Complete task015 (Elanor, Amar, Yi) (#13)

---------

Co-authored-by: Amar Shah <[email protected]>

tasks/human_eval_015.rs

@@ -9,10 +9,169 @@ use vstd::prelude::*;
 
 verus! {
 
-// TODO: Put your solution (the specification, implementation, and proof) to the task here
+// specification
+pub closed spec fn single_digit_number_to_char(n: nat) -> char {
+    if n == 0 {
+        '0'
+    } else if n == 1 {
+        '1'
+    } else if n == 2 {
+        '2'
+    } else if n == 3 {
+        '3'
+    } else if n == 4 {
+        '4'
+    } else if n == 5 {
+        '5'
+    } else if n == 6 {
+        '6'
+    } else if n == 7 {
+        '7'
+    } else if n == 8 {
+        '8'
+    } else {
+        '9'
+    }
+}
+
+pub closed spec fn number_to_char(n: nat) -> Seq<char>
+    decreases n,
+{
+    if (n == 0) {
+        seq![]
+    } else {
+        number_to_char(n / 10).add(seq![single_digit_number_to_char(n % 10)])
+    }
+}
+
+pub open spec fn string_sequence(n: nat) -> Seq<char>
+    decreases n,
+{
+    if n == 0 {
+        seq!['0']
+    } else {
+        string_sequence((n - 1) as nat).add(seq![' '].add(number_to_char(n)))
+    }
+}
+
+proof fn sanity_check() {
+    assert(string_sequence(1) == seq!['0', ' ', '1']) by (compute);
+    assert(string_sequence(3) == seq!['0', ' ', '1', ' ', '2', ' ', '3']) by (compute);
+    assert(string_sequence(12) == seq![
+        '0',
+        ' ',
+        '1',
+        ' ',
+        '2',
+        ' ',
+        '3',
+        ' ',
+        '4',
+        ' ',
+        '5',
+        ' ',
+        '6',
+        ' ',
+        '7',
+        ' ',
+        '8',
+        ' ',
+        '9',
+        ' ',
+        '1',
+        '0',
+        ' ',
+        '1',
+        '1',
+        ' ',
+        '1',
+        '2',
+    ]) by (compute);
+    assert((number_to_char(158) == seq!['1', '5', '8'])) by (compute);
+}
+
+// implementation
+fn single_digit_number_to_char_impl(n: u8) -> (output: char)
+    requires
+        0 <= n <= 9,
+    ensures
+        single_digit_number_to_char(n as nat) == output,
+{
+    if n == 0 {
+        '0'
+    } else if n == 1 {
+        '1'
+    } else if n == 2 {
+        '2'
+    } else if n == 3 {
+        '3'
+    } else if n == 4 {
+        '4'
+    } else if n == 5 {
+        '5'
+    } else if n == 6 {
+        '6'
+    } else if n == 7 {
+        '7'
+    } else if n == 8 {
+        '8'
+    } else {
+        '9'
+    }
+}
+
+pub fn number_to_char_impl(n: u8) -> (char_vec: Vec<char>)
+    ensures
+        char_vec@ == number_to_char(n as nat),
+{
+    let mut i = n;
+    let mut output = vec![];
+
+    while (i > 0)
+        invariant
+            number_to_char(n as nat) == number_to_char(i as nat).add(output@),
+    {
+        let m = i % 10;
+        let current = single_digit_number_to_char_impl(m);
+        output.insert(0, current);
+        i = i / 10;
+
+        assert(number_to_char(n as nat) == number_to_char(i as nat).add(output@));
+    }
+    return output;
+}
+
+fn string_sequence_impl(n: u8) -> (string_seq: Vec<char>)
+    ensures
+        string_seq@ == string_sequence(n as nat),
+{
+    let mut i = n;
+    let mut output = vec![];
+    while (i > 0)
+        invariant
+            n >= i >= 0,
+            string_sequence(n as nat) == string_sequence(i as nat) + output@,
+        decreases i,
+    {
+        let mut next = number_to_char_impl(i);
+        next.append(&mut output);
+        output = next;
+        output.insert(0, ' ');
+        i = i - 1;
+
+        assert(string_sequence((n) as nat) == string_sequence((i) as nat) + output@);
+    }
+    output.insert(0, '0');
+    assert(string_sequence(n as nat) == output@);
+    return output;
+}
 
 } // verus!
-fn main() {}
+fn main() {
+    print!("{:?}", string_sequence_impl(0));
+    print!("{:?}", string_sequence_impl(5));
+    print!("{:?}", string_sequence_impl(20));
+}
 
 /*
 ### VERUS END