vstd/std_specs/
iter.rs

1use super::super::prelude::*;
2use super::super::seq::{
3    group_seq_lemmas, lemma_seq_empty, lemma_seq_subrange_index, lemma_seq_subrange_len,
4};
5use core::iter::{Filter, FromIterator, Iterator, Rev, Skip, Take, Zip};
6
7use verus as verus_skip_verusfmt;
8verus_skip_verusfmt! {
9
10#[verifier::external_trait_specification]
11#[verifier::external_trait_extension(IteratorSpec via IteratorSpecImpl)]
12pub trait ExIterator {
13    type ExternalTraitSpecificationFor: Iterator;
14
15    type Item;
16
17    /// This iterator obeys the specifications below on `next`,
18    /// expressed in terms of prophetic spec functions.
19    /// Only iterators that terminate (i.e., eventually return None
20    /// and then continue to return None) should use this interface.
21    spec fn obeys_prophetic_iter_laws(&self) -> bool;
22
23    /// Sequence of items that will (eventually) be returned
24    #[verifier::prophetic]
25    spec fn remaining(&self) -> Seq<Self::Item>;
26
27    /// Does this iterator complete with a `None` after the above sequence?
28    /// (As opposed to hanging indefinitely on a `next()` call)
29    /// Trivially true for most iterators but important for iterators
30    /// that apply an exec closure that may not terminate.
31    #[verifier::prophetic]
32    spec fn will_return_none(&self) -> bool;
33
34    /// Advances the iterator and returns the next value.
35    fn next(&mut self) -> (ret: Option<Self::Item>)
36        ensures
37            // The iterator consistently obeys, completes, and decreases throughout its lifetime
38            final(self).obeys_prophetic_iter_laws() == old(self).obeys_prophetic_iter_laws(),
39            final(self).obeys_prophetic_iter_laws() ==> final(self).will_return_none() == old(self).will_return_none(),
40            final(self).obeys_prophetic_iter_laws() ==> (old(self).decrease() is Some <==> final(self).decrease() is Some),
41            // `next` pops the head of the prophesized remaining(), or returns None
42            final(self).obeys_prophetic_iter_laws() ==>
43            ({
44                if old(self).remaining().len() > 0 {
45                    &&& final(self).remaining() == old(self).remaining().drop_first()
46                    &&& ret == Some(old(self).remaining()[0])
47                } else {
48                    final(self).remaining() == old(self).remaining() && ret == None && final(self).will_return_none()
49                }
50            }),
51            // If the iterator isn't done yet, then it successfully decreases its metric (if any)
52            final(self).obeys_prophetic_iter_laws() && old(self).remaining().len() > 0 && final(self).decrease() is Some ==>
53                decreases_to!(old(self).decrease()->0 => final(self).decrease()->0),
54    ;
55
56    /******* Mechanisms that support ergonomic `for` loops *********/
57
58    /// Value used by default for the decreases clause when no explicit decreases clause is provided
59    /// (the user can override this with an explicit decreases clause).
60    /// If there's no appropriate metric to decrease, this can return None,
61    /// and the user will have to provide an explicit decreases clause.
62    spec fn decrease(&self) -> Option<nat>;
63
64    // If we can make a useful guess as to what the i-th value will be, return it.
65    // Otherwise, return None.
66    spec fn peek(&self, index: int) -> Option<Self::Item>;
67
68
69
70    /******* Provided methods (in alphabetical order) *********/
71    // For provided method that returns a new iterator (e.g., filter, map, or zip),
72    // ideally we would write their postconditions here.  However, this requires
73    // a trait bound of `Self: IteratorSpec`, which introduces a cyclic dependency.
74    // Hence, we introduce a layer of indirection via an uninterp spec function that
75    // describes the postconditions.
76
77    // TODO: The Rust implementations of `all` and `any` depend on a correct implementation of `try_fold`
78    //       For now, we assume obeys_prophetic_iter_laws() entails such an implementation, but we should
79    //       eventually constrain implementations of `try_fold` to actually be correct enough to uphold the specs below.
80
81    fn all<F>(&mut self, f: F) -> (r: bool)
82        where Self: Sized,
83            F: FnMut(Self::Item) -> bool
84        requires
85            forall |k| #![auto] 0 <= k < self.remaining().len() ==> call_requires(f, (self.remaining()[k], )),
86        ensures
87            // The iterator consistently obeys, completes, and decreases throughout its lifetime
88            final(self).obeys_prophetic_iter_laws() == old(self).obeys_prophetic_iter_laws(),
89            final(self).obeys_prophetic_iter_laws() ==> final(self).will_return_none() == old(self).will_return_none(),
90            final(self).obeys_prophetic_iter_laws() ==> (old(self).decrease() is Some <==> final(self).decrease() is Some),
91            final(self).obeys_prophetic_iter_laws() ==> {
92                final(self).remaining().is_suffix_of(old(self).remaining())
93            },
94            // If all returns true, then the iterator has no remaining elements,
95            // and the predicate was true for all of the original iterator's elements.
96            final(self).obeys_prophetic_iter_laws() && r ==> {
97                &&& final(self).remaining().len() == 0
98                &&& forall |i| 0 <= i < old(self).remaining().len() ==>
99                    f.ensures((#[trigger] old(self).remaining()[i],), true)
100            },
101            // If all returns false, then there is some element for which the
102            // predicate was false, and all previous elements satisfied the predicate.
103            final(self).obeys_prophetic_iter_laws() && !r ==> {
104                let idx = old(self).remaining().len() - final(self).remaining().len() - 1;
105                {
106                    // The failing element was consumed, so the remaining sequence strictly shrank
107                    &&& final(self).remaining().len() < old(self).remaining().len()
108                    &&& f.ensures((old(self).remaining()[idx],), false)
109                    &&& forall |i| 0 <= i < idx ==>
110                        f.ensures((#[trigger] old(self).remaining()[i],), true)
111                }
112            };
113
114    fn any<F>(&mut self, f: F) -> (r: bool)
115        where Self: Sized,
116            F: FnMut(Self::Item) -> bool
117        requires
118            forall |k| #![auto] 0 <= k < self.remaining().len() ==> call_requires(f, (self.remaining()[k], )),
119        ensures
120            // The iterator consistently obeys, completes, and decreases throughout its lifetime
121            final(self).obeys_prophetic_iter_laws() == old(self).obeys_prophetic_iter_laws(),
122            final(self).obeys_prophetic_iter_laws() ==> final(self).will_return_none() == old(self).will_return_none(),
123            final(self).obeys_prophetic_iter_laws() ==> (old(self).decrease() is Some <==> final(self).decrease() is Some),
124            final(self).obeys_prophetic_iter_laws() ==> {
125                final(self).remaining().is_suffix_of(old(self).remaining())
126            },
127            // If any returns false, then the iterator has no remaining elements,
128            // and the predicate was false for all of the original iterator's elements.
129            final(self).obeys_prophetic_iter_laws() && !r ==> {
130                &&& final(self).remaining().len() == 0
131                &&& forall |i| 0 <= i < old(self).remaining().len() ==>
132                    f.ensures((#[trigger] old(self).remaining()[i],), false)
133            },
134            // If any returns true, then there is some element that satisfied the predicate,
135            // and all previous elements did not satisfy the predicate.
136            final(self).obeys_prophetic_iter_laws() && r ==> {
137                let idx = old(self).remaining().len() - final(self).remaining().len() - 1;
138                {
139                    // The satisfying element was consumed, so the remaining sequence strictly shrank
140                    &&& final(self).remaining().len() < old(self).remaining().len()
141                    &&& f.ensures((old(self).remaining()[idx],), true)
142                    &&& forall |i| 0 <= i < idx ==>
143                        f.ensures((#[trigger] old(self).remaining()[i],), false)
144                }
145            };
146
147    fn collect<B>(self) -> (collection: B)
148        where
149            B: FromIterator<Self::Item>,
150            Self: Sized,
151        ensures
152            self.obeys_prophetic_iter_laws() ==>
153                self.will_return_none() &&
154                FromIteratorSpec::from_iter_ensures(self.remaining(), collection),
155    ;
156
157    fn filter<P>(self, predicate: P) -> (r: core::iter::Filter<Self, P>)
158        where
159            Self: Sized,
160            P: FnMut(&Self::Item) -> bool,
161        requires
162            // `filter`'s implementation loops over the inner iterator until the predicate accepts an element,
163            // so it needs a decreases metric to prove termination.
164            self.decrease() is Some,
165            forall |k| #![auto] 0 <= k < self.remaining().len() ==> call_requires(predicate, (&self.remaining()[k], )),
166        ensures
167            self.obeys_prophetic_iter_laws() ==> filter_post(self, predicate, r),
168    ;
169
170    fn find<P>(&mut self, predicate: P) -> (r: Option<Self::Item>)
171        where Self: Sized,
172            P: FnMut(&Self::Item) -> bool
173        requires
174            forall |k| #![auto] 0 <= k < self.remaining().len() ==> call_requires(predicate, (&self.remaining()[k], )),
175        ensures
176            // The iterator consistently obeys, completes, and decreases throughout its lifetime
177            final(self).obeys_prophetic_iter_laws() == old(self).obeys_prophetic_iter_laws(),
178            final(self).obeys_prophetic_iter_laws() ==> final(self).will_return_none() == old(self).will_return_none(),
179            final(self).obeys_prophetic_iter_laws() ==> (old(self).decrease() is Some <==> final(self).decrease() is Some),
180            final(self).obeys_prophetic_iter_laws() ==> {
181                final(self).remaining().is_suffix_of(old(self).remaining())
182            },
183            // If find returns None, then the iterator has no remaining
184            // elements, and the predicate was false for all of the original
185            // iterator's elements.
186            final(self).obeys_prophetic_iter_laws() && r.is_none() ==> {
187                &&& final(self).remaining().len() == 0
188                &&& forall |i| 0 <= i < old(self).remaining().len() ==>
189                    predicate.ensures((#[trigger]&old(self).remaining()[i],), false)
190            },
191            // If find returns Some, then the returned value satisfies the
192            // predicate, and all previous elements did not satisfy the
193            // predicate.
194            final(self).obeys_prophetic_iter_laws() && r.is_some() ==> {
195                let idx = old(self).remaining().len() - final(self).remaining().len() - 1;
196                {
197                    &&& 0 <= final(self).remaining().len() < old(self).remaining().len()
198                    &&& predicate.ensures((&r.unwrap(),), true)
199                    &&& old(self).remaining()[idx] == r.unwrap()
200                    &&& forall |i| 0 <= i < idx ==>
201                        predicate.ensures((#[trigger] &old(self).remaining()[i],), false)
202                }
203            };
204
205    fn map<B, F>(self, f: F) -> (r: core::iter::Map<Self, F>)
206        where
207            Self: Sized,
208            F: FnMut(Self::Item) -> B,
209        requires
210            forall |k| #![auto] 0 <= k < self.remaining().len() ==> call_requires(f, (self.remaining()[k], )),
211        ensures
212            self.obeys_prophetic_iter_laws() ==> map_post(self, f, r),
213    ;
214
215    fn rev(self) -> (r: Rev<Self>)
216        where Self: Sized,
217        ensures
218            self.obeys_prophetic_iter_laws() ==> rev_post(self, r),
219    ;
220
221    fn skip(self, n: usize) -> (s: Skip<Self>)
222        where Self: Sized,
223        ensures
224            self.obeys_prophetic_iter_laws() ==> skip_post(self, n, s),
225    ;
226
227    fn take(self, n: usize) -> (t: Take<Self>)
228        where Self: Sized,
229        ensures
230            self.obeys_prophetic_iter_laws() ==> take_post(self, n, t),
231    ;
232
233    #[verifier::impls_cannot_extend_spec]
234    fn zip<U>(self, other: U) -> (r: Zip<Self, <U as IntoIterator>::IntoIter>)
235        where
236            Self: Sized,
237            U: IntoIterator,
238        ensures
239            self.obeys_prophetic_iter_laws() ==> zip_post(self, other, r),
240    ;
241}
242
243#[verifier::external_trait_specification]
244#[verifier::external_trait_extension(DoubleEndedIteratorSpec via DoubleEndedIteratorSpecImpl)]
245pub trait ExDoubleEndedIterator : Iterator {
246    type ExternalTraitSpecificationFor: DoubleEndedIterator;
247
248    // In the specs below, we write out the type parameters explicitly, rather than using the more concise form,
249    // e.g., `final(self).obeys_prophetic_iter_laws()`.  If we use the latter, then Rust elaborates it to
250    // `(&final(self)).obeys_prophetic_iter_laws()`, which means the type of the argument is `& &mut Self`,
251    // which means the type argument inferred for `obeys_prophetic_iter_laws` is `&mut Self`.
252    // This happens because of the existing Rust [trait impl](https://doc.rust-lang.org/std/iter/trait.Iterator.html#impl-Iterator-for-%26mut+I):
253    // ```
254    // impl<I> Iterator for &mut I
255    // where
256    //     I: Iterator + ?Sized,[4:21 AM]
257    // ```
258    fn next_back(&mut self) -> (ret: Option<<Self as core::iter::Iterator>::Item>)
259        ensures
260            // The iterator consistently obeys, completes, and decreases throughout its lifetime
261            <Self as IteratorSpec>::obeys_prophetic_iter_laws(final(self)) == <Self as IteratorSpec>::obeys_prophetic_iter_laws(old(self)),
262            <Self as IteratorSpec>::obeys_prophetic_iter_laws(final(self)) ==> <Self as IteratorSpec>::will_return_none(final(self)) == <Self as IteratorSpec>::will_return_none(old(self)),
263            <Self as IteratorSpec>::obeys_prophetic_iter_laws(final(self)) ==> (<Self as IteratorSpec>::decrease(old(self)) is Some <==> <Self as IteratorSpec>::decrease(final(self)) is Some),
264            // `next` pops the tail of the prophesized remaining(), or returns None
265            <Self as IteratorSpec>::obeys_prophetic_iter_laws(final(self)) ==>
266            ({
267                if <Self as IteratorSpec>::remaining(old(self)).len() > 0 {
268                    <Self as IteratorSpec>::remaining(final(self)) == <Self as IteratorSpec>::remaining(old(self)).drop_last()
269                        && ret == Some(<Self as IteratorSpec>::remaining(old(self)).last())
270                } else {
271                    <Self as IteratorSpec>::remaining(final(self)) == <Self as IteratorSpec>::remaining(old(self)) && ret == None && <Self as IteratorSpec>::will_return_none(final(self))
272                }
273            }),
274            // If the iterator isn't done yet, then it successfully decreases its metric (if any)
275            <Self as IteratorSpec>::obeys_prophetic_iter_laws(final(self)) && <Self as IteratorSpec>::remaining(old(self)).len() > 0 && <Self as IteratorSpec>::decrease(final(self)) is Some ==>
276                <Self as IteratorSpec>::decrease(old(self))->0 > <Self as IteratorSpec>::decrease(final(self))->0,
277    ;
278
279    /******* Mechanisms that support ergonomic `for` loops *********/
280
281    // If we can make a useful guess as to what the i-th value from the back will be, return it.
282    // Otherwise, return None.
283    spec fn peek_back(&self, index: int) -> Option<Self::Item>;
284}
285
286#[verifier::external_trait_specification]
287#[verifier::external_trait_extension(ExactSizeIteratorSpec via ExactSizeIteratorSpecImpl)]
288pub trait ExExactSizeIterator: Iterator {
289    type ExternalTraitSpecificationFor: ExactSizeIterator;
290
291    // An `ExactSizeIterator` can specify its length non-prophetically,
292    // i.e., without using `self.remaining().len()`.
293    spec fn exact_len(&self) -> usize;
294
295    fn len(&self) -> (len: usize)
296        ensures
297            self.obeys_prophetic_iter_laws() ==> len == self.exact_len() == self.remaining().len();
298}
299
300/********************************************************************************
301 * Definitions for `IntoIterator` and `FromIterator``
302 ********************************************************************************/
303#[verifier::external_trait_specification]
304pub trait ExIntoIterator {
305    type ExternalTraitSpecificationFor: core::iter::IntoIterator;
306
307    type Item;
308    type IntoIter: Iterator<Item = Self::Item>;
309
310    fn into_iter(self) -> Self::IntoIter;
311}
312
313pub open spec fn iter_into_iter_spec<I: Iterator>(i: I) -> I {
314    i
315}
316
317#[verifier::when_used_as_spec(iter_into_iter_spec)]
318pub assume_specification<I: Iterator>[ <I as IntoIterator>::into_iter ](i: I) -> (r: I)
319    ensures
320        r == i,
321;
322
323// Uninterpreted function representing the sequence of elements that will be
324// produced by the iterator obtained from an IntoIterator value.
325// This avoids requiring IteratorSpec bounds in from_iter's ensures clause.
326pub uninterp spec fn into_iter_remaining<A, T>(iter: T) -> Seq<A>;
327
328// Connects into_iter_remaining to remaining() for types implementing Iterator + IteratorSpec.
329// This allows callers of from_iter to relate the result to the iterator's remaining elements.
330pub broadcast axiom fn axiom_from_iterator_ensures<A, I: Iterator<Item = A> + IteratorSpec>(iter: I)
331    ensures
332        #[trigger] into_iter_remaining::<A, I>(iter) == iter.remaining(),
333;
334
335#[verifier::external_trait_specification]
336#[verifier::external_trait_extension(FromIteratorSpec via FromIteratorSpecImpl)]
337pub trait ExFromIterator<A>: Sized {
338    type ExternalTraitSpecificationFor: FromIterator<A>;
339
340    spec fn from_iter_ensures(remaining: Seq<A>, s: Self) -> bool;
341
342    #[verifier::impls_cannot_extend_spec]
343    fn from_iter<T>(iter: T) -> (s: Self)
344       where T: IntoIterator<Item = A>
345        ensures
346            Self::from_iter_ensures(into_iter_remaining(iter), s),
347    ;
348}
349
350/********************************************************************************
351 * Definitions for `&mut I`
352 ********************************************************************************/
353// Forwarding spec impl for the Rust-supplied blanket `impl<I> Iterator for &mut I`.
354// Without this, bare method-call syntax on a `i: &mut I` receiver (e.g. `i.remaining()`)
355// resolves to these (otherwise uninterpreted) functions on `&mut I` rather than on `I`,
356// silently disconnecting clients from `I`'s actual specs.
357impl <I> IteratorSpecImpl for &mut I
358    where I: Iterator {
359    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
360        <I as IteratorSpec>::obeys_prophetic_iter_laws(*self)
361    }
362
363    #[verifier::prophetic]
364    open spec fn remaining(&self) -> Seq<Self::Item> {
365        <I as IteratorSpec>::remaining(*self)
366    }
367
368    #[verifier::prophetic]
369    open spec fn will_return_none(&self) -> bool {
370        <I as IteratorSpec>::will_return_none(*self)
371    }
372
373    open spec fn decrease(&self) -> Option<nat> {
374        <I as IteratorSpec>::decrease(*self)
375    }
376
377    open spec fn peek(&self, index: int) -> Option<Self::Item> {
378        <I as IteratorSpec>::peek(*self, index)
379    }
380}
381
382/********************************************************************************
383 * Definitions for `filter()`
384 ********************************************************************************/
385#[verifier::external_body]
386#[verifier::external_type_specification]
387#[verifier::reject_recursive_types(I)]
388#[verifier::reject_recursive_types(F)]
389pub struct ExFilter<I, F>(Filter<I, F>);
390
391// Ghost accessor for the inner iterator
392pub uninterp spec fn filter_iter<I, F>(r: Filter<I, F>) -> I;
393
394// Ghost accessor for the inner predicate
395pub uninterp spec fn filter_fun<I, F>(r: Filter<I, F>) -> F;
396
397// Ghost accessor for the sequence of predicate decisions made for the (prefix of) the
398// inner iterator's elements
399#[verifier::prophetic]
400pub uninterp spec fn filter_keep<I, F>(r: Filter<I, F>) -> Seq<bool>;
401
402// Define Iter::filter's postcondition
403pub uninterp spec fn filter_post<I, F>(i: I, f: F, r: Filter<I, F>) -> bool;
404
405pub broadcast axiom fn filter_postcondition<I, F>(i: I, f: F, r: core::iter::Filter<I, F>)
406    where
407        I: IteratorSpec,
408        F: FnMut(&I::Item) -> bool,
409    requires
410        i.obeys_prophetic_iter_laws(),
411        i.decrease() is Some,
412        forall |k| #![auto] 0 <= k < i.remaining().len() ==> call_requires(f, (&i.remaining()[k], )),
413        #[trigger] filter_post(i, f, r),
414    ensures
415        {
416            let keep = filter_keep(r);
417            {
418            // `keep` records, for each inspected inner element, the predicate's decision
419            &&& keep.len() <= i.remaining().len()
420            &&& forall |j| 0 <= j < keep.len() ==> call_ensures(f, (&i.remaining()[j],), #[trigger] keep[j])
421            // Completeness: Every inner element the predicate keeps is retained and in order.
422            &&& IteratorSpec::remaining(&r) == i.remaining()[..keep.len()].filter_index(|j: int| keep[j])
423            // The two facts below follow from the `filter_index` above; we expose them directly for convenience.
424            &&& IteratorSpec::remaining(&r).len() <= i.remaining().len()
425            &&& forall |k| #![trigger IteratorSpec::remaining(&r)[k]] 0 <= k < IteratorSpec::remaining(&r).len() ==>
426                    exists |j| 0 <= j < i.remaining().len()
427                        && IteratorSpec::remaining(&r)[k] == #[trigger] i.remaining()[j]
428                        && call_ensures(f, (&i.remaining()[j],), true)
429            &&& IteratorSpec::will_return_none(&r) ==> i.will_return_none() && keep.len() == i.remaining().len()
430            &&& IteratorSpec::decrease(&r) is Some == i.decrease() is Some
431            &&& filter_iter(r) == i
432            &&& filter_fun(r) == f
433            }
434        },
435;
436
437// See examples/iterators/map_and_filter.rs for a verified version of this interface.
438// Any changes here should first be verified over there.
439impl <I, P> IteratorSpecImpl for core::iter::Filter<I, P>
440    where
441        I: Iterator + IteratorSpec,
442        P: FnMut(&I::Item) -> bool,
443{
444    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
445        filter_iter(*self).obeys_prophetic_iter_laws()
446    }
447
448    #[verifier::prophetic]
449    uninterp spec fn remaining(&self) -> Seq<Self::Item>;
450
451    #[verifier::prophetic]
452    uninterp spec fn will_return_none(&self) -> bool;
453
454    uninterp spec fn decrease(&self) -> Option<nat>;
455
456    // `filter` cannot make a useful static guess about which element will be returned at a given index,
457    // since that depends on prophetic evaluations of the predicate.
458    open spec fn peek(&self, index: int) -> Option<Self::Item> {
459        None
460    }
461}
462
463/********************************************************************************
464 * Definitions for `map()`
465 ********************************************************************************/
466#[verifier::external_body]
467#[verifier::external_type_specification]
468#[verifier::reject_recursive_types(I)]
469#[verifier::reject_recursive_types(F)]
470pub struct ExMap<I, F>(core::iter::Map<I, F>);
471
472// Ghost accessor for the inner iterator
473pub uninterp spec fn map_iter<I, F>(r: core::iter::Map<I, F>) -> I;
474
475// Ghost accessor for the inner function
476pub uninterp spec fn map_fun<I, F>(r: core::iter::Map<I, F>) -> F;
477
478// Define Iter::map's postcondition
479pub uninterp spec fn map_post<I, F>(i: I, f: F, r: core::iter::Map<I, F>) -> bool;
480
481pub broadcast axiom fn map_postcondition<I, F>(i: I, f: F, r: core::iter::Map<I, F>)
482    where
483        I: IteratorSpec,
484        F: FnMut<(I::Item,)>,
485    requires
486        i.obeys_prophetic_iter_laws(),
487        #[trigger] map_post(i, f, r),
488    ensures
489        IteratorSpec::remaining(&r).len() <= i.remaining().len(),
490        forall |k| #![auto] 0 <= k < IteratorSpec::remaining(&r).len() ==> call_ensures(f, (i.remaining()[k],), IteratorSpec::remaining(&r)[k]),
491        IteratorSpec::will_return_none(&r) ==> i.will_return_none() && IteratorSpec::remaining(&r).len() == i.remaining().len(),
492        IteratorSpec::decrease(&r) is Some == i.decrease() is Some,
493        map_iter(r) == i,
494        map_fun(r) == f,
495;
496
497// See examples/iterators/map_and_filter.rs for a verified version of this interface.
498// Any changes here should first be verified over there.
499impl <B, I, F> IteratorSpecImpl for core::iter::Map<I, F>
500    where
501        I: Iterator + IteratorSpec,
502        F: FnMut(I::Item) -> B,
503{
504
505    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
506        map_iter(*self).obeys_prophetic_iter_laws()
507    }
508
509    #[verifier::prophetic]
510    uninterp spec fn remaining(&self) -> Seq<B>;
511
512    #[verifier::prophetic]
513    uninterp spec fn will_return_none(&self) -> bool;
514
515    uninterp spec fn decrease(&self) -> Option<nat>;
516
517    open spec fn peek(&self, index: int) -> Option<B> {
518        match map_iter(*self).peek(index) {
519            Some(v) => {
520                let x = choose |x| map_fun(*self).ensures((v,), x);
521                Some(x)
522            }
523            None => None,
524        }
525    }
526}
527
528impl <B, I, F> DoubleEndedIteratorSpecImpl for core::iter::Map<I, F>
529    where I: DoubleEndedIterator + IteratorSpec,
530          F: FnMut(I::Item) -> B,
531{
532    open spec fn peek_back(&self, index: int) -> Option<B> {
533        match map_iter(*self).peek_back(index) {
534            Some(v) => {
535                let x = choose |x| map_fun(*self).ensures((v,), x);
536                Some(x)
537            }
538            None => None,
539        }
540    }
541}
542
543/********************************************************************************
544 * Definitions for `rev()`
545 ********************************************************************************/
546#[verifier::external_body]
547#[verifier::external_type_specification]
548#[verifier::reject_recursive_types(I)]
549pub struct ExRev<I>(Rev<I>);
550
551// Ghost accessor for the inner iterator
552pub uninterp spec fn rev_iter<I>(r: Rev<I>) -> I;
553
554// Define Iter::rev's postcondition
555pub uninterp spec fn rev_post<I>(i: I, r: Rev<I>) -> bool;
556
557pub broadcast axiom fn rev_postcondition<I: DoubleEndedIteratorSpec>(i: I, r: Rev<I>)
558    requires
559        #[trigger] rev_post(i, r),
560    ensures
561        IteratorSpec::remaining(&r) == IteratorSpec::remaining(&i).reverse(),
562        IteratorSpec::will_return_none(&r) == i.will_return_none(),
563        IteratorSpec::decrease(&r) is Some == i.decrease() is Some,
564;
565
566impl <I> IteratorSpecImpl for Rev<I>
567    where I: DoubleEndedIterator + DoubleEndedIteratorSpec {
568    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
569        rev_iter(*self).obeys_prophetic_iter_laws()
570    }
571
572    #[verifier::prophetic]
573    closed spec fn remaining(&self) -> Seq<Self::Item> {
574        rev_iter(*self).remaining().reverse()
575    }
576
577    #[verifier::prophetic]
578    closed spec fn will_return_none(&self) -> bool {
579        rev_iter(*self).will_return_none()
580    }
581
582    closed spec fn decrease(&self) -> Option<nat> {
583        rev_iter(*self).decrease()
584    }
585
586    open spec fn peek(&self, index: int) -> Option<Self::Item> {
587        rev_iter(*self).peek_back(index)
588    }
589}
590
591impl <I> DoubleEndedIteratorSpecImpl for Rev<I>
592    where I: DoubleEndedIterator + IteratorSpec {
593
594    open spec fn peek_back(&self, index: int) -> Option<Self::Item> {
595        rev_iter(*self).peek(index)
596    }
597}
598
599/********************************************************************************
600 * Definitions for `skip()`
601 ********************************************************************************/
602#[verifier::external_body]
603#[verifier::external_type_specification]
604#[verifier::reject_recursive_types(I)]
605pub struct ExSkip<I>(Skip<I>);
606
607// Ghost accessor for the inner iterator
608pub uninterp spec fn skip_iter<I>(s: Skip<I>) -> I;
609
610// Ghost accessor for the initial count of items to skip
611pub uninterp spec fn skip_init_n<I>(s: Skip<I>) -> usize;
612
613// Define Iter::skip's postcondition
614pub uninterp spec fn skip_post<I>(i: I, n: usize, s: Skip<I>) -> bool;
615
616pub broadcast axiom fn skip_postcondition<I: IteratorSpec>(i: I, n: usize, r: Skip<I>)
617    requires
618        i.obeys_prophetic_iter_laws(),
619        #[trigger] skip_post(i, n, r),
620    ensures
621        IteratorSpec::remaining(&r) == if i.remaining().len() < n { Seq::empty() } else { i.remaining()[n..] },
622        skip_iter(r) == i,
623        skip_init_n(r) == n,
624        IteratorSpec::will_return_none(&r) <==> i.will_return_none(),
625        IteratorSpec::decrease(&r) is Some == i.decrease() is Some,
626;
627
628impl <I> IteratorSpecImpl for Skip<I>
629    where I: Iterator {
630    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
631        skip_iter(*self).obeys_prophetic_iter_laws()
632    }
633
634    #[verifier::prophetic]
635    uninterp spec fn remaining(&self) -> Seq<Self::Item>;
636
637    #[verifier::prophetic]
638    uninterp spec fn will_return_none(&self) -> bool;
639
640    uninterp spec fn decrease(&self) -> Option<nat>;
641
642    open spec fn peek(&self, index: int) -> Option<Self::Item> {
643        skip_iter(*self).peek(skip_init_n(*self) + index)
644    }
645}
646
647impl <I> DoubleEndedIteratorSpecImpl for Skip<I>
648    where I: DoubleEndedIteratorSpec + ExactSizeIteratorSpec
649{
650    open spec fn peek_back(&self, index: int) -> Option<Self::Item> {
651        // Skip only drops elements from the front, so the back of the skipped
652        // sequence coincides with the back of the inner iterator, as long as
653        // `index` stays within the (un-skipped) remaining elements.
654        let len = skip_iter(*self).exact_len();
655        if len < skip_init_n(*self) || index >= len - skip_init_n(*self) {
656            None
657        } else {
658            skip_iter(*self).peek_back(index)
659        }
660    }
661}
662
663/********************************************************************************
664 * Definitions for `take()`
665 ********************************************************************************/
666#[verifier::external_body]
667#[verifier::external_type_specification]
668#[verifier::reject_recursive_types(I)]
669pub struct ExTake<I>(Take<I>);
670
671// Ghost accessor for the inner iterator
672pub uninterp spec fn take_iter<I>(r: Take<I>) -> I;
673
674// Ghost accessor for the count
675pub uninterp spec fn take_count<I>(r: Take<I>) -> usize;
676
677// Define Iter::take's postcondition
678pub uninterp spec fn take_post<I>(i: I, n: usize, t: Take<I>) -> bool;
679
680pub broadcast axiom fn take_postcondition<I: IteratorSpec>(i: I, n: usize, r: Take<I>)
681    requires
682        i.obeys_prophetic_iter_laws(),
683        #[trigger] take_post(i, n, r),
684    ensures
685        IteratorSpec::remaining(&r) == if i.remaining().len() < n { i.remaining() } else { i.remaining()[..n] },
686        take_iter(r) == i,
687        take_count(r) == n,
688        IteratorSpec::will_return_none(&r) <==> i.will_return_none() || i.remaining().len() >= n,
689        IteratorSpec::decrease(&r) is Some,
690;
691
692// See examples/iterators/take.rs for a verified version of this interface.
693// Any changes here should first be verified over there.
694impl <I> IteratorSpecImpl for Take<I>
695    where I: Iterator {
696    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
697        take_iter(*self).obeys_prophetic_iter_laws()
698    }
699
700    #[verifier::prophetic]
701    uninterp spec fn remaining(&self) -> Seq<Self::Item>;
702
703    #[verifier::prophetic]
704    uninterp spec fn will_return_none(&self) -> bool;
705
706    uninterp spec fn decrease(&self) -> Option<nat>;
707
708    open spec fn peek(&self, index: int) -> Option<Self::Item> {
709        take_iter(*self).peek(index)
710    }
711}
712
713impl <I> DoubleEndedIteratorSpecImpl for Take<I>
714    where I: DoubleEndedIteratorSpec + ExactSizeIteratorSpec
715{
716    open spec fn peek_back(&self, index: int) -> Option<Self::Item> {
717        let len = take_iter(*self).exact_len();
718        if len < take_count(*self) {
719            None
720        } else {
721            take_iter(*self).peek_back(len - take_count(*self) - index - 1)
722        }
723    }
724}
725
726/********************************************************************************
727 * Definitions for `zip()`
728 ********************************************************************************/
729#[verifier::external_body]
730#[verifier::external_type_specification]
731#[verifier::reject_recursive_types(A)]
732#[verifier::reject_recursive_types(B)]
733pub struct ExZip<A, B>(Zip<A, B>);
734
735// Ghost accessor for the first inner iterator
736pub uninterp spec fn zip_iter_fst<A, B>(z: Zip<A, B>) -> A;
737
738// Ghost accessor for the second inner iterator
739pub uninterp spec fn zip_iter_snd<A, B>(z: Zip<A, B>) -> B;
740
741impl<A, B> IteratorSpecImpl for Zip<A, B>
742    where A: Iterator + IteratorSpec, B: Iterator + IteratorSpec
743{
744    open spec fn obeys_prophetic_iter_laws(&self) -> bool {
745        &&& zip_iter_fst(*self).obeys_prophetic_iter_laws()
746        &&& zip_iter_snd(*self).obeys_prophetic_iter_laws()
747    }
748
749    #[verifier::prophetic]
750    closed spec fn remaining(&self) -> Seq<Self::Item> {
751        zip_iter_fst(*self).remaining().zip_truncate(zip_iter_snd(*self).remaining())
752    }
753
754    #[verifier::prophetic]
755    closed spec fn will_return_none(&self) -> bool {
756        zip_iter_fst(*self).will_return_none() || zip_iter_snd(*self).will_return_none()
757    }
758
759    closed spec fn decrease(&self) -> Option<nat> {
760        match (zip_iter_fst(*self).decrease(), zip_iter_snd(*self).decrease()) {
761            (Some(a), Some(b)) => if a <= b { Some(a) } else { Some(b) },
762            (Some(a), None) => Some(a),
763            (None, Some(b)) => Some(b),
764            (None, None) => None,
765        }
766    }
767
768    open spec fn peek(&self, index: int) -> Option<Self::Item> {
769        match (zip_iter_fst(*self).peek(index), zip_iter_snd(*self).peek(index)) {
770            (Some(a), Some(b)) => Some((a, b)),
771            _ => None,
772        }
773    }
774}
775
776// Define Iter::zip's postcondition
777pub uninterp spec fn zip_post<I, U, Z>(i: I, other: U, r: Z) -> bool;
778
779pub broadcast axiom fn zip_postcondition<I, U>(i: I, other: U, r: Zip<I, <U as IntoIterator>::IntoIter>)
780    where
781            I: Sized + IteratorSpec,
782            U: IntoIterator, //Spec,
783    requires
784        i.obeys_prophetic_iter_laws(),
785        #[trigger] zip_post(i, other, r),
786    ensures
787        call_ensures(U::into_iter, (other,), zip_iter_snd(r)),
788        zip_iter_fst(r) == i,
789        IteratorSpec::remaining(&r) == i.remaining().zip_truncate(zip_iter_snd(r).remaining()),
790        IteratorSpec::will_return_none(&r) ==> i.will_return_none() || zip_iter_snd(r).will_return_none(),
791        IteratorSpec::decrease(&r) is Some == (i.decrease() is Some || zip_iter_snd(r).decrease() is Some),
792;
793
794/********************************************************************************
795 * Defines a convenient wrapper type that bundles state and invariants needed
796 * for ergonomic for-loop support.
797 ********************************************************************************/
798
799pub struct VerusForLoopWrapper<I: Iterator> {
800    pub index: Ghost<int>,
801    pub snapshot: Ghost<I>,
802    pub iter: I,
803    pub history: Ghost<Seq<I::Item>>,
804}
805
806impl <I: Iterator> VerusForLoopWrapper<I> {
807    #[verifier::prophetic]
808    pub open spec fn seq(self) -> Seq<I::Item> {
809        self.snapshot@.remaining()
810    }
811
812    // Keep the interface for history and seq the same
813    pub open spec fn history(self) -> Seq<I::Item> {
814        self.history@
815    }
816
817    pub open spec fn index(self) -> int {
818        self.index@
819    }
820
821    /// These properties help maintain the properties in wf,
822    /// but they don't need to be exposed to the client
823    #[verifier::prophetic]
824    pub closed spec fn wf_inner(self) -> bool {
825        &&& self.iter.remaining().len() == self.seq().len() - self.index()
826        &&& forall |i| 0 <= i < self.iter.remaining().len() ==> #[trigger] self.iter.remaining()[i] == self.seq()[self.index() + i]
827        &&& self.iter.will_return_none() ==> self.snapshot@.will_return_none()
828    }
829
830    /// These properties are needed for the client code to verify
831    #[verifier::prophetic]
832    pub open spec fn wf(self) -> bool {
833        &&& 0 <= self.index() <= self.seq().len()
834        &&& self.wf_inner()
835        &&& self.iter.obeys_prophetic_iter_laws() ==> {
836                &&& self.history@.len() == self.index()
837                &&& forall |i| 0 <= i < self.index() ==> #[trigger] self.history@[i] == self.seq()[i]
838            }
839    }
840
841    /// Bundle the real iterator with its ghost state and loop invariants
842    pub fn new(iter: I) -> (s: Self)
843        ensures
844            s.index == 0,
845            s.snapshot == iter,
846            s.iter == iter,
847            s.history@ == Seq::<I::Item>::empty(),
848            s.wf(),
849    {
850        broadcast use lemma_seq_empty;
851        VerusForLoopWrapper {
852            index: Ghost(0),
853            snapshot: Ghost(iter),
854            iter,
855            history: Ghost(Seq::empty()),
856        }
857    }
858
859    /// Advance the underlying (real) iterator and prove
860    /// that the loop invariants are preserved.
861    pub fn next(&mut self) -> (ret: Option<I::Item>)
862        requires
863            old(self).wf(),
864        ensures
865            final(self).seq() == old(self).seq(),
866            final(self).index() == old(self).index() + if ret is Some { 1int } else { 0 },
867            final(self).snapshot == old(self).snapshot,
868            final(self).iter.obeys_prophetic_iter_laws() ==> final(self).wf(),
869            final(self).iter.obeys_prophetic_iter_laws() && ret is None ==>
870                final(self).snapshot@.will_return_none() && final(self).index() == final(self).seq().len(),
871            final(self).iter.obeys_prophetic_iter_laws() ==> (ret matches Some(r) ==>
872                r == old(self).seq()[old(self).index()]),
873            // History updates always hold
874            ret matches Some(i) ==> final(self).history@ == old(self).history@.push(i),
875            ret is None ==> final(self).history@ == old(self).history@,
876            // All of the standard Iterator::next guarantees still hold
877            exists |m: &mut I| #![auto] call_ensures(I::next, (m,), ret) && *m == old(self).iter && *final(m) == final(self).iter,
878    {
879        let ghost old_history = self.history@;
880        let ret = self.iter.next();
881        if ret.is_some() {
882            self.history = Ghost(old_history.push(ret->0));
883        }
884        proof {
885            broadcast use group_seq_lemmas;
886            if ret.is_some() {
887                self.index@ = self.index@ + 1;
888            }
889        }
890        ret
891    }
892}
893
894// Artificial function used when we desguar a for loop.
895// It helps bring the definition of `peek` into scope,
896// resulting in better automation for some proofs.
897pub open spec fn trigger_peek_implications<T>(x: T) -> bool { true }
898
899/********************************************************************************
900 * Definitions for the Step trait
901 ********************************************************************************/
902#[verifier::external_trait_specification]
903#[verifier::external_trait_extension(StepSpec via StepSpecImpl)]
904pub trait ExIterStep: Clone + PartialOrd + Sized {
905    type ExternalTraitSpecificationFor: core::iter::Step;
906
907    // REVIEW: it would be nice to be able to use SpecOrd::spec_lt (not yet supported)
908    // TODO: We should now be able to use cmp_spec or partial_cmp_spec here.
909    spec fn spec_is_lt(self, other: Self) -> bool;
910
911    spec fn spec_steps_between(self, end: Self) -> Option<usize>;
912
913    spec fn spec_steps_between_int(self, end: Self) -> int;
914
915    spec fn spec_forward_checked(self, count: usize) -> Option<Self>;
916
917    spec fn spec_forward_checked_int(self, count: int) -> Option<Self>;
918
919    spec fn spec_backward_checked(self, count: usize) -> Option<Self>;
920
921    spec fn spec_backward_checked_int(self, count: int) -> Option<Self>;
922}
923
924
925/********************************************************************************
926 * Collect our broadcast definitions
927 ********************************************************************************/
928
929pub broadcast group group_iter_axioms {
930    rev_postcondition,
931    zip_postcondition,
932    filter_postcondition,
933    take_postcondition,
934    skip_postcondition,
935    map_postcondition,
936}
937
938} // verus!
vstd/std_specs/iter.rs

vstd/std_specs/
iter.rs
