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values | path stringlengths 5 283 | license stringclasses 13
values | stars int64 0 3.47k | default_branch stringclasses 15
values | commit_sha stringclasses 966
values | pushed_at stringdate 2015-04-17 10:56:12 2026-07-22 05:29:38 | size_bytes int64 0 1.91M | sha256 stringlengths 64 64 | content stringlengths 0 1.91M |
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sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/feup-mfes_tmp_tmp6_a1y5a5_examples_SelectionSort.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,034 | 074dd8b560b0803e93d060689b97e3d41190a69b28027dee975df8f1e28b39ee | /*
* Formal verification of the selection sort algorithm with Dafny.
* FEUP, MIEIC, MFES, 2020/21.
*/
// Checks if array 'a' is sorted between positions 'from' (inclusive) and 'to' (exclusive).
predicate isSorted(a: array<real>, from: nat, to: nat)
requires 0 <= from <= to <= a.Length
reads a
{
fora... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Exercise3_Increment_Array.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 632 | 0a2dff318de617317c0fab2d353899ed4f2f4066df6e760986c0718a2d6f03cc | method incrementArray(a:array<int>)
requires a.Length > 0
ensures forall i :: 0 <= i < a.Length ==> a[i] == old(a[i]) + 1
modifies a
{
var j : int := 0;
while(j < a.Length)
invariant 0 <= j <= a.Length
invariant forall i :: j <= i < a.Length ==> a[i] == old(a[i])
invariant forall i :: 0 <... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Exercise4_Find_Max.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 736 | bedc1022300f181fdfafd31f0727b1c0cb64cba3d8bf861a3b7825eadd1b65dd | method findMax(a:array<int>) returns (pos:int, maxVal: int)
requires a.Length > 0;
requires forall i :: 0 <= i < a.Length ==> a[i] >= 0;
ensures forall i :: 0 <= i < a.Length ==> a[i] <= maxVal;
ensures exists i :: 0 <= i < a.Length && a[i] == maxVal;
ensures 0 <= pos < a.Length
ensures a[pos] == max... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Exercise6_Binary_Search.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 901 | 5a250d9c22776e27612e4651eca4071ac7d43bd64a2830fd6e97f63e84bd1317 | method binarySearch(a:array<int>, val:int) returns (pos:int)
requires a.Length > 0
requires forall i, j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
ensures 0 <= pos < a.Length ==> a[pos] == val
ensures pos < 0 || pos >= a.Length ==> forall i :: 0 <= i < a.Length ==> a[i] != val
{
var left := 0;
va... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Insertion_Sorted_Standard.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 876 | 4e3a46709db944d31f8181d8cfed72463b0c7452b518a7050c166cff829d156d | predicate InsertionSorted(Array: array<int>, left: int, right: int)
requires 0 <= left <= right <= Array.Length
reads Array
{
forall i,j :: left <= i < j < right ==> Array[i] <= Array[j]
}
method sorting(Array: array<int>)
requires Array.Length > 1
ensures InsertionSort... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Insertion_Sort_Normal.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,025 | 32f02dfa415f3378083c2c51873899e6ad03c36402026ebc44ff6f8135215b1d | predicate sorted (a: array<int>)
reads a
{
sortedA(a, a.Length)
}
predicate sortedA (a: array<int>, i: int)
requires 0 <= i <= a.Length
reads a
{
forall k :: 0 < k < i ==> a[k-1] <= a[k]
}
method lookForMin (a: array<int>, i: int) returns (m: int)
requires 0 <= i < a.Length
ensures i <= m ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Merge_Sort.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,698 | e519db7aa0e15a6543728acda080ae1bbef6314c05d35ceb666e04d18d32dd5d | method mergeSort(a: array<int>)
modifies a
{
sorting(a, 0, a.Length-1);
}
method merging(a: array<int>, low: int, medium: int, high: int)
requires 0 <= low <= medium <= high < a.Length
modifies a
{
var x := 0;
var y := 0;
var z := 0;
var a1: array<int> := new [medium - low + 1];
var a2: array... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Quick_Sort.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,888 | 2d1624d3e65c4f2d94a40fbd5555ab4b7c45a34335d5f6b2b39e7be04dbee469 | predicate quickSorted(Seq: seq<int>)
{
forall idx_1, idx_2 :: 0 <= idx_1 < idx_2 < |Seq| ==> Seq[idx_1] <= Seq[idx_2]
}
method threshold(thres:int,Seq:seq<int>) returns (Seq_1:seq<int>,Seq_2:seq<int>)
ensures (forall x | x in Seq_1 :: x <= thres) && (forall x | x in Seq_2 :: x >= thres)
ensures |Seq_1| + ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Attempts_Selection_Sort_Standard.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 916 | 6893defa648c1500649172b486c6a329bad5810e9b2a6215705b2213cddcd231 | method selectionSorted(Array: array<int>)
modifies Array
ensures multiset(old(Array[..])) == multiset(Array[..])
{
var idx := 0;
while (idx < Array.Length)
invariant 0 <= idx <= Array.Length
invariant forall i,j :: 0 <= i < idx <= j < Array.Length ==> Array[i] <= Array[j]
invariant forall ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Final-Project-Dafny_tmp_tmpmcywuqox_Final_Project_3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 215 | 8172d5abdf6a880aa2a026737348549a919975a1a714541559d3ad6193c94adb | method nonZeroReturn(x: int) returns (y: int)
ensures y != 0
{
if x == 0 {
return x + 1;
} else {
return -x;
}
}
method test() {
var input := nonZeroReturn(-1);
assert input != 0;
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FlexWeek_tmp_tmpc_tfdj_3_ex2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 815 | a13088c143ff34c152b0604741313d075bbc34d1ca09b12bca93319bc8026cfb | // 2. Given an array of positive and negative integers, it returns an array of the absolute value of all the integers. [-4,1,5,-2,-5]->[4,1,5,2,5]
function abs(a:int):nat
{
if a < 0 then -a else a
}
method aba(a:array<int>)returns (b:array<int>)
ensures a.Length == b.Length // needed for next line
ensure... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FlexWeek_tmp_tmpc_tfdj_3_ex3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,142 | b4bb951a4fb4133948a208985e48152d167b8bfcf332e7759c80286682486733 | method Max(a:array<nat>)returns(m:int)
ensures a.Length > 0 ==> forall k :: 0<=k<a.Length ==> m >= a[k]// not strong enough
ensures a.Length == 0 ==> m == -1
ensures a.Length > 0 ==> m in a[..] // finally at the top // approach did not work for recusrive function
{
if(a.Length == 0){
return -1;
}... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FlexWeek_tmp_tmpc_tfdj_3_ex4.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,017 | 5b18c2dbfc0981ba4859646ff147795761673624e0aa91350d85682a9098425f | method join(a:array<int>,b:array<int>) returns (c:array<int>)
ensures a[..] + b[..] == c[..]
ensures multiset(a[..] + b[..]) == multiset(c[..])
ensures multiset(a[..]) + multiset(b[..]) == multiset(c[..])
ensures a.Length+b.Length == c.Length
// Forall
ensures forall i :: 0<=i<a.Length ==> c[i] == a[i]
ensur... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FlexWeek_tmp_tmpc_tfdj_3_reverse.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,742 | c875e4650e458b65c3ede2af9e258640b868cd3e9faa72da1d526ba913b26840 | // Write an *iterative* Dafny method Reverse with signature:
// method Reverse(a: array<char>) returns (b: array<char>)
// which takes an input array of characters 'a' and outputs array 'b' consisting of
// the elements of the input array in reverse order. The following conditions apply:
// - the input ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FMSE-2022-2023_tmp_tmp6_x_ba46_Lab10_Lab10.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 13,531 | d2fef05fcf590b758b32ef505c826221d1c6bb6777cb31d7964902253b340ed0 | predicate IsOdd(x: int) {
x % 2 == 1
}
newtype Odd = n : int | IsOdd(n) witness 3
trait OddListSpec
{
var s: seq<Odd>
var capacity: nat
predicate Valid()
reads this
{
0 <= |s| <= this.capacity &&
forall i :: 0 <= i < |s| ==> IsOdd(s[i] as int)
}
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FMSE-2022-2023_tmp_tmp6_x_ba46_Lab1_Lab1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 4,105 | 3492533f11549a46830e9c8e465cf34f2d664f71c956d4affe711a83b0d0b4b3 | /// Types defined as part of Tasks 3, 5 and 9
// Since we have created the IsOddNat predicate we use it to define the new Odd subsort
newtype Odd = n : int | IsOddNat(n) witness 1
// Since we have created the IsEvenNat predicate we use it to define the new Even subsort
newtype Even = n : int | IsEvenNat(n) witn... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FMSE-2022-2023_tmp_tmp6_x_ba46_Lab2_Lab2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 11,282 | 7d3df4fcb1bddbb90ba78d5c99040c7d6519e79f2a9e0c2607dca01a07a9becd | /*
* Task 2: Define the natural numbers as an algebraic data type
*
* Being an inductive data type, it's required that we have a base case constructor and an inductive one.
*/
datatype Nat = Zero | S(Pred: Nat)
/// Task 2
// Exercise (a'): proving that the successor constructor is injective
/*
* It's k... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FMSE-2022-2023_tmp_tmp6_x_ba46_Lab3_Lab3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 4,448 | 5092da921c534e3e6d802de1bc2b0b4d11b5d215696ccd09ccd5c8edb339737c | /*
* Task 2: Define in Dafny the conatural numbers as a coinductive datatype
*
* Being a coinductive data type, it's required that we have a base case constructor and an inductive one
* (as is the case with inductive ones as well)
*/
codatatype Conat = Zero | Succ(Pred: Conat)
// Exercise (a): explain w... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal-methods-in-software-engineering_tmp_tmpe7fjnek6_Labs2_gr2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,190 | 55c30241544eefd6280d423cfe4f346ca6e592750d1dcdab512d009149417b32 | datatype Nat = Zero | Succ(Pred: Nat)
/*
Nat: Zero, Succ(Zero), Succ(Succ(Zero)), ...
*/
lemma Disc(n: Nat)
ensures n.Succ? || n.Zero?
{
//
}
lemma LPred(n: Nat)
ensures Succ(n).Pred == n
{
//
}
// Succ(m') > m'
function add(m: Nat, n: Nat) : Nat
decreases m
{
match m
ca... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal-methods-in-software-engineering_tmp_tmpe7fjnek6_Labs2_hw1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 844 | ff1c2a959b0e7c6e9d35b400012e1cae00ab0d8ffd4cd8a91ed7bf7871e0d1ee | /*
HW1: Define over naturals (as an algebraic data type) the predicates odd(x) and even(x)
and prove that the addition of two odd numbers is an even number.
Deadline: Tuesday 12.10, 14:00
*/
datatype Nat = Zero | Succ(Pred: Nat)
function add(m: Nat, n: Nat) : Nat
decreases m
{
match m
case Z... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal-methods-in-software-engineering_tmp_tmpe7fjnek6_Labs4_gr2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 4,507 | aa6b3976d35f76bc4334265120ef59ae779baa2c1b2b16db1cfdf05a75b6e3ef | /*
Dafny include 2 limbaje:
* un limbaj pentru specificare
MSFOL (ce am discutat până acum)
adnotări care să ajute în procesul de verificare
* un limbaj pentru scris programe
*/
// Exemplu de program
method SqrSum(n: int) returns (s: int)
{
var i,k : int;
s := 0;
k := 1;
i ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-methods-of-software-development_tmp_tmppryvbyty_Bloque 1_Lab3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,306 | 233e02b45df4841bd8ea639b8d9c34ba2f85ee8e81cfde40146bd7cd848dc65a |
method multipleReturns (x:int, y:int) returns (more:int, less:int)
requires y > 0
ensures less < x < more
method multipleReturns2 (x:int, y:int) returns (more:int, less:int)
requires y > 0
ensures more + less == 2*x
// TODO: Hacer en casa
method multipleReturns3 (x:int, y:int) returns (more:int, less:int... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-methods-of-software-development_tmp_tmppryvbyty_Bloque 2_Lab6.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 10,727 | fabda5a88d8805ab5026b6dc2d6f65b1d27e9970674cec9dd69bb8b535227853 | /*predicate palindrome<T(==)> (s:seq<T>)
{
forall i:: 0<=i<|s| ==> s[i] == s[|s|-i-1]
}
*/
// SUM OF A SEQUENCE OF INTEGERS
function sum(v: seq<int>): int
decreases v
{
if v==[] then 0
else if |v|==1 then v[0]
else v[0]+sum(v[1..])
}
/*
method vector_Sum(v:seq<int>) returns (x:int)
ens... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-methods-of-software-development_tmp_tmppryvbyty_Examenes_Beni_Heusel-Benedikt-Ass-1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 7,128 | 9756e5a767204b359c29a7545abd7516961c77a2c4593560593ce5a700afac69 | // APELLIDOS: Heusel
// NOMBRE: Benedikt
// ESPECIALIDAD: ninguna (Erasmus)
// ESTÁ PERFECTO, NO HAY NINGUN COMENTARIO MAS ABAJO
// EJERCICIO 1
// Demostrar el lemma div10_Lemma por inducción en n
// y luego usarlo para demostrar el lemma div10Forall_Lemma
function exp (x:int,e:nat):int
{
if e == 0 the... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-Methods-Project_tmp_tmphh2ar2xv_BubbleSort.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,138 | 0dc65070befda1d0fba31d838fbad2767d6b61e3c824c72741731f78aa6ad173 | predicate sorted(a: array?<int>, l: int, u: int)
reads a;
requires a != null;
{
forall i, j :: 0 <= l <= i <= j <= u < a.Length ==> a[i] <= a[j]
}
predicate partitioned(a: array?<int>, i: int)
reads a
requires a != null
{
forall k, k' :: 0 <= k <= i < k' < a.Length ==> a[k] <= a[k']
}... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-Methods-Project_tmp_tmphh2ar2xv_Factorial.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 283 | 5454b72c383bf7a202bdc293b53ebb97ce957f0b8cbf03859caa0d77d1625843 |
method Fact(x: int) returns (y: int)
requires x >= 0;
{
y := 1;
var z := 0;
while(z != x)
decreases x - z;
invariant 0 <= x-z;
{
z := z + 1;
y := y * z;
}
}
method Main() {
var a := Fact(87);
print a;
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-Verification-Project_tmp_tmp9gmwsmyp_strings3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,926 | 333ad0b893166da540dc57f9cc81aee44576488560a09a39b523945b11e59609 | predicate isPrefixPred(pre:string, str:string)
{
(|pre| <= |str|) &&
pre == str[..|pre|]
}
predicate isNotPrefixPred(pre:string, str:string)
{
(|pre| > |str|) ||
pre != str[..|pre|]
}
lemma PrefixNegationLemma(pre:string, str:string)
ensures isPrefixPred(pre,str) <==> !isNotPrefixPred(pre,str)
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal-verification_tmp_tmpoepcssay_strings3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,933 | 049f9ea13253b25e506ed2b59ac4a7c61ea28c3551cd91a72b42f07d3753d1e1 | predicate isPrefixPred(pre:string, str:string)
{
(|pre| <= |str|) &&
pre == str[..|pre|]
}
predicate isNotPrefixPred(pre:string, str:string)
{
(|pre| > |str|) ||
pre != str[..|pre|]
}
lemma PrefixNegationLemma(pre:string, str:string)
ensures isPrefixPred(pre,str) <==> !isNotPrefixPred(pre,str)
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-Verification_tmp_tmpuyt21wjt_Dafny_strings1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,738 | 8eae1cc0b0d59e6ef3f9d5586554308bc34663485c7f67a49002b33b271059d8 | predicate isPrefixPredicate(pre: string, str:string)
{
|str| >= |pre| && pre <= str
}
method isPrefix(pre: string, str: string) returns (res: bool)
ensures |pre| > |str| ==> !res
ensures res == isPrefixPredicate(pre, str)
{
if |pre| > |str|
{return false;}
var i := 0;
while i < |pre|
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal-Verification_tmp_tmpuyt21wjt_Dafny_strings3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,909 | 04f8c50eb862162332bc8e9b6016c414b79e3d81df2d7dd04ae35f1b6fc9c9f8 | // We spent 2h each on this assignment
predicate isPrefixPred(pre:string, str:string)
{
(|pre| <= |str|) &&
pre == str[..|pre|]
}
predicate isNotPrefixPred(pre:string, str:string)
{
(|pre| > |str|) ||
pre != str[..|pre|]
}
lemma PrefixNegationLemma(pre:string, str:string)
ensures isPrefixPred(... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FormalMethods_tmp_tmpvda2r3_o_dafny_Invariants_ex1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 724 | 9584d6d1252fb59185c77e154020d75655aea21789c677d7daf7ed315470db15 | method Mult(x:nat, y:nat) returns (r:nat)
ensures r == x * y
{
// Valores passados por parâmetros são imutáveis
var m := x;
var n := y;
r := 0;
// Soma sucessiva para multiplicar dois números.
while m > 0
invariant m*n+r == x*y
invariant m>=0
{
r := r + n;
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/FormalMethods_tmp_tmpvda2r3_o_dafny_Invariants_ex2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 638 | 0117cf7c1838080e949fccea9b35c22ed5f1c35b2b44542139a77d067ea54bde | function Potencia(x:nat, y:nat):nat
{
if y == 0
then 1
else x * Potencia(x, y-1)
}
method Pot(x:nat, y:nat) returns (r:nat)
ensures r == Potencia(x,y)
{
r := 1;
var b := x;
var e := y;
while e > 0
invariant Potencia(b,e) * r == Potencia(x,y)
{
r := r * b;
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal_verication_dafny_tmp_tmpwgl2qz28_Challenges_ex1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,311 | 9af369e1f3ecfb79d2377770ca14f8cf404911093017354f16a02be8ce0b92aa | // ex3errors.dfy in Assignment 1
// verify that an array of characters is a Palindrome
/*
A Palindrome is a word that is the same when written forwards and when written backwards.
For example, the word ”refer” is a Palindrome.
The method PalVerify is supposed to verify whether a word is a Palindrome,
where the ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal_verication_dafny_tmp_tmpwgl2qz28_Challenges_ex2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,499 | b238110e361785835ba5cbf9b112e75ac624e5fbbc5342f3a9e3b35cc6d21939 | /*
i) Write a verified method with signature
method Forbid42(x:int, y:int) returns (z: int)
that returns x/(42 − y). The method is not defined for y = 42.
ii) Write a verified method with signature
method Allow42(x:int, y:int) returns (z: int, err:bool)
If y is n... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal_verication_dafny_tmp_tmpwgl2qz28_Challenges_ex6.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,378 | 3559590c0d6a387eeeef371abc31592cfc4c0f980f8da71d22b282a03ac2f22f | // see pdf 'ex6 & 7 documentation' for excercise question
function bullspec(s:seq<nat>, u:seq<nat>): nat
requires 0 <= |u| == |s| && nomultiples(u)
{reccbull(s, u, 0)}
function cowspec(s:seq<nat>, u:seq<nat>): nat
requires 0 <= |u| == |s| && nomultiples(u)
{recccow(s, u, 0)}
function reccbull(s: seq<nat>, ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/formal_verication_dafny_tmp_tmpwgl2qz28_Challenges_ex7.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,654 | 95d1319da3f80376614f7ad19ff6dec9aef5db72d857e403b6c78e1cc1a738f7 | // see pdf 'ex6 & 7 documentation' for excercise question
datatype Bases = A | C | G | T
//swaps two sequence indexes
method Exchanger(s: seq<Bases>, x:nat, y:nat) returns (t: seq<Bases>)
requires 0 < |s| && x < |s| && y < |s|
ensures |t| == |s|
ensures forall b:nat :: 0 <= b < |s| && b != x && b != y ==> t[b... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal_Verification_With_Dafny_tmp_tmp5j79rq48_Counter.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 697 | d59236d8df66154ee05ddc1b6993680642d48ae7604dd255340ca77e22b5eb52 | class Counter {
var value : int ;
constructor init()
ensures value == 0;
{
value := 0 ;
}
method getValue() returns (x:int)
ensures x == value;
{
x := value ;
}
method inc()
modifies this`value
requires value >= 0;
ensures value == old(value) + 1;
{
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Formal_Verification_With_Dafny_tmp_tmp5j79rq48_LimitedStack.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 4,783 | 3c45128cc282eb8bd2bcfc8e33c1016569a670a7d48fb36d6b809b7decaf3b9f | // A LIFO queue (aka a stack) with limited capacity.
class LimitedStack{
var capacity : int; // capacity, max number of elements allowed on the stack.
var arr : array<int>; // contents of stack.
var top : int; // The index of the top of the stack, or -1 if the stack is empty
// This pr... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/fv2020-tms_tmp_tmpnp85b47l_modeling_concurrency_safety.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,040 | af73a577902403068dff8219616244ad8fb6ea62456c706f46368f25ab50ca52 | /*
* Model of the ticket system and correctness theorem
* Parts 4 and 5 in the paper
*/
type Process(==) = int // Philosopher
datatype CState = Thinking | Hungry | Eating // Control states
// A class can have state, with multiple fields, methods, a constructor, and declare functions and lemmas
class Tic... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/fv2020-tms_tmp_tmpnp85b47l_simple_tm.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 19,409 | 821bd75c0b86fa3cc2f8ba23c99cc5a6ca4dccd2c864597f863a79ae4947b650 | module ModelingTM {
type ProcessId = nat
type MemoryObject = nat
type TimeStamp = nat
class Operation {
const isWrite: bool
const memObject: MemoryObject
}
class Transaction {
const ops: seq<Operation>
}
// Process state : transaction progress and... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/groupTheory_tmp_tmppmmxvu8h_assignment1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,787 | 6a4fe7b56f0c92637bf819fb77ffe12a49a93de99f4a440f944477fe0a552cab | /*
Student name: Mark Valman
Id: 342439593
*/
/* Question/Exercise 1 of 4 */
lemma Q1_logical_equivalence_as_a_conjunction_of_two_implications__PROOF_BY_TRUTH_TABLE__in_a_comment(L: bool, R: bool)
ensures (L <==> R) <==> (L ==> R) && (!L ==> !R)
{
/*
This lemma states that logical equivalence (L <==> R) ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/groupTheory_tmp_tmppmmxvu8h_tutorial2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 983 | 5bba44b5d33ed7660075ef21f1dc3c634092bb164cb8abfb6a84f4ff88005e42 | ghost method M1()
{
assert 1 != 3;
// assert 1 == 2;
assume 1 == 2;
assert 1 == 2;
}
lemma IntersectionIsSubsetOfBoth(A: set, B: set, C: set)
requires C == A*B
ensures C <= A && C <= B
{}
lemma BothSetsAreSubsetsOfTheirUnion(A: set, B: set, C: set)
requires C == A+B
ensures A <= C && B <= C
{... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/groupTheory_tmp_tmppmmxvu8h_yair_yair2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,431 | 4be831f1a38d71e2b9ee7ab705030c33cf9db7643a4a85ed20210ca9f304e8f0 |
///////////////////////////
// Lemma to prove Transitive
// Got A<B, B<C.
// Prove A<C
///////////////////////////
predicate IsSubset(A: set, B: set) // <=
{
forall n :: n in A ==> n in B // same as the next line
//forall n :: if n in A then n in B else true // same as "A <= B"
}
// lemma - משפט
// subse... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/HATRA-2022-Paper_tmp_tmp5texxy8l_copilot_verification_Binary Search_binary_search.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,758 | 0f80e5df829e5778b079719c6eb727cd06e141c2ff9fa62fb1b75a2592407d7b | // Dafny verification of binary search alogirthm from binary_search.py
// Inspired by: https://ece.uwaterloo.ca/~agurfink/stqam/rise4fun-Dafny/#h211
method BinarySearch(arr: array<int>, target: int) returns (index: int)
requires distinct(arr)
requires sorted(arr)
ensures -1 <= index < arr.Length
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/HATRA-2022-Paper_tmp_tmp5texxy8l_copilot_verification_Largest Sum_largest_sum.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,464 | d8baafb2b5602fcf2c86a450bc4d66c2a3558528d3f933d918744a37a8107ce7 | // CoPilot function converted to dafny
method largest_sum(nums: array<int>, k: int) returns (sum: int)
requires nums.Length > 0
ensures max_sum_subarray(nums, sum, 0, nums.Length)
{
var max_sum := 0;
var current_sum := 0;
var i := 0;
while (i < nums.Length)
invariant 0 <=... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/HATRA-2022-Paper_tmp_tmp5texxy8l_copilot_verification_Sort Array_sort_array.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,964 | ce9613416a2ce23670d340ad28068063e3c979c15fcb062c0927ea5790ec5888 | method sortArray(arr: array<int>) returns (arr_sorted: array<int>)
// Requires array length to be between 0 and 10000
requires 0 <= arr.Length < 10000
// Ensuring the arry has been sorted
ensures sorted(arr_sorted, 0, arr_sorted.Length)
// Ensuring that we have not modified elements but have on... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/HATRA-2022-Paper_tmp_tmp5texxy8l_copilot_verification_Two Sum_two_sum.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,207 | 17362eb26ae91f737cc94b8571a722a3c143bbcb500fda0deda8542fd2c2233f | method twoSum(nums: array<int>, target: int) returns (index1: int, index2: int)
requires 2 <= nums.Length
requires exists i, j :: (0 <= i < j < nums.Length && nums[i] + nums[j] == target)
ensures index1 != index2
ensures 0 <= index1 < nums.Length
ensures 0 <= index2 < nums.Length
ensures n... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Invoker_tmp_tmpypx0gs8x_dafny_abstract-interpreter_SimpleVerifier.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 7,522 | 3edeb1be573a7a4b298121dc7899c2c46322acd06cc2db566b20dfc026bb5514 | module Ints {
const U32_BOUND: nat := 0x1_0000_0000
newtype u32 = x:int | 0 <= x < 0x1_0000_0000
newtype i32 = x: int | -0x8000_0000 <= x < 0x8000_0000
}
module Lang {
import opened Ints
datatype Reg = R0 | R1 | R2 | R3
datatype Expr =
| Const(n: u32)
// overflow during addition i... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/iron-sync_tmp_tmps49o3tyz_concurrency_docs_code_ShardedStateMachine.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,725 | fe3fbc3c1c6a9d59c2fea0f874adf311e8773e39ecca6b7e3c7a27be38806da4 | // General form of a ShardedStateMachine
// To instantiate one, fill in the 'Shard' type, the 'glue' function
// provide the 'Next' predicate and the invariant 'Inv',
// and then meet various proof obligations in the form of lemmas.
abstract module ShardedStateMachine {
/*
* A ShardedStateMachine contains ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/iron-sync_tmp_tmps49o3tyz_Impl_CommitterCommitModel.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 29,563 | 26cd536f3425189ff9139bac91cc814455fa7a57ac785690398a4130f33b484c | // include "IOModel.i.dfy"
// include "../lib/DataStructures/LinearMutableMap.i.dfy"
// module CommitterCommitModel {
// import opened NativeTypes
// import opened Options
// import opened DiskLayout
// import opened InterpretationDiskOps
// import opened ViewOp
// import JC = JournalCache
// ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/iron-sync_tmp_tmps49o3tyz_lib_Base_MapRemove.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,013 | 94c9cdd34eb50df53c308acb78703769ca487778a0670e1f6238b412c03f071c | // Defines a MapRemove1 operation for removing a key from a
// the built-in map<K,V> type, and declares a trusted, compilable
// version.
//
// TODO On principle, it'd be nice to remove our dependence
// on compiling the built-in map<K, V> entirely, and just
// replace them with our own hash tables. There are onl... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_lib_Marshalling_Math.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,899 | 931794ea6cc3bc0b5ac50d46d123e16c72f9692842581dcd50c5edfa0a6af036 | // Based on IronFleet's math library.
// I pulled out only the functions we need for the marshalling code,
// and in a few cases rewrote the proof from scratch to avoid pulling in
// a lot of dependencies.
module Math {
function {:opaque} power2(exp: nat) : nat
ensures power2(exp) > 0;
{
if (e... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_lib_Math_div_def.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,252 | fffeda606841915724cc3e2d313e5671de343e12947bead7b9baadd0dc374f4f | //- Specs/implements mathematical div and mod, not the C version.
//- This may produce "surprising" results for negative values
//- For example, -3 div 5 is -1 and -3 mod 5 is 2.
//- Note this is consistent: -3 * -1 + 2 == 5
module Math__div_def_i {
/*
function mod(x:int, m:int) : int
requires m > 0;
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 810 | ab755bb90567622488d27c0d53a6f76bdcccbb04fb2d43fcf03b28daf04a802c | class A {
var value: int
method m(i: int)
requires i == 6
requires value == 42
modifies this
{
var j: int := 17;
value := 43;
label L:
j := 18;
value := 44;
label M:
assert old(i) == 6; // i is local, but can't be changed anyway
assert old(j) == 18; //... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 993 | 5d97e55183bc3306f14c43789d141937e9ed1fa1e3f9350b0d8381b985a4e2c4 | class A {
var value: int
constructor ()
ensures value == 10
{
value := 10;
}
}
class B {
var a: A
constructor () { a := new A(); }
method m()
requires a.value == 11
modifies this, this.a
{
label L:
a.value := 12;
label M:
a := new A(); //... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 608 | 2f5b022ad3fdcf072a9f750eb49176842eb5a1747cc1035ca989bd6520f1dd68 | class A {
var z1: array<nat>
var z2: array<nat>
method mm()
requires z1.Length > 10 && z1[0] == 7
requires z2.Length > 10 && z2[0] == 17
modifies z2
{
var a: array<nat> := z1;
assert a[0] == 7;
a := z2;
assert a[0] == 17;
assert old(a[0]) == 17; // a is local with v... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_arrays.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,977 | 3fe1e6d7f2248bb10113ddfc42158caf2fce669685e29059b06d29d01e019b85 | // RUN: %dafny /compile:3 /spillTargetCode:2 /compileTarget:cpp "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
newtype uint32 = i:int | 0 <= i < 0x100000000
method returnANullArray() returns (a: array?<uint32>)
ensures a == null
{
a := null;
}
method returnANonNullArray() returns (a: array?<uint32>)
en... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_maps.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,628 | 318ff0283f6c25118a4536450005e16a130fc01d8ab2766c9f39e8f1ad69f25a | // RUN: %dafny /compile:3 /spillTargetCode:2 /compileTarget:cpp "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
newtype uint32 = i:int | 0 <= i < 0x100000000
method Test(name:string, b:bool)
requires b
{
if b {
print name, ": This is expected\n";
} else {
print name, ": This is *** UNEXPECTED *** ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_sets.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,292 | 4e2057c591d17dbbe1d9011c07c85788a7c068932fc8d9def7763520135a92ba | // RUN: %dafny /compile:3 /spillTargetCode:2 /compileTarget:cpp "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
newtype uint32 = i:int | 0 <= i < 0x100000000
datatype Example0 = Example0(u:uint32, b:bool)
method Test0(e0:Example0)
{
var s := { e0 };
}
datatype Example1 = Ex1a(u:uint32) | Ex1b(b:bool)
met... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-1158.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 531 | f7c81f30526c0ac67131e0e95032d35588f6613fac811986f606dd933f51c182 | // RUN: %dafny /compile:0 "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
type Id(==)
function F(s: set<Id>): int
lemma Test(x: Id)
{
var X := {x};
var a := map i | i <= X :: F(i);
var b := map[{} := F({}), X := F(X)];
assert a.Keys == b.Keys by { // spurious error reported here
forall i
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-283.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,603 | 80ed82d2559ecf696e57f9b87a6b0ec4331502c3d961fb8fd65f3ba5e7726767 | // RUN: %dafny /compile:0 "%s" > "%t"
// RUN: %dafny /noVerify /compile:4 /compileTarget:cs "%s" >> "%t"
// RUN: %dafny /noVerify /compile:4 /compileTarget:js "%s" >> "%t"
// RUN: %dafny /noVerify /compile:4 /compileTarget:go "%s" >> "%t"
// RUN: %dafny /noVerify /compile:4 /compileTarget:java "%s" >> "%t"
// RUN:... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-506.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,876 | 600397ec1ba5eb5bcddf4ce1644cefa9a1f6896f5a6ce34455d68922b9c366a2 | // RUN: %dafny /compile:4 /compileTarget:cs "%s" > "%t"
// RUN: %dafny /compile:4 /compileTarget:js "%s" >> "%t"
// RUN: %dafny /compile:4 /compileTarget:go "%s" >> "%t"
// RUN: %dafny /compile:4 /compileTarget:java "%s" >> "%t"
// RUN: %diff "%s.expect" "%t"
method Main() {
var a := new int[10];
var ind... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-975.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 235 | 78ac66c7319d0c9e741851b5fb5877de9875fc95e63e7c5bcc6bfb0e3aee6b03 | // RUN: %dafny /compile:0 "%s" > "%t"
// RUN: %diff "%s.expect" "%t"
function f():nat
ensures f() == 0
{ // no problem for methods
var x := 0; // no problem without this
assert true by {}
0
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/laboratory_tmp_tmps8ws6mu2_dafny-tutorial_exercise12.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 761 | cb49e935f3d1f7977a238845bc301e978aa722831e216eebc30a37486de3b445 | method FindMax(a: array<int>) returns (i: int)
// Annotate this method with pre- and postconditions
// that ensure it behaves as described.
requires 0 < a.Length
ensures 0 <= i < a.Length
ensures forall k: int :: 0 <= k < a.Length ==> a[k] <= a[i]
{
// Fill in the body that calculates the... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/laboratory_tmp_tmps8ws6mu2_dafny-tutorial_exercise9.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 609 | 3600a4bd09e0a88107c21b7ea9916e359dd6671267d7e756f482ec70a0382c9f | function fib(n: nat): nat
{
if n == 0 then 0 else
if n == 1 then 1 else
fib(n - 1) + fib(n - 2)
}
method ComputeFib(n: nat) returns (b: nat)
ensures b == fib(n) // Do not change this postcondition
{
// Change the method body to instead use c as described.
// You will ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/lets-prove-blocking-queue_tmp_tmptd_aws1k_dafny_prod-cons.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 4,783 | 1bc0b3dd8f3a57d8a71b1f2f672d8ea11791b84de4b9015560688ed54320ab25 | /**
* A proof in Dafny of the non blocking property of a queue.
* @author Franck Cassez.
*
* @note: based off Modelling Concurrency in Dafny, K.R.M. Leino
* @link{http://leino.science/papers/krml260.pdf}
*/
module ProdCons {
// A type for process id that supports equality (i.e. p == q is define... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/libraries_tmp_tmp9gegwhqj_examples_MutableMap_MutableMapDafny.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 5,271 | 8de2f484719f446ec127dc04eb3490481de1c77eb5b0961cdffa19151939e573 | /*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
// RUN: %verify "%s"
/**
* Implements mutable maps in Da... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_0.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,298 | 526e26369d7ba4798526975c80ac16918262ca9260becd4430e80f05799d781c | function abs(x: real): real
{
if x < 0.0 then -x else x
}
method has_close_elements(numbers: seq<real>, threshold: real) returns (result: bool)
ensures result <==> exists i, j ::
0 <= i < |numbers| &&
0 <= j < |numbers| &&
i != j &&
abs(numbers[i] - numbers[j]) < threshold
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_160.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,054 | 71584ca4dac9f6590b831057eeb53836595f2e71d6efd2f19ebd20118c91c102 | function pow(base: int, exponent: int): int
requires exponent >= 0
decreases exponent
{
if exponent == 0 then 1
else if exponent % 2 == 0 then pow(base * base, exponent / 2)
else base * pow(base, exponent - 1)
}
method do_algebra(operators: seq<char>, operands: seq<int>) returns (result: int)
req... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_161.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,902 | f37b4eb013e56b1ac778d16cbc18fb489ae098b13649910dabc0662617cabbef | function IsLetter(c: char): bool
{
(c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z')
}
function NoLetters(s: string, n: nat): bool
requires n <= |s|
{
forall c :: 0 <= c < n ==> !IsLetter(s[c])
}
function ToggleCase(c: char): char
{
if c >= 'a' && c <= 'z'
then
(c - 'a' + 'A')
else... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 716 | b8365c4805fa9d027f9884670ae2ec1f4f00c44701e4544f3e0c14f6018d6f55 | function sum(s: seq<int>, n: nat): int
requires n <= |s|
{
if |s| == 0 || n == 0 then
0
else
s[0] + sum(s[1..], n-1)
}
lemma sum_plus(s: seq<int>, i: nat)
requires i < |s|
ensures sum(s, i) + s[i] == sum(s, i+1)
{
}
method below_zero(ops: seq<int>) returns (result: b... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_5.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 929 | 03d3f0438e9d24b3203c11ec847196371243eb89c8720da95579144886774a78 | method intersperse(numbers: seq<int>, delimiter: int) returns (interspersed: seq<int>)
ensures |interspersed| == if |numbers| > 0 then 2 * |numbers| - 1 else 0
ensures forall i :: 0 <= i < |interspersed| ==> i % 2 == 0 ==>
interspersed[i] == numbers[i / 2]
ensures forall i :: 0 <= i < |... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/llm-verified-eval_tmp_tmpd2deqn_i_dafny_9.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 985 | d59b6b47d3704edd4b52f596e3be195093624ca6cd38e9bdbaec83e3e1a52008 | function isMax(m: int, numbers: seq<int>): bool
{
m in numbers &&
forall i :: 0 <= i < |numbers| ==> numbers[i] <= m
}
method max(numbers: seq<int>) returns (result: int)
requires numbers != []
ensures isMax(result, numbers)
{
result := numbers[0];
for i := 1 to |numbers|
invariant is... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/M2_tmp_tmp2laaavvl_Software Verification_Exercices_Exo4-CountAndReturn.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 208 | 668fce6e62cecfbefe63a6ecdcc2ceb10c5d20a9d5f0f2aa06095d7e2e8008b0 | method CountToAndReturnN(n: int) returns (r: int)
requires n >= 0
ensures r == n
{
var i := 0;
while i < n
invariant 0 <= i <= n
{
i := i + 1;
}
r := i;
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/M2_tmp_tmp2laaavvl_Software Verification_Exercices_Exo7-ComputeSum.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 311 | e984232635fe014fb0445fe5c677aac231a384f817f66b8103c393d280f31ee2 | function Sum(n:nat):nat
{
if n==0 then 0 else n + Sum(n-1)
}
method ComputeSum(n:nat) returns (s:nat)
ensures s ==Sum(n)
{
s := 0;
var i := 0;
while i< n
invariant 0 <= i <= n
invariant s == Sum(i)
{
s := s + i + 1;
i := i+1;
}
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/M2_tmp_tmp2laaavvl_Software Verification_Exercices_Exo9-Carre.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 232 | c7cee0201769db7c1faf2290c3592581014f910bc44a59ee1a330008a4155e4d | method Carre(a: nat) returns (c: nat)
ensures c == a*a
{
var i := 0;
c := 0;
while i != a
invariant 0 <= i <= a
invariant c == i*i
decreases a - i
{
c := c + 2*i +1;
i := i + 1;
}
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/metodosFormais_tmp_tmp4q2kmya4_T1-MetodosFormais_examples_ex1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 533 | e66f50730cb8704134466e720f1d1c5e9b0c87cc9a34c5801fc9ffb18f3d2655 | /*
Buscar
r = 0
enquanto(r<|a|){
se (a[r] == x) retorne r
r = r+1
}
retorne -1
*/
method buscar(a:array<int>, x:int) returns (r:int)
ensures r < 0 ==> forall i :: 0 <= i <a.Length ==> a[i] != x
ensures 0 <= r < a.Length ==> a[r] == x
{
r := 0;
while r < a.Length
decreases a.Length -... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/metodosFormais_tmp_tmp4q2kmya4_T1-MetodosFormais_examples_somatoriov2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 369 | c1ccc23edeb971cb5f8dd7e08204d01135d5cb21571f36f1939807b5f5619de2 | function somaAteAberto(a:array<nat>, i:nat):nat
requires i <= a.Length
reads a
{
if i ==0
then 0
else a[i-1] + somaAteAberto(a,i-1)
}
method somatorio(a:array<nat>) returns (s:nat)
ensures s == somaAteAberto(a, a.Length)
{
s := 0;
for i:= 0 to a.Length
invariant s == somaAteAberto... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpbez22nnn_Aula_2_ex1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 257 | fd78e3837110b2aa1b312875a990d5466783640b34040f7cf26a023e4491c899 | method Mult(x:nat, y:nat) returns (r: nat)
ensures r == x * y
{
var m := x;
var n := y;
r:=0;
while m > 0
invariant m >= 0
invariant m*n+r == x*y
{
r := r + n;
m := m - 1;
}
return r;
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpbez22nnn_Aula_2_ex2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 376 | e113e45cdb259d1cc19c17a15e435fb4618b69716083353ae23b2b45a91fdbf5 | function Potencia(x: nat, y: nat): nat
{
if y == 0
then 1
else x * Potencia(x, y-1)
}
method Pot(x: nat, y: nat) returns (r: nat)
ensures r == Potencia(x,y)
{
var b := x;
var e := y;
r := 1;
while e > 0
invariant Potencia(b, e) * r == Potencia(x,y)
{
r := ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpbez22nnn_Aula_4_ex1.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 301 | 4a6256f738d0e4c716a94a4b741cff9bbaf1c2655b341b34bbb8f725e0456d2d | predicate Par(n:int)
{
n % 2 == 0
}
method FazAlgo (a:int, b:int) returns (x:int, y:int)
requires a >= b && Par (a-b)
{
x := a;
y := b;
while x != y
invariant x >= y
invariant Par(x-y)
decreases x-y
{
x := x - 1;
y := y + 1;
}
}
|
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpbez22nnn_Aula_4_ex3.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 478 | 8a482ccad34c652f9f3a888207669be7966f3549f4c93b04cba34468fe92eb6c | function Fib(n:nat):nat
{
if n < 2
then n
else Fib(n-2) + Fib(n-1)
}
method ComputeFib(n:nat) returns (x:nat)
ensures x == Fib(n)
{
var i := 0;
x := 0;
var y := 1;
while i < n
decreases n - i
invariant 0 <= i <= n
invariant x == Fib(i)
invariant y == Fib(i+1... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Arrays_explicacao.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,467 | 81a91fbf29edfe2f4bacf4e0e257f6bd2d724e35ca9507b7e2da98c35af0c3ea | // Array<T> = visualização de um array
// Uma busca ordenada em um array
// Buscar: Array<Z>xZ -> Z (Z é inteiro)
// Pré: True (pré-condição é sempre verdadeira)
// Pos: R < 0 => Para todo i pertencente aos naturais(0 <= i < A.length => A[i] != X) e
// 0 <= R < A.length => A[R] = x
//
// método em qualquer ling... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Arrays_somatorioArray.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,084 | 2cd98cee86d46391ad9a37a9973ff6f03775da210c3d35ecf055608df23b0f91 | // Deve ser criado uma função explicando o que é um somatório
// Somatorio: Array<N> -> N
// Pre: True
// Pos: Somatorio(A) = somatório de i = 0 até |A|-1 os valores das posições do array pelo i
//
// function é uma fórmula matemática, ele não possui variaveis globais
// Soma: Array<N>xN -> N
// { Soma(A,0) = ... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Invariantes_fatorial2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 520 | c5917649f26d9f1f4e6cd7194f63535e9fd4b80ff2d7a6fb1f3ebb72a3979305 | function Fat(n:nat):nat
{
if n == 0 then 1 else n*Fat(n-1)
}
method Fatorial(n:nat) returns (f:nat)
ensures f == Fat(n)
{
f := 1;
var i := 1;
while i <= n
decreases n-i //variante
invariant 1 <= i <= n+1 //invariante
invariant f == Fat(i-1) //invariante
{
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Invariantes_fibonacci.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 938 | ff86114c026cf051ee83121b98b8f478eb18c7d7a2c9f759f25158185d695bb4 | // Provando fibonacci
function Fib(n:nat):nat
{
if n < 2
then n
else Fib(n-2) + Fib(n-1)
}
method ComputeFib(n:nat) returns (x:nat)
ensures x == Fib(n)
{
var i := 0;
x := 0;
var y := 1;
while i < n
decreases n-i
invariant 0 <= i <= n
invariant x == Fib(i)
i... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Invariantes_multiplicador.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,373 | 925f33a2dc117db568bb2dfa9e57aae94036e3cc313f196e85465e8cec99f1ad | // Exemplo de invariantes
// Invariante significa que o valor não muda desde a pré-condição até a pós-condição
method Mult(x:nat, y:nat) returns (r:nat)
ensures r == x * y
{
// parâmetros de entrada são imutáveis, por isso
// é preciso a atribuir a variáveis locais para usar em blocos de códigos para mu... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/Metodos_Formais_tmp_tmpql2hwcsh_Invariantes_potencia.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,442 | 70c9450ca4ed800937c27691a2ae147ed6f1a8d0d074ede9e456d7fb53b93f1a | // Potência
// deve ser especificado a potência, porque ele não existe n dafny
// Função recursiva da potência
function Potencia(x:nat, y:nat):nat
{
if y == 0
then 1
else x * Potencia(x,y-1)
}
// Quero agora implementar como uma função não recursiva
method Pot(x:nat, y:nat) returns (r:nat)
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFDS_tmp_tmpvvr5y1t9_Assignments_Ass-1-2020-21-Sol-eGela.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 3,649 | 0f68fbaea6121e81d4d1d3f7af503f310c025691971b88652e3e391c83ff8221 | // Ejercicio 1: Demostrar por inducci�n el siguiente lema:
lemma EcCuadDiv2_Lemma (x:int)
requires x >= 1
ensures (x*x + x) % 2 == 0
{
if x != 1 {
EcCuadDiv2_Lemma(x-1);
assert x*x+x == ((x-1)*(x-1) + (x-1)) + 2*x;
}
}
// Ejercicio 2: Demostrar por inducci�n el siguient... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFES_2021_tmp_tmpuljn8zd9_Exams_Special_Exam_03_2020_4_CatalanNumbers.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 672 | e144d9de0a0d64c2116abd986e53c89da39d99b25b36765ed0eec23d92c9bfae | function C(n: nat): nat
decreases n
{
if n == 0 then 1 else (4 * n - 2) * C(n-1) / (n + 1)
}
method calcC(n: nat) returns (res: nat)
ensures res == C(n)
{
var i := 0;
res := 1;
assert res == C(i) && 0 <= i <= n;
while i < n
decreases n - i //a - loop variant
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFES_2021_tmp_tmpuljn8zd9_FCUL_Exercises_10_find.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 429 | 431f258b52c96e01838aec134b1a95a81d416a1ae98d3798ba226706e9391e21 | method find(a: array<int>, key: int) returns(index: int)
requires a.Length > 0;
ensures 0 <= index <= a.Length;
ensures index < a.Length ==> a[index] == key;
{
index := 0;
while index < a.Length && a[index] != key
decreases a.Length - index
invariant 0 <= index <= a.Length
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFES_2021_tmp_tmpuljn8zd9_FCUL_Exercises_8_sum.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 339 | 7fffc0ca6f75a6ecdd6ca4f93def4794aa6548f0a35e638e3cbdf313c9deadec | function calcSum(n: nat) : nat
{
n * (n - 1) / 2
}
method sum(n: nat) returns(s: nat)
ensures s == calcSum(n + 1)
{
s := 0;
var i := 0;
while i < n
decreases n - i
invariant 0 <= i <= n
invariant s == calcSum(i + 1)
{
i := i + 1;
s :=... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFES_2021_tmp_tmpuljn8zd9_PracticalClasses_TP3_2_Insertion_Sort.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,229 | 4bd6e53cba8e76733973f4159d77a1c438b94be59997793205b043cad82bcc0a | // Sorts array 'a' using the insertion sort algorithm.
method insertionSort(a: array<int>)
modifies a
ensures isSorted(a, 0, a.Length)
ensures multiset(a[..]) == multiset(old(a[..]))
{
var i := 0;
while i < a.Length
decreases a.Length - i
invariant 0 <= i <= a.Length
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFES_2021_tmp_tmpuljn8zd9_TheoreticalClasses_Power.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,971 | 306c56561bef814aadd3dc2afe7c1b20f955584f256de8029de5ea79a01f2ab4 | /*
* Formal verification of O(n) and O(log n) algorithms to calculate the natural
* power of a real number (x^n), illustrating the usage of lemmas.
* FEUP, MIEIC, MFES, 2020/21.
*/
// Initial specification/definition of x^n, recursive, functional style,
// with time and space complexity O(n).
function power(... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFS_tmp_tmpmmnu354t_Praticas_TP9_Power.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 2,278 | 59ff0ed82fcf4c01d8e8c6dae2592f3c56b8528201f353f82be8655a1842923c | /*
* Formal verification of O(n) and O(log n) algorithms to calculate the natural
* power of a real number (x^n), illustrating the usage of lemmas.
* FEUP, M.EIC, MFS, 2021/22.
*/
// Initial specification/definition of x^n, recursive, functional style,
// with time and space complexity O(n).
function power(x... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MFS_tmp_tmpmmnu354t_Testes anteriores_T2_ex5_2020_2.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,041 | 0497747bb4884f54b50fdae469d07b18dbd67b1db708765f5894c52375cab2b1 | method leq(a: array<int>, b: array<int>) returns (result: bool)
ensures result <==> (a.Length <= b.Length && a[..] == b[..a.Length]) || (exists k :: 0 <= k < a.Length && k < b.Length && a[..k] == b[..k] && a[k] < b[k])
{
var i := 0;
while i < a.Length && i < b.Length
decreases a.Length - i
... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MIEIC_mfes_tmp_tmpq3ho7nve_exams_appeal_20_p4.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 376 | 0076c3834377bda264e6d9e58209ed53e383e96cc68dbf1e24df637f98029582 | function F(n: nat): nat { if n <= 2 then n else F(n-1) + F(n-3)}
method calcF(n: nat) returns (res: nat)
ensures res == F(n)
{
var a, b, c := 0, 1, 2;
var i := 0;
while i < n
decreases n-i
invariant 0 <= i <= n
invariant a == F(i) && b == F(i+1) && c == F(i+2)
{
a, b, c := b, c... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MIEIC_mfes_tmp_tmpq3ho7nve_exams_mt2_19_p4.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 445 | 9ed61e1fb59442a4b1e0aca30efd3a7e8969fbe70a84ee759a9415f6610c49ef | function R(n: nat): nat {
if n == 0 then 0 else if R(n-1) > n then R(n-1) - n else R(n-1) + n
}
method calcR(n: nat) returns (r: nat)
ensures r == R(n)
{
r := 0;
var i := 0;
while i < n
decreases n-i
invariant 0 <= i <= n
invariant r == R(i)
{
i :=... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MIEIC_mfes_tmp_tmpq3ho7nve_exams_mt2_19_p5.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,500 | 1a9153ad4830034c5ab0ec7834ee8ac9565497b900cfaf450f9b566ce2aacb34 | type T = int // example
// Partitions a nonempty array 'a', by reordering the elements in the array,
// so that elements smaller than a chosen pivot are placed to the left of the
// pivot, and values greater or equal than the pivot are placed to the right of
// the pivot. Returns the pivot position.
method par... |
sun-wendy/DafnyBench | DafnyBench/dataset/ground_truth/MIEIC_mfes_tmp_tmpq3ho7nve_exams_special_20_p5.dfy | Apache-2.0 | 67 | main | 0cd28feed9cd0179b07fdb9d002f8c39063658e4 | 2024-12-12T07:08:20Z | 1,640 | b5bd001396797eaaa4bcbb071ba52b3c3f25d5a40b8b8db35964bcde10d91962 | type T = int // for demo purposes, but could be another type
predicate sorted(a: array<T>, n: nat)
requires n <= a.Length
reads a
{
forall i,j :: 0 <= i < j < n ==> a[i] <= a[j]
}
// Use binary search to find an appropriate position to insert a value 'x'
// in a sorted array 'a', so that it remai... |
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