vstd/std_specs/
vec.rs

1use super::super::prelude::*;
2use verus_builtin::*;
3
4use alloc::collections::TryReserveError;
5use alloc::vec::{IntoIter, Vec};
6use core::alloc::Allocator;
7use core::clone::Clone;
8use core::marker::PhantomData;
9use core::option::Option;
10use core::option::Option::None;
11
12use verus as verus_;
13verus_! {
14
15#[verifier::external_type_specification]
16#[verifier::external_body]
17#[verifier::accept_recursive_types(T)]
18#[verifier::reject_recursive_types(A)]
19pub struct ExVec<T, A: Allocator>(Vec<T, A>);
20
21pub trait VecAdditionalSpecFns<T>: View<V = Seq<T>> {
22    spec fn spec_index(&self, i: int) -> T
23        recommends
24            0 <= i < self.view().len(),
25    ;
26}
27
28impl<T, A: Allocator> VecAdditionalSpecFns<T> for Vec<T, A> {
29    #[verifier::inline]
30    open spec fn spec_index(&self, i: int) -> T {
31        self.view().index(i)
32    }
33}
34
35#[verifier::external_type_specification]
36#[verifier::external_body]
37pub struct ExTryReserveError(alloc::collections::TryReserveError);
38
39// TODO this should really be an 'assume_specification' function
40// but it's difficult to handle vec.index right now because
41// it uses more trait polymorphism than we can handle right now.
42//
43// So this is a bit of a hack, but I'm just manually redirecting
44// `vec[i]` to this function here from rust_to_vir_expr.
45//
46// It's not ideal, but I think it's better than the alternative, which would
47// be to have users call some function with a nonstandard name to perform indexing.
48/// This is a specification for the indexing operator `vec[i]` when it expands to the `Index` trait
49#[verifier::external_body]
50#[cfg_attr(verus_keep_ghost, rustc_diagnostic_item = "verus::vstd::std_specs::vec::vec_index")]
51pub fn vec_index<T, A: Allocator>(vec: &Vec<T, A>, i: usize) -> (element: &T)
52    requires
53        i < vec.view().len(),
54    ensures
55        *element == vec.view().index(i as int),
56    no_unwind
57{
58    &vec[i]
59}
60
61/// This is a specification for the indexing operator `vec[i]` when it expands to the `IndexMut` trait
62#[doc(hidden)]
63#[verifier::ignore_outside_new_mut_ref_experiment]
64#[verifier::external_body]
65#[cfg_attr(verus_keep_ghost, rustc_diagnostic_item = "verus::vstd::std_specs::vec::vec_index_mut")]
66pub fn vec_index_mut<T, A: Allocator>(vec: &mut Vec<T, A>, i: usize) -> (element: &mut T)
67    requires
68        i < vec.view().len(),
69    ensures
70        *element == (*vec).view().index(i as int),
71        fin(vec)@ == vec@.update(i as int, *fin(element)),
72
73        *fin(element) == fin(vec).view().index(i as int),
74    no_unwind
75{
76    &mut vec[i]
77}
78
79////// Len (with autospec)
80pub uninterp spec fn spec_vec_len<T, A: Allocator>(v: &Vec<T, A>) -> usize;
81
82// This axiom is slightly better than defining spec_vec_len to just be `v@.len() as usize`
83// (the axiom also shows that v@.len() is in-bounds for usize)
84pub broadcast proof fn axiom_spec_len<T, A: Allocator>(v: &Vec<T, A>)
85    ensures
86        #[trigger] spec_vec_len(v) == v@.len(),
87{
88    admit();
89}
90
91#[verifier::when_used_as_spec(spec_vec_len)]
92pub assume_specification<T, A: Allocator>[ Vec::<T, A>::len ](vec: &Vec<T, A>) -> (len: usize)
93    ensures
94        len == spec_vec_len(vec),
95    no_unwind
96;
97
98////// Other functions
99pub assume_specification<T>[ Vec::<T>::new ]() -> (v: Vec<T>)
100    ensures
101        v@ == Seq::<T>::empty(),
102;
103
104pub assume_specification<T, A: Allocator>[ Vec::<T, A>::new_in ](alloc: A) -> (v: Vec<T, A>)
105    ensures
106        v@ == Seq::<T>::empty(),
107;
108
109pub assume_specification<T>[ Vec::<T>::with_capacity ](capacity: usize) -> (v: Vec<T>)
110    ensures
111        v@ == Seq::<T>::empty(),
112;
113
114pub assume_specification<T, A: Allocator>[ Vec::<T, A>::with_capacity_in ](capacity: usize, alloc: A) -> (v: Vec<T, A>)
115    ensures
116        v@ == Seq::<T>::empty(),
117;
118
119pub assume_specification<T, A: Allocator>[ Vec::<T, A>::reserve ](
120    vec: &mut Vec<T, A>,
121    additional: usize,
122)
123    ensures
124        vec@ == old(vec)@,
125;
126
127pub assume_specification<T, A: Allocator>[ Vec::<T, A>::try_reserve ](
128    vec: &mut Vec<T, A>,
129    additional: usize,
130) -> (result: Result<(), TryReserveError>)
131    ensures
132        vec@ == old(vec)@,
133;
134
135pub assume_specification<T, A: Allocator>[ Vec::<T, A>::push ](vec: &mut Vec<T, A>, value: T)
136    ensures
137        vec@ == old(vec)@.push(value),
138;
139
140pub assume_specification<T, A: Allocator>[ Vec::<T, A>::pop ](vec: &mut Vec<T, A>) -> (value:
141    Option<T>)
142    ensures
143        old(vec)@.len() > 0 ==> value == Some(old(vec)@[old(vec)@.len() - 1]) && vec@ == old(
144            vec,
145        )@.subrange(0, old(vec)@.len() - 1),
146        old(vec)@.len() == 0 ==> value == None::<T> && vec@ == old(vec)@,
147;
148
149pub assume_specification<T, A: Allocator>[ Vec::<T, A>::append ](
150    vec: &mut Vec<T, A>,
151    other: &mut Vec<T, A>,
152)
153    ensures
154        vec@ == old(vec)@ + old(other)@,
155        other@ == Seq::<T>::empty(),
156;
157
158pub assume_specification<T: core::clone::Clone, A: Allocator>[ Vec::<T, A>::extend_from_slice ](
159    vec: &mut Vec<T, A>,
160    other: &[T],
161)
162    ensures
163        vec@.len() == old(vec)@.len() + other@.len(),
164        forall|i: int|
165            #![trigger vec@[i]]
166            0 <= i < vec@.len() ==> if i < old(vec)@.len() {
167                vec@[i] == old(vec)@[i]
168            } else {
169                cloned::<T>(other@[i - old(vec)@.len()], vec@[i])
170            },
171;
172
173/*
174// TODO find a way to support this
175// This is difficult because of the SliceIndex trait
176use std::ops::Index;
177
178pub assume_specification<T, A: Allocator>[Vec::<T,A>::index](vec: &Vec<T>, i: usize) -> (r: &T)
179    requires
180        i < vec.len(),
181    ensures
182        *r == vec[i as int];
183*/
184
185pub assume_specification<T, A: Allocator>[ Vec::<T, A>::swap_remove ](
186    vec: &mut Vec<T, A>,
187    i: usize,
188) -> (element: T)
189    requires
190        i < old(vec).len(),
191    ensures
192        element == old(vec)[i as int],
193        vec@ == old(vec)@.update(i as int, old(vec)@.last()).drop_last(),
194;
195
196pub assume_specification<T, A: Allocator>[ Vec::<T, A>::insert ](
197    vec: &mut Vec<T, A>,
198    i: usize,
199    element: T,
200)
201    requires
202        i <= old(vec).len(),
203    ensures
204        vec@ == old(vec)@.insert(i as int, element),
205;
206
207pub assume_specification<T, A: Allocator> [ <Vec<T, A>>::is_empty ](
208    v: &Vec<T, A>,
209) -> (res: bool)
210    ensures res <==> v@.len() == 0,
211;
212
213pub assume_specification<T, A: Allocator>[ Vec::<T, A>::remove ](
214    vec: &mut Vec<T, A>,
215    i: usize,
216) -> (element: T)
217    requires
218        i < old(vec).len(),
219    ensures
220        element == old(vec)[i as int],
221        vec@ == old(vec)@.remove(i as int),
222;
223
224pub assume_specification<T, A: Allocator>[ Vec::<T, A>::clear ](vec: &mut Vec<T, A>)
225    ensures
226        vec.view() == Seq::<T>::empty(),
227;
228
229pub assume_specification<T, A: Allocator>[ Vec::<T, A>::as_slice ](vec: &Vec<T, A>) -> (slice: &[T])
230    ensures
231        slice@ == vec@,
232;
233
234#[doc(hidden)]
235#[verifier::ignore_outside_new_mut_ref_experiment]
236pub assume_specification<T, A: Allocator>[ Vec::<T, A>::as_mut_slice ](vec: &mut Vec<T, A>) -> (slice: &mut [T])
237    ensures
238        slice@ == vec@,
239        fin(slice)@ == fin(vec)@,
240;
241
242pub assume_specification<T, A: Allocator>[ <Vec<T, A> as core::ops::Deref>::deref ](
243    vec: &Vec<T, A>,
244) -> (slice: &[T])
245    ensures
246        slice@ == vec@,
247;
248
249pub assume_specification<T, A: Allocator + core::clone::Clone>[ Vec::<T, A>::split_off ](
250    vec: &mut Vec<T, A>,
251    at: usize,
252) -> (return_value: Vec<T, A>)
253    requires
254        at <= old(vec)@.len(),
255    ensures
256        vec@ == old(vec)@.subrange(0, at as int),
257        return_value@ == old(vec)@.subrange(at as int, old(vec)@.len() as int),
258;
259
260pub open spec fn vec_clone_trigger<T, A: Allocator>(v1: Vec<T, A>, v2: Vec<T, A>) -> bool {
261    true
262}
263
264pub assume_specification<T: Clone, A: Allocator + Clone>[ <Vec<T, A> as Clone>::clone ](
265    vec: &Vec<T, A>,
266) -> (res: Vec<T, A>)
267    ensures
268        res.len() == vec.len(),
269        forall|i| #![all_triggers] 0 <= i < vec.len() ==> cloned::<T>(vec[i], res[i]),
270        vec_clone_trigger(*vec, res),
271        vec@ =~= res@ ==> vec@ == res@,
272;
273
274pub broadcast proof fn vec_clone_deep_view_proof<T: DeepView, A: Allocator>(
275    v1: Vec<T, A>,
276    v2: Vec<T, A>,
277)
278    requires
279        #[trigger] vec_clone_trigger(v1, v2),
280        v1.deep_view() =~= v2.deep_view(),
281    ensures
282        v1.deep_view() == v2.deep_view(),
283{
284}
285
286pub assume_specification<T, A: Allocator>[ Vec::<T, A>::truncate ](vec: &mut Vec<T, A>, len: usize)
287    ensures
288        len <= old(vec).len() ==> vec@ == old(vec)@.subrange(0, len as int),
289        len > old(vec).len() ==> vec@ == old(vec)@,
290;
291
292pub assume_specification<T: Clone, A: Allocator>[ Vec::<T, A>::resize ](
293    vec: &mut Vec<T, A>,
294    len: usize,
295    value: T,
296)
297    ensures
298        len <= old(vec).len() ==> vec@ == old(vec)@.subrange(0, len as int),
299        len > old(vec).len() ==> {
300            &&& vec@.len() == len
301            &&& vec@.subrange(0, old(vec).len() as int) == old(vec)@
302            &&& forall|i| #![all_triggers] old(vec).len() <= i < len ==> cloned::<T>(value, vec@[i])
303        },
304;
305
306pub broadcast proof fn axiom_vec_index_decreases<A>(v: Vec<A>, i: int)
307    requires
308        0 <= i < v.len(),
309    ensures
310        #[trigger] (decreases_to!(v => v[i])),
311{
312    admit();
313}
314
315impl<T, A: Allocator> super::core::TrustedSpecSealed for Vec<T, A> {
316
317}
318
319impl<T, A: Allocator> super::core::IndexSetTrustedSpec<usize> for Vec<T, A> {
320    open spec fn spec_index_set_requires(&self, index: usize) -> bool {
321        0 <= index < self.len()
322    }
323
324    open spec fn spec_index_set_ensures(&self, new_container: &Self, index: usize, val: T) -> bool {
325        new_container@ === self@.update(index as int, val)
326    }
327}
328
329pub assume_specification<T: PartialEq<U>, U, A1: Allocator, A2: Allocator>[ <Vec<T, A1> as PartialEq<Vec<U, A2>>>::eq ](
330    x: &Vec<T, A1>,
331    y: &Vec<U, A2>,
332) -> bool
333;
334
335impl<T: super::cmp::PartialEqSpec<U>, U, A1: Allocator, A2: Allocator> super::cmp::PartialEqSpecImpl<Vec<U, A2>> for Vec<T, A1> {
336    open spec fn obeys_eq_spec() -> bool {
337        T::obeys_eq_spec()
338    }
339
340    open spec fn eq_spec(&self, other: &Vec<U, A2>) -> bool {
341        &&& self.len() == other.len()
342        &&& forall|i: int| #![auto] 0 <= i < self.len() ==> self[i].eq_spec(&other[i])
343    }
344}
345
346// The `into_iter` method of a `Vec` returns an iterator of type `IntoIter`,
347// so we specify that type here.
348#[verifier::external_type_specification]
349#[verifier::external_body]
350#[verifier::accept_recursive_types(T)]
351#[verifier::reject_recursive_types(A)]
352pub struct ExIntoIter<T, A: Allocator>(IntoIter<T, A>);
353
354impl<T, A: Allocator> View for IntoIter<T, A> {
355    type V = (int, Seq<T>);
356
357    uninterp spec fn view(self: &IntoIter<T, A>) -> (int, Seq<T>);
358}
359
360pub assume_specification<T, A: Allocator>[ IntoIter::<T, A>::next ](
361    elements: &mut IntoIter<T, A>,
362) -> (r: Option<T>)
363    ensures
364        ({
365            let (old_index, old_seq) = old(elements)@;
366            match r {
367                None => {
368                    &&& elements@ == old(elements)@
369                    &&& old_index >= old_seq.len()
370                },
371                Some(element) => {
372                    let (new_index, new_seq) = elements@;
373                    &&& 0 <= old_index < old_seq.len()
374                    &&& new_seq == old_seq
375                    &&& new_index == old_index + 1
376                    &&& element == old_seq[old_index]
377                },
378            }
379        }),
380;
381
382pub struct IntoIterGhostIterator<T, A: Allocator> {
383    pub pos: int,
384    pub elements: Seq<T>,
385    pub _marker: PhantomData<A>,
386}
387
388impl<T, A: Allocator> super::super::pervasive::ForLoopGhostIteratorNew for IntoIter<T, A> {
389    type GhostIter = IntoIterGhostIterator<T, A>;
390
391    open spec fn ghost_iter(&self) -> IntoIterGhostIterator<T, A> {
392        IntoIterGhostIterator { pos: self@.0, elements: self@.1, _marker: PhantomData }
393    }
394}
395
396// This is used by `vec![x; n]`
397pub assume_specification<T: Clone>[ alloc::vec::from_elem ](elem: T, n: usize) -> (v: Vec<T>)
398    ensures
399        v.len() == n,
400        forall |i| 0 <= i < n ==> cloned(elem, #[trigger] v@[i]);
401
402impl<T, A: Allocator> super::super::pervasive::ForLoopGhostIterator for IntoIterGhostIterator<
403    T,
404    A,
405> {
406    type ExecIter = IntoIter<T, A>;
407
408    type Item = T;
409
410    type Decrease = int;
411
412    open spec fn exec_invariant(&self, exec_iter: &IntoIter<T, A>) -> bool {
413        &&& self.pos == exec_iter@.0
414        &&& self.elements == exec_iter@.1
415    }
416
417    open spec fn ghost_invariant(&self, init: Option<&Self>) -> bool {
418        init matches Some(init) ==> {
419            &&& init.pos == 0
420            &&& init.elements == self.elements
421            &&& 0 <= self.pos <= self.elements.len()
422        }
423    }
424
425    open spec fn ghost_ensures(&self) -> bool {
426        self.pos == self.elements.len()
427    }
428
429    open spec fn ghost_decrease(&self) -> Option<int> {
430        Some(self.elements.len() - self.pos)
431    }
432
433    open spec fn ghost_peek_next(&self) -> Option<T> {
434        if 0 <= self.pos < self.elements.len() {
435            Some(self.elements[self.pos])
436        } else {
437            None
438        }
439    }
440
441    open spec fn ghost_advance(&self, _exec_iter: &IntoIter<T, A>) -> IntoIterGhostIterator<T, A> {
442        Self { pos: self.pos + 1, ..*self }
443    }
444}
445
446impl<T, A: Allocator> View for IntoIterGhostIterator<T, A> {
447    type V = Seq<T>;
448
449    open spec fn view(&self) -> Seq<T> {
450        self.elements.take(self.pos)
451    }
452}
453
454// To allow reasoning about the ghost iterator when the executable
455// function `into_iter()` is invoked in a `for` loop header (e.g., in
456// `for x in it: v.into_iter() { ... }`), we need to specify the behavior of
457// the iterator in spec mode. To do that, we add
458// `#[verifier::when_used_as_spec(spec_into_iter)` to the specification for
459// the executable `into_iter` method and define that spec function here.
460pub uninterp spec fn spec_into_iter<T, A: Allocator>(v: Vec<T, A>) -> (iter: <Vec<
461    T,
462    A,
463> as core::iter::IntoIterator>::IntoIter);
464
465pub broadcast proof fn axiom_spec_into_iter<T, A: Allocator>(v: Vec<T, A>)
466    ensures
467        (#[trigger] spec_into_iter(v))@ == (0int, v@),
468{
469    admit();
470}
471
472#[verifier::when_used_as_spec(spec_into_iter)]
473pub assume_specification<T, A: Allocator>[ Vec::<T, A>::into_iter ](vec: Vec<T, A>) -> (iter: <Vec<
474    T,
475    A,
476> as core::iter::IntoIterator>::IntoIter)
477    ensures
478        iter@ == (0int, vec@),
479;
480
481pub broadcast proof fn lemma_vec_obeys_eq_spec<T: PartialEq>()
482    requires
483        super::super::laws_eq::obeys_eq_spec::<T>(),
484    ensures
485        #[trigger] super::super::laws_eq::obeys_eq_spec::<Vec<T>>(),
486{
487    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
488    reveal(super::super::laws_eq::obeys_eq_spec_properties);
489}
490
491pub broadcast proof fn lemma_vec_obeys_view_eq<T: PartialEq + View>()
492    requires
493        super::super::laws_eq::obeys_concrete_eq::<T>(),
494    ensures
495        #[trigger] super::super::laws_eq::obeys_view_eq::<Vec<T>>(),
496{
497    use super::cmp::PartialEqSpec;
498    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
499    reveal(super::super::laws_eq::obeys_eq_spec_properties);
500    reveal(super::super::laws_eq::obeys_concrete_eq);
501    reveal(super::super::laws_eq::obeys_view_eq);
502    assert(forall|x: Vec<T>, y: Vec<T>| x.eq_spec(&y) ==> x@ == y@);
503}
504
505pub broadcast proof fn lemma_vec_obeys_deep_eq<T: PartialEq + DeepView>()
506    requires
507        super::super::laws_eq::obeys_deep_eq::<T>(),
508    ensures
509        #[trigger] super::super::laws_eq::obeys_deep_eq::<Vec<T>>(),
510{
511    use super::cmp::PartialEqSpec;
512    broadcast use {axiom_spec_len, super::super::seq::group_seq_axioms};
513    reveal(super::super::laws_eq::obeys_eq_spec_properties);
514    reveal(super::super::laws_eq::obeys_deep_eq);
515    assert(forall|x: Vec<T>, y: Vec<T>| x.eq_spec(&y) ==> x.deep_view() == y.deep_view());
516    assert forall|x: Vec<T>, y: Vec<T>| x.deep_view() == y.deep_view() implies x.eq_spec(&y) by {
517        assert(x.deep_view().len() == y.deep_view().len());
518        assert forall|i: int| #![auto] 0 <= i < x.len() implies x[i].eq_spec(&y[i]) by {
519            assert(x.deep_view()[i] == y.deep_view()[i]);
520        }
521    }
522}
523
524pub broadcast axiom fn axiom_vec_has_resolved<T>(vec: Vec<T>, i: int)
525    ensures
526        0 <= i < vec.len() ==> #[trigger] has_resolved::<Vec<T>>(vec) ==> has_resolved(
527            #[trigger] vec@[i],
528        ),
529;
530
531pub broadcast group group_vec_axioms {
532    axiom_spec_len,
533    axiom_vec_index_decreases,
534    vec_clone_deep_view_proof,
535    axiom_spec_into_iter,
536    axiom_vec_has_resolved,
537}
538
539} // verus!
vstd/std_specs/vec.rs

vstd/std_specs/
vec.rs
