Add Challenges 20 21 22 for str Pattern and iter

doc/src/challenges/0020-str-pattern-pt1.md

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+# Challenge 20: Verify the safety of char-related functions in str::pattern
+
+- **Status:** Open
+- **Tracking Issue:** [#29](https://github.com/model-checking/verify-rust-std/issues/29)
+- **Start date:** *2025-03-07*
+- **End date:** *2025-10-17*
+- **Reward:** *? USD*
+
+-------------------
+
+
+### Context
+
+A majority portion in str library functions take a Pattern (https://doc.rust-lang.org/std/str/pattern/trait.Pattern.html) as input. 
+The functions which take Pattern as input turn the input str into a kind of Searcher which iterates over positions where the Pattern match, then perform their desired operations (split, find, ...).
+Those functions is implemented in (library/core/src/str/mod.rs), but the core of them is the searching algorithms which are implemented in (library/core/src/str/pattern.rs).
+
+# Details
+
+IMPORTANT NOTE: for this challenge, you can assume: 
+1. The safety and functional correctness of all functions in `slice` module 
+2. That all functions in (library/core/src/str/validations.rs) are functionally correct (consistent with the UTF8 encoding description in https://en.wikipedia.org/wiki/UTF-8) . 
+3. That all the Searchers in (library/core/src/str/iter.rs) are created by the into_searcher(_, haystack) with haystack is a valid utf8 string (str). You can assume any utf8 string property of haystack.
+
+Verify the safety of the functions in (library/core/src/str/pattern.rs) listed in the next section.
+
+The safety properties we are targeting are: 
+1. There is no UB happens when calling the functions after the Searcher is created.
+2. The impls of unsafe traits `Searcher` and `ReverseSearcher` satisfies the SAFETY condition stated in the file: 
+```
+/// The trait is marked unsafe because the indices returned by the
+/// [`next()`][Searcher::next] methods are required to lie on valid utf8
+/// boundaries in the haystack. This enables consumers of this trait to
+/// slice the haystack without additional runtime checks.
+```
+This property should hold for next_back() of `ReverseSearcher` too.
+
+
+### Success Criteria
+
+Verify the safety of the following functions in (library/core/src/str/pattern.rs) : `next`, `next_match`, `next_back`, `next_match_back`, `next_reject`, `next_back_reject`
+which are implemented for the following `Searcher`s:  `CharSearcher`, `MultiCharEqSearcher`, `CharArraySearcher` , `CharArrayRefSearcher`, `CharSliceSearcher`, `CharPredicateSearcher`.
+
+The verification is consider successful if for each `Searcher` above, you can specify a condition (a "type invariant") C and prove that:
+1. If the `Searcher` is created from any valid utf8 haystack, it satisfies C.
+2. If the `Searcher` satisfies C, it ensures the two safety properties mentioned in the previous section.
+3. If the `Searcher` satisfies C, after it calls any function above and gets modified, it still statisfies C.
+
+
+The verification must be unbounded---it must hold for inputs of arbitrary size.
+
+### List of UBs
+
+All proofs must automatically ensure the absence of the following undefined behaviors [ref](https://github.com/rust-lang/reference/blob/142b2ed77d33f37a9973772bd95e6144ed9dce43/src/behavior-considered-undefined.md):
+
+* Accessing (loading from or storing to) a place that is dangling or based on a misaligned pointer.
+* Reading from uninitialized memory except for padding or unions.
+* Mutating immutable bytes.
+* Producing an invalid value
+
+
+Note: All solutions to verification challenges need to satisfy the criteria established in the [challenge book](../general-rules.md)
+in addition to the ones listed above.

doc/src/challenges/0021-str-pattern-pt2.md

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+# Challenge 21: Verify the correctness of char-related functions in str::pattern
+
+- **Status:** Open
+- **Tracking Issue:** [#29](https://github.com/model-checking/verify-rust-std/issues/29)
+- **Start date:** *2025-03-07*
+- **End date:** *2025-10-17*
+- **Reward:** *? USD*
+
+-------------------
+
+
+### Context
+
+A majority portion in str library functions take a Pattern (https://doc.rust-lang.org/std/str/pattern/trait.Pattern.html) as input. 
+The functions which take Pattern as input turn the input str into a kind of `Searcher` which iterates over positions where the Pattern matches, then perform their desired operations (split, find, ...).
+Those functions is implemented in (library/core/src/str/mod.rs), but the core of them is the searching algorithms which are implemented in (library/core/src/str/pattern.rs).
+
+# Details
+
+IMPORTANT NOTE: for this challenge, you can assume: 
+1. The safety and functional correctness of all functions in `slice` module 
+2. That all functions in (library/core/src/str/validations.rs) are functionally correct (consistent with the UTF8 encoding description in https://en.wikipedia.org/wiki/UTF-8) . 
+3. That all the Searchers in (library/core/src/str/iter.rs) are created by the into_searcher(_, haystack) with haystack is a valid utf8 string (str). You can assume any utf8 string property of haystack.
+
+Verify the safety of the functions in (library/core/src/str/pattern.rs) listed in the next section.
+
+The safety properties we are targeting are: 
+1. There is no UB happens when calling the functions after the Searcher is created.
+2. The impls of unsafe traits `Searcher` and `ReverseSearcher` satisfies the SAFETY condition stated in the file: 
+```
+/// The trait is marked unsafe because the indices returned by the
+/// [`next()`][Searcher::next] methods are required to lie on valid utf8
+/// boundaries in the haystack. This enables consumers of this trait to
+/// slice the haystack without additional runtime checks.
+```
+This property should hold for next_back() of `ReverseSearcher` too.
+
+
+### Success Criteria
+
+Verify the safety of the following functions in (library/core/src/str/pattern.rs) : `next`, `next_match`, `next_back`, `next_match_back`, `next_reject`, `next_back_reject`
+which are implemented for `StrSearcher`.
+
+The verification is consider successful if you can specify a condition (a "type invariant") C and prove that:
+1. If the `StrSearcher` is created from any valid utf8 haystack, it satisfies C.
+2. If the `StrSearcher` satisfies C, it ensures the two safety properties mentioned in the previous section.
+3. If the `StrSearcher` satisfies C, after it calls any function above and gets modified, it still statisfies C.
+
+
+The verification must be unbounded---it must hold for inputs of arbitrary size.
+
+### List of UBs
+
+All proofs must automatically ensure the absence of the following undefined behaviors [ref](https://github.com/rust-lang/reference/blob/142b2ed77d33f37a9973772bd95e6144ed9dce43/src/behavior-considered-undefined.md):
+
+* Accessing (loading from or storing to) a place that is dangling or based on a misaligned pointer.
+* Reading from uninitialized memory except for padding or unions.
+* Mutating immutable bytes.
+* Producing an invalid value
+
+
+Note: All solutions to verification challenges need to satisfy the criteria established in the [challenge book](../general-rules.md)
+in addition to the ones listed above.

doc/src/challenges/0022-str-iter.md

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+# Challenge 22: Verify the safety of `str` iter functions - part 2
+
+- **Status:** Open
+- **Tracking Issue:** [#29](https://github.com/model-checking/verify-rust-std/issues/29)
+- **Start date:** *2025-03-07*
+- **End date:** *2025-10-17*
+- **Reward:** *?*
+
+-------------------
+
+
+## Goal
+
+Verify the safety of [`std::str`] functions that are defined in (library/core/src/str/iter.rs):
+
+IMPORTANT NOTE: for this challenge, you can assume: 
+1. The safety and functional correctness of all functions in `slice` module 
+2. The safety and functional correctness of all functions in (library/core/src/str/pattern.rs)
+3. That all functions in (library/core/src/str/validations.rs) are functionally correct (consistent with the UTF8 encoding description in https://en.wikipedia.org/wiki/UTF-8). 
+4. That all the Iterators in (library/core/src/str/iter.rs) are derived from a valid utf8 string (str) (You can assume any property of valid utf8 encoded string)
+
+
+### Success Criteria
+
+Write and prove the contract for the safety of the following functions:
+
+
+| Function | Impl for |
+|---------| ---------|
+|next| Chars|
+|advance_by| Chars|
+|next_back| Chars|
+|as_str| Chars|
+|get_end| SplitInternal|
+|next| SplitInternal|
+|next_inclusive| SplitInternal|
+|next_match_back| SplitInternal|
+|next_back_inclusive| SplitInternal|
+|remainder| SplitInternal|
+|next| MatchIndicesInternal|
+|next_back| MatchIndicesInternal|
+|next| MatchesInternal|
+|next_back| MatchesInternal|
+|remainder| SplitAsciiWhitespace|
+
+The verification must be unbounded---it must hold for str of arbitrary length.
+
+
+### List of UBs
+
+All proofs must automatically ensure the absence of the following undefined behaviors [ref](https://github.com/rust-lang/reference/blob/142b2ed77d33f37a9973772bd95e6144ed9dce43/src/behavior-considered-undefined.md):
+
+* Accessing (loading from or storing to) a place that is dangling or based on a misaligned pointer.
+* Reading from uninitialized memory except for padding or unions.
+* Mutating immutable bytes.
+* Producing an invalid value
+
+
+Note: All solutions to verification challenges need to satisfy the criteria established in the [challenge book](../general-rules.md)
+in addition to the ones listed above.