub assume_specification<T, A: Allocator>[ Vec::<T, A>::swap_remove ](
145    vec: &mut Vec<T, A>,
146    i: usize,
147) -> (element: T)
148    requires
149        i < old(vec).len(),
150    ensures
151        element == old(vec)[i as int],
152        vec@ == old(vec)@.update(i as int, old(vec)@.last()).drop_last(),
153;
154
155pub assume_specification<T, A: Allocator>[ Vec::<T, A>::insert ](
156    vec: &mut Vec<T, A>,
157    i: usize,
158    element: T,
159)
160    requires
161        i <= old(vec).len(),
162    ensures
163        vec@ == old(vec)@.insert(i as int, element),
164;
165
166pub assume_specification<T, A: Allocator> [ <Vec<T, A>>::is_empty ](
167    v: &Vec<T, A>,
168) -> (res: bool)
169    ensures res <==> v@.len() == 0,
170;
171
172pub assume_specification<T, A: Allocator>[ Vec::<T, A>::remove ](
173    vec: &mut Vec<T, A>,
174    i: usize,
175) -> (element: T)
176    requires
177        i < old(vec).len(),
178    ensures
179        element == old(vec)[i as int],
180        vec@ == old(vec)@.remove(i as int),
181;
182
183pub assume_specification<T, A: Allocator>[ Vec::<T, A>::clear ](vec: &mut Vec<T, A>)
184    ensures
185        vec.view() == Seq::<T>::empty(),
186;
187
188pub assume_specification<T, A: Allocator>[ Vec::<T, A>::as_slice ](vec: &Vec<T, A>) -> (slice: &[T])
189    ensures
190        slice@ == vec@,
191;
192
193pub assume_specification<T, A: Allocator>[ <Vec<T, A> as core::ops::Deref>::deref ](
194    vec: &Vec<T, A>,
195) -> (slice: &[T])
196    ensures
197        slice@ == vec@,
198;
199
200pub assume_specification<T, A: Allocator + core::clone::Clone>[ Vec::<T, A>::split_off ](
201    vec: &mut Vec<T, A>,
202    at: usize,
203) -> (return_value: Vec<T, A>)
204    requires
205        at <= old(vec)@.len(),
206    ensures
207        vec@ == old(vec)@.subrange(0, at as int),
208        return_value@ == old(vec)@.subrange(at as int, old(vec)@.len() as int),
209;
210
211pub open spec fn vec_clone_trigger<T, A: Allocator>(v1: Vec<T, A>, v2: Vec<T, A>) -> bool {
212    true
213}
214
215pub assume_specification<T: Clone, A: Allocator + Clone>[ <Vec<T, A> as Clone>::clone ](
216    vec: &Vec<T, A>,
217) -> (res: Vec<T, A>)
218    ensures
219        res.len() == vec.len(),
220        forall|i| #![all_triggers] 0 <= i < vec.len() ==> cloned::<T>(vec[i], res[i]),
221        vec_clone_trigger(*vec, res),
222        vec@ =~= res@ ==> vec@ == res@,
223;
224
225pub broadcast proof fn vec_clone_deep_view_proof<T: DeepView, A: Allocator>(
226    v1: Vec<T, A>,
227    v2: Vec<T, A>,
228)
229    requires
230        #[trigger] vec_clone_trigger(v1, v2),
231        v1.deep_view() =~= v2.deep_view(),
232    ensures
233        v1.deep_view() == v2.deep_view(),
234{
235}
236
237pub assume_specification<T, A: Allocator>[ Vec::<T, A>::truncate ](vec: &mut Vec<T, A>, len: usize)
238    ensures
239        len <= old(vec).len() ==> vec@ == old(vec)@.subrange(0, len as int),
240        len > old(vec).len() ==> vec@ == old(vec)@,
241;
242
243pub assume_specification<T: Clone, A: Allocator>[ Vec::<T, A>::resize ](
244    vec: &mut Vec<T, A>,
245    len: usize,
246    value: T,
247)
248    ensures
249        len <= old(vec).len() ==> vec@ == old(vec)@.subrange(0, len as int),
250        len > old(vec).len() ==> {
251            &&& vec@.len() == len
252            &&& vec@.subrange(0, old(vec).len() as int) == old(vec)@
253            &&& forall|i| #![all_triggers] old(vec).len() <= i < len ==> cloned::<T>(value, vec@[i])
254        },
255;
256
257pub broadcast proof fn axiom_vec_index_decreases<A>(v: Vec<A>, i: int)
258    requires
259        0 <= i < v.len(),
260    ensures
261        #[trigger] (decreases_to!(v => v[i])),
262{
263    admit();
264}
265
266impl<T, A: Allocator> super::core::TrustedSpecSealed for Vec<T, A> {
267
268}
269
270impl<T, A: Allocator> super::core::IndexSetTrustedSpec<usize> for Vec<T, A> {
271    open spec fn spec_index_set_requires(&self, index: usize) -> bool {
272        0 <= index < self.len()
273    }
274
275    open spec fn spec_index_set_ensures(&self, new_container: &Self, index: usize, val: T) -> bool {
276        new_container@ === self@.update(index as int, val)
277    }
278}
279
280pub assume_specification<T: PartialEq<U>, U, A1: Allocator, A2: Allocator>[ <Vec<T, A1> as PartialEq<Vec<U, A2>>>::eq ](
281    x: &Vec<T, A1>,
282    y: &Vec<U, A2>,
283) -> bool
284;
285
286impl<T: super::cmp::PartialEqSpec<U>, U, A1: Allocator, A2: Allocator> super::cmp::PartialEqSpecImpl<Vec<U, A2>> for Vec<T, A1> {
287    open spec fn obeys_eq_spec() -> bool {
288        T::obeys_eq_spec()
289    }
290
291    open spec fn eq_spec(&self, other: &Vec<U, A2>) -> bool {
292        &&& self.len() == other.len()
293        &&& forall|i: int| #![auto] 0 <= i < self.len() ==> self[i].eq_spec(&other[i])
294    }
295}
296
297// The `into_iter` method of a `Vec` returns an iterator of type `IntoIter`,
298// so we specify that type here.
299#[verifier::external_type_specification]
300#[verifier::external_body]
301#[verifier::accept_recursive_types(T)]
302#[verifier::reject_recursive_types(A)]
303pub struct ExIntoIter<T, A: Allocator>(IntoIter<T, A>);
304
305impl<T, A: Allocator> View for IntoIter<T, A> {
306    type V = (int, Seq<T>);
307
308    uninterp spec fn view(self: &IntoIter<T, A>) -> (int, Seq<T>);
309}
310
311pub assume_specification<T, A: Allocator>[ IntoIter::<T, A>::next ](
312    elements: &mut IntoIter<T, A>,
313) -> (r: Option<T>)
314    ensures
315        ({
316            let (old_index, old_seq) = old(elements)@;
317            match r {
318                None => {
319                    &&& elements@ == old(elements)@
320                    &&& old_index >= old_seq.len()
321                },
322                Some(element) => {
323                    let (new_index, new_seq) = elements@;
324                    &&& 0 <= old_index < old_seq.len()
325                    &&& new_seq == old_seq
326                    &&& new_index == old_index + 1
327                    &&& element == old_seq[old_index]
328                },
329            }
330        }),
331;
332
333pub struct IntoIterGhostIterator<T, A: Allocator> {
334    pub pos: int,
335    pub elements: Seq<T>,
336    pub _marker: PhantomData<A>,
337}
338
339impl<T, A: Allocator> super::super::pervasive::ForLoopGhostIteratorNew for IntoIter<T, A> {
340    type GhostIter = IntoIterGhostIterator<T, A>;
341
342    open spec fn ghost_iter(&self) -> IntoIterGhostIterator<T, A> {
343        IntoIterGhostIterator { pos: self@.0, elements: self@.1, _marker: PhantomData }
344    }
345}
346
347// This is used by `vec![x; n]`
348pub assume_specification<T: Clone>[ alloc::vec::from_elem ](elem: T, n: usize) -> (v: Vec<T>)
349    ensures
350        v.len() == n,
351        forall |i| 0 <= i < n ==> cloned(elem, #[trigger] v@[i]);
352
353impl<T, A: Allocator> super::super::pervasive::ForLoopGhostIterator for IntoIterGhostIterator<
354    T,
355    A,
356> {
357    type ExecIter = IntoIter<T, A>;
358
359    type Item = T;
360
361    type Decrease = int;
362
363    open spec fn exec_invariant(&self, exec_iter: &IntoIter<T, A>) -> bool {
364        &&& self.pos == exec_iter@.0
365        &&& self.elements == exec_iter@.1
366    }
367
368    open spec fn ghost_invariant(&self, init: Option<&Self>) -> bool {
369        init matches Some(init) ==> {
370            &&& init.pos == 0
371            &&& init.elements == self.elements
372            &&& 0 <= self.pos <= self.elements.len()
373        }
374    }
375
376    open spec fn ghost_ensures(&self) -> bool {
377        self.pos == self.elements.len()
378    }
379
380    open spec fn ghost_decrease(&self) -> Option<int> {
381        Some(self.elements.len() - self.pos)
382    }
383
384    open spec fn ghost_peek_next(&self) -> Option<T> {
385        if 0 <= self.pos < self.elements.len() {
386            Some(self.elements[self.pos])
387        } else {
388            None
389        }
390    }
391
392    open spec fn ghost_advance(&self, _exec_iter: &IntoIter<T, A>) -> IntoIterGhostIterator<T, A> {
393        Self { pos: self.pos + 1, ..*self }
394    }
395}
396
397impl<T, A: Allocator> View for IntoIterGhostIterator<T, A> {
398    type V = Seq<T>;
399
400    open spec fn view(&self) -> Seq<T> {
401        self.elements.take(self.pos)
402    }
403}
404
405// To allow reasoning about the ghost iterator when the executable
406// function `into_iter()` is invoked in a `for` loop header (e.g., in
407// `for x in it: v.into_iter() { ... }`), we need to specify the behavior of
408// the iterator in spec mode. To do that, we add
409// `#[verifier::when_used_as_spec(spec_into_iter)` to the specification for
410// the executable `into_iter` method and define that spec function here.
411pub uninterp spec fn spec_into_iter<T, A: Allocator>(v: Vec<T, A>) -> (iter: <Vec<
412    T,
413    A,
414> as core::iter::IntoIterator>::IntoIter);
415
416pub broadcast proof fn axiom_spec_into_iter<T, A: Allocator>(v: Vec<T, A>)
417    ensures
418        (#[trigger] spec_into_iter(v))@ == (0int, v@),
419{
420    admit();
421}
422
423#[verifier::when_used_as_spec(spec_into_iter)]
424pub assume_specification<T, A: Allocator>[ Vec::<T, A>::into_iter ](vec: Vec<T, A>) -> (iter: <Vec<
425    T,
426    A,
427> as core::iter::IntoIterator>::IntoIter)
428    ensures
429        iter@ == (0int, vec@),
430;
431
432pub broadcast proof fn lemma_vec_obeys_eq_spec<T: PartialEq>()
433    requires
434        super::super::laws_eq::obeys_eq_spec::<T>(),
435    ensures
436        #[trigger] super::super::laws_eq::obeys_eq_spec::<Vec<T>>(),
437{
438    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
439    reveal(super::super::laws_eq::obeys_eq_spec_properties);
440}
441
442pub broadcast proof fn lemma_vec_obeys_view_eq<T: PartialEq + View>()
443    requires
444        super::super::laws_eq::obeys_concrete_eq::<T>(),
445    ensures
446        #[trigger] super::super::laws_eq::obeys_view_eq::<Vec<T>>(),
447{
448    use super::cmp::PartialEqSpec;
449    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
450    reveal(super::super::laws_eq::obeys_eq_spec_properties);
451    reveal(super::super::laws_eq::obeys_concrete_eq);
452    reveal(super::super::laws_eq::obeys_view_eq);
453    assert(forall|x: Vec<T>, y: Vec<T>| x.eq_spec(&y) ==> x@ == y@);
454}
455
456pub broadcast proof fn lemma_vec_obeys_deep_eq<T: PartialEq + DeepView>()
457    requires
458        super::super::laws_eq::obeys_deep_eq::<T>(),
459    ensures
460        #[trigger] super::super::laws_eq::obeys_deep_eq::<Vec<T>>(),
461{
462    use super::cmp::PartialEqSpec;
463    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
464    reveal(super::super::laws_eq::obeys_eq_spec_properties);
465    reveal(super::super::laws_eq::obeys_deep_eq);
466    assert(forall|x: Vec<T>, y: Vec<T>| x.eq_spec(&y) ==> x.deep_view() == y.deep_view());
467    assert forall|x: Vec<T>, y: Vec<T>| x.deep_view() == y.deep_view() implies x.eq_spec(&y) by {
468        assert(x.deep_view().len() == y.deep_view().len());
469        assert forall|i: int| #![auto] 0 <= i < x.len() implies x[i].eq_spec(&y[i]) by {
470            assert(x.deep_view()[i] == y.deep_view()[i]);
471        }
472    }
473}
474
475pub broadcast group group_vec_axioms {
476    axiom_spec_len,
477    axiom_vec_index_decreases,
478    vec_clone_deep_view_proof,
479    axiom_spec_into_iter,
480}
481
482} // verus!
vstd/std_specs/vec.rs

vstd/std_specs/
vec.rs
