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Make all asserts one-liners (easier to strip when neccesary) #32

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Make all asserts one-liners (easier to strip when neccesary) #32

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8 changes: 4 additions & 4 deletions 003-below_zero.dfy
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Expand Up @@ -11,7 +11,9 @@ lemma psum_property(s: seq<int>, i: int)
calc == {
psum(s[..(i+1)]);
psum(s[..(i+1)][..(i+1)-1]) + s[..(i+1)][(i+1) - 1];
{ assert s[..(i+1)][..(i+1)-1] == s[..i]; }
{
assert s[..(i+1)][..(i+1)-1] == s[..i];
}
psum(s[..i]) + s[i];
}
}
Expand All @@ -28,9 +30,7 @@ method below_zero(ops: seq<int>) returns (res : bool)
invariant balance == psum(ops[..i])
invariant forall j : int :: 0 <= j <= i ==> psum(ops[..j]) >= 0
{
assert psum(ops[..(i + 1)]) == psum(ops[..i]) + ops[i] by {
psum_property(ops, i);
}
assert psum(ops[..(i + 1)]) == psum(ops[..i]) + ops[i] by { psum_property(ops, i); }
balance := balance + ops[i];
if (balance < 0) {
return false;
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10 changes: 2 additions & 8 deletions 004-mean_absolute_derivation.dfy
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Expand Up @@ -35,10 +35,7 @@ method mean_absolute_derivation(numbers: seq<real>) returns (derivation: real)
invariant s == sum(numbers[..i])
{
s := s + numbers[i];
assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by {
assert numbers[..i+1][..i] == numbers[..i];
sum_prop(numbers[..i + 1]);
}
assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by { assert numbers[..i+1][..i] == numbers[..i]; sum_prop(numbers[..i + 1]); }
i := i + 1;
}

Expand All @@ -61,10 +58,7 @@ method mean_absolute_derivation(numbers: seq<real>) returns (derivation: real)

pref_seq := pref_seq + [abs(numbers[i] - m)];

assert sum(pref_seq[..i + 1]) == sum(pref_seq[..i]) + pref_seq[i] by {
assert pref_seq[..i+1][..i] == pref_seq[..i];
sum_prop(pref_seq[..i + 1]);
}
assert sum(pref_seq[..i + 1]) == sum(pref_seq[..i]) + pref_seq[i] by { assert pref_seq[..i+1][..i] == pref_seq[..i]; sum_prop(pref_seq[..i + 1]); }

t := t + abs(numbers[i] - m);
i := i + 1;
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10 changes: 2 additions & 8 deletions 008-sum_product.dfy
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Expand Up @@ -37,16 +37,10 @@ method sum_product(numbers: seq<int>) returns (s : int, p : int)
invariant s == sum(numbers[..i])
invariant p == prod(numbers[..i])
{
assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by {
assert numbers[..i+1][..i] == numbers[..i];
sum_prop(numbers[..i + 1]);
}
assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by { assert numbers[..i+1][..i] == numbers[..i]; sum_prop(numbers[..i + 1]); }
s := s + numbers[i];

assert prod(numbers[..i + 1]) == prod(numbers[..i]) * numbers[i] by {
assert numbers[..i+1][..i] == numbers[..i];
prod_prop(numbers[..i + 1]);
}
assert prod(numbers[..i + 1]) == prod(numbers[..i]) * numbers[i] by { assert numbers[..i+1][..i] == numbers[..i]; prod_prop(numbers[..i + 1]); }
p := p * numbers[i];

i := i + 1;
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5 changes: 1 addition & 4 deletions 026-remove_duplicates.dfy
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Expand Up @@ -51,10 +51,7 @@ method count(a: seq<int>, x: int) returns (cnt: int)
cnt := cnt + 1;
positions := positions + {i};
}
assert count_rec(a[..i + 1], x) == count_rec(a[..i], x) + (if a[i] == x then 1 else 0) by {
assert a[..i+1][..i] == a[..i];
count_prop(a[..i + 1], x);
}
assert count_rec(a[..i + 1], x) == count_rec(a[..i], x) + (if a[i] == x then 1 else 0) by { assert a[..i+1][..i] == a[..i]; count_prop(a[..i + 1], x); }
i := i + 1;
}
assert a == a[..|a|];
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8 changes: 2 additions & 6 deletions 034-unique.dfy
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Expand Up @@ -27,12 +27,8 @@ method unique(s: seq<int>) returns (result: seq<int>)
{
var sorted := SortSeq(s);
result := uniqueSorted(sorted);
assert forall x :: x in sorted ==> x in s by {
assert forall x :: x in multiset(sorted) ==> x in s;
}
assert forall x :: x in s ==> x in sorted by {
assert forall x :: x in multiset(s) ==> x in sorted;
}
assert forall x :: x in sorted ==> x in s by { assert forall x :: x in multiset(sorted) ==> x in s; }
assert forall x :: x in s ==> x in sorted by { assert forall x :: x in multiset(s) ==> x in sorted; }
}

method SortSeq(s: seq<int>) returns (sorted: seq<int>)
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5 changes: 1 addition & 4 deletions 066-digitSum.dfy
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Expand Up @@ -34,10 +34,7 @@ method upper_sum(s: string) returns (res: int)
invariant res == upper_sum_rec(s[..i])
{
res := res + to_int(s[i]);
assert upper_sum_rec(s[..i + 1]) == upper_sum_rec(s[..i]) + to_int(s[i]) by {
assert s[..i+1][..i] == s[..i];
upper_sum_rec_prop(s[..i + 1]);
}
assert upper_sum_rec(s[..i + 1]) == upper_sum_rec(s[..i]) + to_int(s[i]) by { assert s[..i+1][..i] == s[..i]; upper_sum_rec_prop(s[..i + 1]); }
i := i + 1;
}
assert s == s[..|s|];
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5 changes: 1 addition & 4 deletions 072-will_it_fly.dfy
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Expand Up @@ -26,10 +26,7 @@ method will_it_fly(s: seq<int>, w: int) returns (result: bool)
invariant total == sum(s[..i])
{
total := total + s[i];
assert sum(s[..i + 1]) == sum(s[..i]) + s[i] by {
assert s[..i+1][..i] == s[..i];
sum_prop(s[..i + 1]);
}
assert sum(s[..i + 1]) == sum(s[..i]) + s[i] by { assert s[..i+1][..i] == s[..i]; sum_prop(s[..i + 1]); }
i := i + 1;
}

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5 changes: 1 addition & 4 deletions 074-total_match.dfy
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Expand Up @@ -40,10 +40,7 @@ method SumChars(list: seq<string>) returns (sum: nat)
invariant sum == sum_chars_rec(list[..i])
{
sum := sum + |list[i]|;
assert sum_chars_rec(list[..i + 1]) == sum_chars_rec(list[..i]) + |list[i]| by {
assert list[..i+1][..i] == list[..i];
sum_prop(list[..i + 1]);
}
assert sum_chars_rec(list[..i + 1]) == sum_chars_rec(list[..i]) + |list[i]| by { assert list[..i+1][..i] == list[..i]; sum_prop(list[..i + 1]); }

i := i + 1;
}
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7 changes: 1 addition & 6 deletions 078-hex_key.dfy
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Expand Up @@ -31,12 +31,7 @@ method count_prime_hex_digits(s: seq<char>) returns (count : int)
invariant 0 <= i <= |s|
invariant count == count_prime_hex_digits_rec(s[..i])
{
assert count_prime_hex_digits_rec(s[..i + 1]) == count_prime_hex_digits_rec(s[..i]) + (
if IsPrimeHexDigit(s[ i ]) then 1 else 0
) by {
assert s[..i+1][..i] == s[..i];
count_prop(s[..i + 1]);
}
assert count_prime_hex_digits_rec(s[..i + 1]) == count_prime_hex_digits_rec(s[..i]) + (if IsPrimeHexDigit(s[ i ]) then 1 else 0) by { assert s[..i+1][..i] == s[..i]; count_prop(s[..i + 1]); }
count := count + if IsPrimeHexDigit(s[i]) then 1 else 0;
i := i + 1;
}
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4 changes: 1 addition & 3 deletions 085-add.dfy
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Expand Up @@ -35,9 +35,7 @@ method add(v: seq<int>) returns (r : int)
assert p[..k + 1][..k] == p[..k];
r := r + if p[k] then v[k] else 0;
k := k + 1;
assert sumc(v[..k], p[..k]) == r by {
sum_prop(v[..k], p[..k]);
}
assert sumc(v[..k], p[..k]) == r by { sum_prop(v[..k], p[..k]); }
}
assert v[..k] == v;
assert p[..k] == p;
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4 changes: 1 addition & 3 deletions 104-unique_digits.dfy
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Expand Up @@ -53,7 +53,5 @@ method UniqueDigits(x: seq<int>) returns (result: seq<int>)

assert forall e :: e in result ==> HasNoEvenDigit(e);
assert forall e :: e in result ==> e in x;
assert forall e :: e in x && HasNoEvenDigit(e) ==> e in result by {
assert forall e :: e in unsorted ==> e in multiset(result);
}
assert forall e :: e in x && HasNoEvenDigit(e) ==> e in result by { assert forall e :: e in unsorted ==> e in multiset(result); }
}
8 changes: 2 additions & 6 deletions 105-by_length.dfy
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Expand Up @@ -16,13 +16,9 @@ method SortReverseAndName(arr: seq<int>) returns (result: seq<string>)

ghost var unsorted := validNumbers;
validNumbers := SortSeq(validNumbers);
assert forall j :: 0 <= j < |validNumbers| ==> 1 <= validNumbers[j] <= 9 by {
assert forall j :: 0 <= j < |validNumbers| ==> validNumbers[j] in multiset(unsorted);
}
assert forall j :: 0 <= j < |validNumbers| ==> 1 <= validNumbers[j] <= 9 by { assert forall j :: 0 <= j < |validNumbers| ==> validNumbers[j] in multiset(unsorted); }
validNumbers := reverse(validNumbers);
assert forall j :: 0 <= j < |validNumbers| ==> 1 <= validNumbers[j] <= 9 by {
assert forall j :: 0 <= j < |validNumbers| ==> validNumbers[j] in multiset(unsorted);
}
assert forall j :: 0 <= j < |validNumbers| ==> 1 <= validNumbers[j] <= 9 by { assert forall j :: 0 <= j < |validNumbers| ==> validNumbers[j] in multiset(unsorted); }

assert forall i, j :: 0 <= i < j < |validNumbers| ==> validNumbers[i] >= validNumbers[j];
result := [];
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10 changes: 3 additions & 7 deletions 120-maximum.dfy
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Expand Up @@ -12,7 +12,7 @@ method maximum(s: seq<int>, k: int) returns (result: seq<int>)
result := sorted[|s| - k..];

// I can't make this a postcondition because it relies on an internal variable
assert forall i, j :: 0 <= i < |s| - k && 0 <= j < k ==> sorted[i] <= result[j];
assert forall i, j :: 0 <= i < |s| - k && 0 <= j < k ==> sorted[i] <= result[j];
}

method SortSeq(s: seq<int>) returns (sorted: seq<int>)
Expand Down Expand Up @@ -51,12 +51,8 @@ method SortSeq(s: seq<int>) returns (sorted: seq<int>)
i := i + 1;
}

assert forall i :: 0 <= i < |s| ==> exists j :: 0 <= j < |sorted| && s[i] == sorted[j] by {
assert forall i :: 0 <= i < |s| ==> s[i] in multiset(sorted);
}
assert forall i :: 0 <= i < |s| ==> exists j :: 0 <= j < |sorted| && s[i] == sorted[j] by { assert forall i :: 0 <= i < |s| ==> s[i] in multiset(sorted); }
assert forall x :: x in s ==> x in sorted;
assert forall i :: 0 <= i < |s| ==> exists j :: 0 <= j < |sorted| && sorted[i] == s[j] by {
assert forall i :: 0 <= i < |s| ==> sorted[i] in multiset(s);
}
assert forall i :: 0 <= i < |s| ==> exists j :: 0 <= j < |sorted| && sorted[i] == s[j] by { assert forall i :: 0 <= i < |s| ==> sorted[i] in multiset(s); }
assert forall x :: x in sorted ==> x in s;
}
10 changes: 2 additions & 8 deletions 122-add_elements.dfy
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Expand Up @@ -33,10 +33,7 @@ method select_at_most_two_digits(arr: seq<int>) returns (result: seq<int>)
if 0 <= arr[i] < 100 {
result := result + [arr[i]];
}
assert select_at_most_two_digits_rec(arr[..i + 1]) == select_at_most_two_digits_rec(arr[..i]) + if 0 <= arr[i] < 100 then [arr[i]] else [] by {
assert arr[..i+1][..i] == arr[..i];
select_prop(arr[..i + 1]);
}
assert select_at_most_two_digits_rec(arr[..i + 1]) == select_at_most_two_digits_rec(arr[..i]) + if 0 <= arr[i] < 100 then [arr[i]] else [] by { assert arr[..i+1][..i] == arr[..i]; select_prop(arr[..i + 1]); }
i := i + 1;
}
assert arr[..|arr|] == arr;
Expand Down Expand Up @@ -69,10 +66,7 @@ method SumElementsWithAtMostTwoDigits(arr: seq<int>, k: int) returns (s: int)
invariant s == sum(two_digits[..i])
{
s := s + two_digits[i];
assert sum(two_digits[..i + 1]) == sum(two_digits[..i]) + two_digits[i] by {
assert two_digits[..i+1][..i] == two_digits[..i];
sum_prop(two_digits[..i + 1]);
}
assert sum(two_digits[..i + 1]) == sum(two_digits[..i]) + two_digits[i] by { assert two_digits[..i+1][..i] == two_digits[..i]; sum_prop(two_digits[..i + 1]); }
i := i + 1;
}
assert two_digits[..|two_digits|] == two_digits;
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4 changes: 1 addition & 3 deletions 151-double_the_difference.dfy
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Expand Up @@ -43,9 +43,7 @@ method double_the_difference(lst: seq<int>) returns (r : int)
assert p[..k + 1][..k] == p[..k];
r := r + if p[k] then v[k] else 0;
k := k + 1;
assert sumc(v[..k], p[..k]) == r by {
sum_prop(v[..k], p[..k]);
}
assert sumc(v[..k], p[..k]) == r by { sum_prop(v[..k], p[..k]); }
}
assert v[..k] == v;
assert p[..k] == p;
Expand Down