test_ID stringlengths 3 3 | test_file stringlengths 14 119 | ground_truth stringlengths 70 28.7k | hints_removed stringlengths 58 28.7k |
|---|---|---|---|
100 | Dafny-Exercises_tmp_tmpjm75muf__Session7Exercises_ExerciseBubbleSort.dfy | predicate sorted_seg(a:array<int>, i:int, j:int) //j excluded
requires 0 <= i <= j <= a.Length
reads a
{
forall l, k :: i <= l <= k < j ==> a[l] <= a[k]
}
method bubbleSorta(a:array<int>, c:int, f:int)//f excluded
modifies a
requires 0 <= c <= f <= a.Length //when c==f empty sequence
ensures sorted_seg(a,c,f)
en... | predicate sorted_seg(a:array<int>, i:int, j:int) //j excluded
requires 0 <= i <= j <= a.Length
reads a
{
forall l, k :: i <= l <= k < j ==> a[l] <= a[k]
}
method bubbleSorta(a:array<int>, c:int, f:int)//f excluded
modifies a
requires 0 <= c <= f <= a.Length //when c==f empty sequence
ensures sorted_seg(a,c,f)
en... |
101 | Dafny-Exercises_tmp_tmpjm75muf__Session7Exercises_ExerciseReplace.dfy |
method replace(v:array<int>, x:int, y:int)
modifies v
ensures forall k::0<=k<old(v.Length) && old(v[k])==x ==> v[k]==y
ensures forall k::0<=k<old(v.Length) && old(v[k])!=x ==> v[k]==old(v[k])
{
var i:=0;
while(i<v.Length)
decreases v.Length - i
invariant 0<=i<=v.Length
invariant forall k::0<=k<i ... |
method replace(v:array<int>, x:int, y:int)
modifies v
ensures forall k::0<=k<old(v.Length) && old(v[k])==x ==> v[k]==y
ensures forall k::0<=k<old(v.Length) && old(v[k])!=x ==> v[k]==old(v[k])
{
var i:=0;
while(i<v.Length)
{
if(v[i]==x){
v[i]:=y;
}
i:=i+1;
}
}
|
102 | Dafny-Exercises_tmp_tmpjm75muf__Session7Exercises_ExerciseSelSort.dfy | predicate sorted_seg(a:array<int>, i:int, j:int) //j not included
requires 0 <= i <= j <= a.Length
reads a
{
forall l, k :: i <= l <= k < j ==> a[l] <= a[k]
}
method selSort (a:array<int>, c:int, f:int)//f excluded
modifies a
requires 0 <= c <= f <= a.Length //when c==f empty sequence
ensures sorted_seg(a,c,f)
... | predicate sorted_seg(a:array<int>, i:int, j:int) //j not included
requires 0 <= i <= j <= a.Length
reads a
{
forall l, k :: i <= l <= k < j ==> a[l] <= a[k]
}
method selSort (a:array<int>, c:int, f:int)//f excluded
modifies a
requires 0 <= c <= f <= a.Length //when c==f empty sequence
ensures sorted_seg(a,c,f)
... |
103 | Dafny-Exercises_tmp_tmpjm75muf__Session7Exercises_ExerciseSeparate.dfy | predicate strictNegative(v:array<int>,i:int,j:int)
reads v
requires 0<=i<=j<=v.Length
{forall u | i<=u<j :: v[u]<0}
predicate positive(s:seq<int>)
{forall u::0<=u<|s| ==> s[u]>=0}
predicate isPermutation(s:seq<int>, t:seq<int>)
{multiset(s)==multiset(t)}
/**
returns an index st new array is a permutation of the old ... | predicate strictNegative(v:array<int>,i:int,j:int)
reads v
requires 0<=i<=j<=v.Length
{forall u | i<=u<j :: v[u]<0}
predicate positive(s:seq<int>)
{forall u::0<=u<|s| ==> s[u]>=0}
predicate isPermutation(s:seq<int>, t:seq<int>)
{multiset(s)==multiset(t)}
/**
returns an index st new array is a permutation of the old ... |
104 | Dafny-Exercises_tmp_tmpjm75muf__Session8Exercises_ExerciseInsertionSort.dfy |
predicate sorted_seg(a:array<int>, i:int, j:int) //i and j included
requires 0 <= i <= j+1 <= a.Length
reads a
{
forall l, k :: i <= l <= k <= j ==> a[l] <= a[k]
}
method InsertionSort(a: array<int>)
modifies a;
ensures sorted_seg(a,0,a.Length-1)
ensures multiset(a[..]) == old(multiset(a[..])) //Add and pr... |
predicate sorted_seg(a:array<int>, i:int, j:int) //i and j included
requires 0 <= i <= j+1 <= a.Length
reads a
{
forall l, k :: i <= l <= k <= j ==> a[l] <= a[k]
}
method InsertionSort(a: array<int>)
modifies a;
ensures sorted_seg(a,0,a.Length-1)
ensures multiset(a[..]) == old(multiset(a[..])) //Add and pr... |
105 | Dafny-Exercises_tmp_tmpjm75muf__Session9Exercises_ExerciseSeqMaxSum.dfy |
function Sum(v:array<int>,i:int,j:int):int
reads v
requires 0<=i<=j<=v.Length
decreases j
{
if (i==j) then 0
else Sum(v,i,j-1)+v[j-1]
}
predicate SumMaxToRight(v:array<int>,i:int,s:int)
reads v
requires 0<=i<v.Length
{
forall l,ss {:induction l}::0<=l<=i && ss==i+1==> Sum(v,l,ss)<=s
}
method segMaxSum(v:arr... |
function Sum(v:array<int>,i:int,j:int):int
reads v
requires 0<=i<=j<=v.Length
{
if (i==j) then 0
else Sum(v,i,j-1)+v[j-1]
}
predicate SumMaxToRight(v:array<int>,i:int,s:int)
reads v
requires 0<=i<v.Length
{
forall l,ss {:induction l}::0<=l<=i && ss==i+1==> Sum(v,l,ss)<=s
}
method segMaxSum(v:array<int>,i:in... |
106 | Dafny-Grind75_tmp_tmpsxfz3i4r_problems_twoSum.dfy | /*
https://leetcode.com/problems/two-sum/
function twoSum(nums: number[], target: number): number[] {
const n = nums.length;
for(let i = 0; i < n; i++) {
for(let k = i+1; k < n; k++) {
if(nums[i] + nums[k] == target) return [i,k];
}
}
};
*/
predicate summingPair(i: nat, j: nat, ... | /*
https://leetcode.com/problems/two-sum/
function twoSum(nums: number[], target: number): number[] {
const n = nums.length;
for(let i = 0; i < n; i++) {
for(let k = i+1; k < n; k++) {
if(nums[i] + nums[k] == target) return [i,k];
}
}
};
*/
predicate summingPair(i: nat, j: nat, ... |
107 | Dafny-Practice_tmp_tmphnmt4ovh_BST.dfy | datatype Tree = Empty | Node(int,Tree,Tree)
method Main() {
var tree := BuildBST([-2,8,3,9,2,-7,0]);
PrintTreeNumbersInorder(tree);
}
method PrintTreeNumbersInorder(t: Tree)
{
match t {
case Empty =>
case Node(n, l, r) =>
PrintTreeNumbersInorder(l);
print n;
print "\n";
PrintTreeNumbersInorder(r);
... | datatype Tree = Empty | Node(int,Tree,Tree)
method Main() {
var tree := BuildBST([-2,8,3,9,2,-7,0]);
PrintTreeNumbersInorder(tree);
}
method PrintTreeNumbersInorder(t: Tree)
{
match t {
case Empty =>
case Node(n, l, r) =>
PrintTreeNumbersInorder(l);
print n;
print "\n";
PrintTreeNumbersInorder(r);
... |
108 | Dafny-Practice_tmp_tmphnmt4ovh_Pattern Matching.dfy |
method {:verify true} FindAllOccurrences(text: string, pattern: string) returns (offsets: set<nat>)
ensures forall i :: i in offsets ==> i + |pattern| <= |text|
ensures forall i :: 0 <= i <= |text| - |pattern| ==> (text[i..i+|pattern|] == pattern <==> i in offsets)
{
offsets := {};
var i:int := 0;
// no pat... |
method {:verify true} FindAllOccurrences(text: string, pattern: string) returns (offsets: set<nat>)
ensures forall i :: i in offsets ==> i + |pattern| <= |text|
ensures forall i :: 0 <= i <= |text| - |pattern| ==> (text[i..i+|pattern|] == pattern <==> i in offsets)
{
offsets := {};
var i:int := 0;
// no pat... |
109 | Dafny-Projects_tmp_tmph399drhy_p2_arraySplit.dfy | method ArraySplit (a : array<int>) returns (b : array<int>, c : array<int>)
ensures fresh(b)
ensures fresh(c)
ensures a[..] == b[..] + c[..]
ensures a.Length == b.Length + c.Length
ensures a.Length > 1 ==> a.Length > b.Length
ensures a.Length > 1 ==> a.Length > c.Length
{
var splitPoint : int := a.Length ... | method ArraySplit (a : array<int>) returns (b : array<int>, c : array<int>)
ensures fresh(b)
ensures fresh(c)
ensures a[..] == b[..] + c[..]
ensures a.Length == b.Length + c.Length
ensures a.Length > 1 ==> a.Length > b.Length
ensures a.Length > 1 ==> a.Length > c.Length
{
var splitPoint : int := a.Length ... |
110 | Dafny-VMC_tmp_tmpzgqv0i1u_src_Math_Exponential.dfy | module Exponential {
ghost function {:axiom} Exp(x: real): real
lemma {:axiom} FunctionalEquation(x: real, y: real)
ensures Exp(x + y) == Exp(x) * Exp(y)
lemma {:axiom} Increasing(x: real, y: real)
requires x < y
ensures Exp(x) < Exp(y)
lemma {:axiom} EvalOne()
ensures 2.718281828 <= Exp(1.0)... | module Exponential {
ghost function {:axiom} Exp(x: real): real
lemma {:axiom} FunctionalEquation(x: real, y: real)
ensures Exp(x + y) == Exp(x) * Exp(y)
lemma {:axiom} Increasing(x: real, y: real)
requires x < y
ensures Exp(x) < Exp(y)
lemma {:axiom} EvalOne()
ensures 2.718281828 <= Exp(1.0)... |
111 | Dafny-VMC_tmp_tmpzgqv0i1u_src_Math_Helper.dfy | /*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
module Helper {
/************
Definitions
************/
fu... | /*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
module Helper {
/************
Definitions
************/
fu... |
112 | Dafny-demo_tmp_tmpkgr_dvdi_Dafny_BinarySearch.dfy |
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]
}
method BinarySearch(a: array?<int>, key: int)
returns (index: int)
requires a != null && sorted(a,0,a.Length-1);
ensures index >= 0 ==> index < a.Length && a[index] ... |
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]
}
method BinarySearch(a: array?<int>, key: int)
returns (index: int)
requires a != null && sorted(a,0,a.Length-1);
ensures index >= 0 ==> index < a.Length && a[index] ... |
113 | Dafny-experiences_tmp_tmp150sm9qy_dafny_started_tutorial_dafny_tutorial_array.dfy | method FindMax(a: array<int>) returns (i: int)
// Annotate this method with pre- and postconditions
// that ensure it behaves as described.
requires a.Length > 0
ensures 0<= i < a.Length
ensures forall k :: 0 <= k < a.Length ==> a[k] <= a[i]
{
// Fill in the body that calculates the INDEX of the maximum.
... | method FindMax(a: array<int>) returns (i: int)
// Annotate this method with pre- and postconditions
// that ensure it behaves as described.
requires a.Length > 0
ensures 0<= i < a.Length
ensures forall k :: 0 <= k < a.Length ==> a[k] <= a[i]
{
// Fill in the body that calculates the INDEX of the maximum.
... |
114 | Dafny-programs_tmp_tmpnso9eu7u_Algorithms + sorting_bubble-sort.dfy | /*
Bubble Sort is the simplest sorting algorithm that works by
repeatedly swapping the adjacent elements if they are in wrong order.
*/
predicate sorted_between(A:array<int>, from:int, to:int)
reads A
{
forall i, j :: 0 <= i <= j < A.Length && from <= i <= j <= to ==> A[i] <= A[j]
}
predicate sorted(A:array<... | /*
Bubble Sort is the simplest sorting algorithm that works by
repeatedly swapping the adjacent elements if they are in wrong order.
*/
predicate sorted_between(A:array<int>, from:int, to:int)
reads A
{
forall i, j :: 0 <= i <= j < A.Length && from <= i <= j <= to ==> A[i] <= A[j]
}
predicate sorted(A:array<... |
115 | DafnyExercises_tmp_tmpd6qyevja_Part1_Q1.dfy | method addArrays(a : array<int>, b : array<int>) returns (c : array<int>)
requires a.Length == b.Length
ensures b.Length == c.Length
ensures forall i:int :: 0 <= i <c.Length ==> c[i] == a[i] + b[i]
{
c := new int[a.Length];
var j := 0;
while (j < a.Length)
invariant 0 <= j <= c.Length
in... | method addArrays(a : array<int>, b : array<int>) returns (c : array<int>)
requires a.Length == b.Length
ensures b.Length == c.Length
ensures forall i:int :: 0 <= i <c.Length ==> c[i] == a[i] + b[i]
{
c := new int[a.Length];
var j := 0;
while (j < a.Length)
{
c[j] := a[j] + b[j];
... |
116 | DafnyExercises_tmp_tmpd6qyevja_QuickExercises_testing2.dfy |
// predicate recSorted(s : string) decreases s
// {
// if (|s| <=1) then true else if(s[0] > s[1]) then false else recSorted(s[1..])
// }
// predicate forallSorted (s : string)
// {
// forall x,y::0<x<y<|s|==>s[x]<s[y]
// }
// lemma forallEQrec(a:string)
// ensures forallSorted(a) == recSorted(a) {
... |
// predicate recSorted(s : string) decreases s
// {
// if (|s| <=1) then true else if(s[0] > s[1]) then false else recSorted(s[1..])
// }
// predicate forallSorted (s : string)
// {
// forall x,y::0<x<y<|s|==>s[x]<s[y]
// }
// lemma forallEQrec(a:string)
// ensures forallSorted(a) == recSorted(a) {
... |
117 | DafnyPrograms_tmp_tmp74_f9k_c_automaton.dfy | /**
Consider cellular automata: a row of cells is repeatedly updated according to a rule. In this exercise I dabbled with,
each cell has the value either false or true. Each cell's next state depends only on the immediate neighbours, in the
case where the cell is at the edges of the row, the inexistent neighbours are ... | /**
Consider cellular automata: a row of cells is repeatedly updated according to a rule. In this exercise I dabbled with,
each cell has the value either false or true. Each cell's next state depends only on the immediate neighbours, in the
case where the cell is at the edges of the row, the inexistent neighbours are ... |
118 | DafnyPrograms_tmp_tmp74_f9k_c_invertarray.dfy | /**
Inverts an array of ints.
*/
method InvertArray(a: array<int>)
modifies a
ensures forall i | 0 <= i < a.Length :: a[i] == old(a[a.Length-1-i])
{
var index := 0;
while index < a.Length / 2
invariant 0 <= index <= a.Length / 2
// the elements i before position index are already switched with the o... | /**
Inverts an array of ints.
*/
method InvertArray(a: array<int>)
modifies a
ensures forall i | 0 <= i < a.Length :: a[i] == old(a[a.Length-1-i])
{
var index := 0;
while index < a.Length / 2
// the elements i before position index are already switched with the old value of position a.Length - 1 - i
... |
119 | DafnyPrograms_tmp_tmp74_f9k_c_map-multiset-implementation.dfy | /**
This ADT represents a multiset.
*/
trait MyMultiset {
// internal invariant
ghost predicate Valid()
reads this
// abstract variable
ghost var theMultiset: multiset<int>
method Add(elem: int) returns (didChange: bool)
modifies this
requires Valid()
ensures Valid()
ensures theMulti... | /**
This ADT represents a multiset.
*/
trait MyMultiset {
// internal invariant
ghost predicate Valid()
reads this
// abstract variable
ghost var theMultiset: multiset<int>
method Add(elem: int) returns (didChange: bool)
modifies this
requires Valid()
ensures Valid()
ensures theMulti... |
120 | DafnyPrograms_tmp_tmp74_f9k_c_prime-database.dfy | //predicate for primeness
ghost predicate prime(n: nat)
{ n > 1 && (forall nr | 1 < nr < n :: n % nr != 0) }
datatype Answer = Yes | No | Unknown
//the class containing a prime database, if a number is prime it returns Yes, if it is not No and if the number
//is not in the database it returns Unknown
class {:autocon... | //predicate for primeness
ghost predicate prime(n: nat)
{ n > 1 && (forall nr | 1 < nr < n :: n % nr != 0) }
datatype Answer = Yes | No | Unknown
//the class containing a prime database, if a number is prime it returns Yes, if it is not No and if the number
//is not in the database it returns Unknown
class {:autocon... |
121 | DafnyProjects_tmp_tmp2acw_s4s_CombNK.dfy |
/*
* Formal specification and verification of a dynamic programming algorithm for calculating C(n, k).
* FEUP, MIEIC, MFES, 2020/21.
*/
// Initial recursive definition of C(n, k), based on the Pascal equality.
function comb(n: nat, k: nat): nat
requires 0 <= k <= n
{
if k == 0 || k == n then 1 else comb(n-1, k)... |
/*
* Formal specification and verification of a dynamic programming algorithm for calculating C(n, k).
* FEUP, MIEIC, MFES, 2020/21.
*/
// Initial recursive definition of C(n, k), based on the Pascal equality.
function comb(n: nat, k: nat): nat
requires 0 <= k <= n
{
if k == 0 || k == n then 1 else comb(n-1, k)... |
122 | DafnyProjects_tmp_tmp2acw_s4s_Graph.dfy | // Simple directed graph with vertices of any type T.
class {:autocontracts} Graph<T(==)> {
var V: set<T>; // vertex-set
var E: set<(T, T)>; // edge-set
// Class invariant.
ghost predicate Valid() {
// edges must refer to vertices that belong to the vertex-set
// and self-loops (edges connec... | // Simple directed graph with vertices of any type T.
class {:autocontracts} Graph<T(==)> {
var V: set<T>; // vertex-set
var E: set<(T, T)>; // edge-set
// Class invariant.
ghost predicate Valid() {
// edges must refer to vertices that belong to the vertex-set
// and self-loops (edges connec... |
123 | DafnyProjects_tmp_tmp2acw_s4s_Power.dfy | /*
* Formal verification of an O(log n) algorithm to calculate the natural power of a real number (x^n),
* illustrating the usage of lemmas and automatic induction in Dafny.
* J. Pascoal Faria, FEUP, Jan/2022.
*/
// Recursive definition of x^n in functional style, with time and space complexity O(n).
function power... | /*
* Formal verification of an O(log n) algorithm to calculate the natural power of a real number (x^n),
* illustrating the usage of lemmas and automatic induction in Dafny.
* J. Pascoal Faria, FEUP, Jan/2022.
*/
// Recursive definition of x^n in functional style, with time and space complexity O(n).
function power... |
124 | DafnyProjects_tmp_tmp2acw_s4s_RawSort.dfy | /**
* Proves the correctness of a "raw" array sorting algorithm that swaps elements out of order, chosen randomly.
* FEUP, MFES, 2020/21.
*/
// Type of each array element; can be any type supporting comparision operators.
type T = int
// Checks if array 'a' is sorted by non-descending order.
ghost predicate sorte... | /**
* Proves the correctness of a "raw" array sorting algorithm that swaps elements out of order, chosen randomly.
* FEUP, MFES, 2020/21.
*/
// Type of each array element; can be any type supporting comparision operators.
type T = int
// Checks if array 'a' is sorted by non-descending order.
ghost predicate sorte... |
125 | DafnyProjects_tmp_tmp2acw_s4s_findMax.dfy | /*
* Formal verification of a simple algorithm to find the maximum value in an array.
* FEUP, MIEIC, MFES, 2020/21.
*/
// Finds the maximum value in a non-empty array.
method findMax(a: array<real>) returns (max: real)
requires a.Length > 0
ensures exists k :: 0 <= k < a.Length && max == a[k]
ensures forall k :... | /*
* Formal verification of a simple algorithm to find the maximum value in an array.
* FEUP, MIEIC, MFES, 2020/21.
*/
// Finds the maximum value in a non-empty array.
method findMax(a: array<real>) returns (max: real)
requires a.Length > 0
ensures exists k :: 0 <= k < a.Length && max == a[k]
ensures forall k :... |
126 | DafnyProjects_tmp_tmp2acw_s4s_longestPrefix.dfy | // MFES, Exam 8/Sept/20201, Exercise 5
// Computes the length (i) of the longest common prefix (initial subarray)
// of two arrays a and b.
method longestPrefix(a: array<int>, b: array <int>) returns (i: nat)
ensures i <= a.Length && i <= b.Length
ensures a[..i] == b[..i]
ensures i < a.Length && i < b.Length ==... | // MFES, Exam 8/Sept/20201, Exercise 5
// Computes the length (i) of the longest common prefix (initial subarray)
// of two arrays a and b.
method longestPrefix(a: array<int>, b: array <int>) returns (i: nat)
ensures i <= a.Length && i <= b.Length
ensures a[..i] == b[..i]
ensures i < a.Length && i < b.Length ==... |
127 | DafnyProjects_tmp_tmp2acw_s4s_partitionOddEven.dfy | // Rearranges the elements in an array 'a' of natural numbers,
// so that all odd numbers appear before all even numbers.
method partitionOddEven(a: array<nat>)
modifies a
ensures multiset(a[..]) == multiset(old(a[..]))
ensures ! exists i, j :: 0 <= i < j < a.Length && even(a[i]) && odd(a[j])
{
var i := 0;... | // Rearranges the elements in an array 'a' of natural numbers,
// so that all odd numbers appear before all even numbers.
method partitionOddEven(a: array<nat>)
modifies a
ensures multiset(a[..]) == multiset(old(a[..]))
ensures ! exists i, j :: 0 <= i < j < a.Length && even(a[i]) && odd(a[j])
{
var i := 0;... |
128 | DafnyProjects_tmp_tmp2acw_s4s_sqrt.dfy |
method sqrt(x: real) returns (r: real)
requires x >= 0.0
ensures r * r == x && r >= 0.0
method testSqrt() {
var r := sqrt(4.0);
//if (2.0 < r) { monotonicSquare(2.0, r); }
if (r < 2.0) { monotonicSquare(r, 2.0); }
assert r == 2.0;
}
lemma monotonicMult(c: real, x: real, y: real)
requires x < y && c > 0... |
method sqrt(x: real) returns (r: real)
requires x >= 0.0
ensures r * r == x && r >= 0.0
method testSqrt() {
var r := sqrt(4.0);
//if (2.0 < r) { monotonicSquare(2.0, r); }
if (r < 2.0) { monotonicSquare(r, 2.0); }
}
lemma monotonicMult(c: real, x: real, y: real)
requires x < y && c > 0.0
ensures c * x ... |
129 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week1_7_A2_Q1_trimmed copy - 副本.dfy | ghost function Count(hi: nat, s:seq<int>): int
requires 0 <= hi <= |s|
decreases hi
{
if hi == 0 then 0
else if s[hi-1]%2 == 0 then 1 + Count(hi-1, s) else Count(hi-1, s)
}
method FooCount(CountIndex:nat, a:seq<int>,b:array<int>) returns (p:nat)
requires CountIndex == 0 || (|a| == b.Length && 1 <=... | ghost function Count(hi: nat, s:seq<int>): int
requires 0 <= hi <= |s|
{
if hi == 0 then 0
else if s[hi-1]%2 == 0 then 1 + Count(hi-1, s) else Count(hi-1, s)
}
method FooCount(CountIndex:nat, a:seq<int>,b:array<int>) returns (p:nat)
requires CountIndex == 0 || (|a| == b.Length && 1 <= CountIndex <= |a... |
130 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week1_7_MaxSum.dfy | method MaxSum(x:int, y:int) returns (s:int, m:int)
ensures s == x+y
ensures (m == x || m == y) && x <= m && y <= m
{
s := x+y;
if x > y{
m := x;
} else if y > x{
m := y;
} else {
m := x;
}
assert m >= y;
}
method Main()
{
var m, n := 4,5;
var a,b := MaxSum(m,n);
... | method MaxSum(x:int, y:int) returns (s:int, m:int)
ensures s == x+y
ensures (m == x || m == y) && x <= m && y <= m
{
s := x+y;
if x > y{
m := x;
} else if y > x{
m := y;
} else {
m := x;
}
}
method Main()
{
var m, n := 4,5;
var a,b := MaxSum(m,n);
print "Search retu... |
131 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week1_7_Week4__LinearSearch.dfy | method LinearSeach0<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures 0 <= n <= a.Length
ensures n == a.Length || P(a[n])
{
n := 0;
while n != a.Length
invariant 0 <= n <= a.Length
{
if P(a[n]) {return;}
n := n + 1;
}
}
predicate P(n: int) {
n % ... | method LinearSeach0<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures 0 <= n <= a.Length
ensures n == a.Length || P(a[n])
{
n := 0;
while n != a.Length
{
if P(a[n]) {return;}
n := n + 1;
}
}
predicate P(n: int) {
n % 2 == 0
}
method TestLinearSearch() {... |
132 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week1_7_week4_tute_ex4.dfy | method LinearSearch<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures -1 <= n < a.Length
ensures n == -1 || P(a[n])
ensures n != -1 ==> forall i :: 0 <= i < n ==> ! P(a[i])
ensures n == -1 ==> forall i :: 0 <= i < a.Length ==> ! P(a[i])
{
n := 0;
while n != a.Length
decreases a.Len... | method LinearSearch<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures -1 <= n < a.Length
ensures n == -1 || P(a[n])
ensures n != -1 ==> forall i :: 0 <= i < n ==> ! P(a[i])
ensures n == -1 ==> forall i :: 0 <= i < a.Length ==> ! P(a[i])
{
n := 0;
while n != a.Length
{
if P(a[n]... |
133 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week1_7_week5_ComputePower.dfy | function Power(n:nat):nat
{
if n == 0 then 1 else 2 * Power(n-1)
}
method CalcPower(n:nat) returns (p:nat)
ensures p == 2*n;
{
p := 2*n;
}
method ComputePower(n:nat) returns (p:nat)
ensures p == Power(n)
{
p:=1;
var i:=0;
while i!=n
invariant 0 <= i <= n
invariant p *Powe... | function Power(n:nat):nat
{
if n == 0 then 1 else 2 * Power(n-1)
}
method CalcPower(n:nat) returns (p:nat)
ensures p == 2*n;
{
p := 2*n;
}
method ComputePower(n:nat) returns (p:nat)
ensures p == Power(n)
{
p:=1;
var i:=0;
while i!=n
{
p:= CalcPower(p);
i:=i+1;
}
}... |
134 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_a3 copy 2.dfy | class TwoStacks<T(0)(==)>
{
//abstract state
ghost var s1 :seq<T>
ghost var s2 :seq<T>
ghost const N :nat // maximum size of the stacks
ghost var Repr : set<object>
//concrete state
var data: array<T>
var n1: nat // number of elements in the stack 1
var n2: nat // number of elements... | class TwoStacks<T(0)(==)>
{
//abstract state
ghost var s1 :seq<T>
ghost var s2 :seq<T>
ghost const N :nat // maximum size of the stacks
ghost var Repr : set<object>
//concrete state
var data: array<T>
var n1: nat // number of elements in the stack 1
var n2: nat // number of elements... |
135 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_a3_search_findPositionOfIndex.dfy | method FindPositionOfElement(a:array<int>,Element:nat,n1:nat,s1:seq<int>) returns (Position:int,Count:nat)
requires n1 == |s1| && 0 <= n1 <= a.Length
requires forall i:: 0<= i < |s1| ==> a[i] == s1[i]
ensures Position == -1 || Position >= 1
ensures |s1| != 0 && Position >= 1 ==> exists i... | method FindPositionOfElement(a:array<int>,Element:nat,n1:nat,s1:seq<int>) returns (Position:int,Count:nat)
requires n1 == |s1| && 0 <= n1 <= a.Length
requires forall i:: 0<= i < |s1| ==> a[i] == s1[i]
ensures Position == -1 || Position >= 1
ensures |s1| != 0 && Position >= 1 ==> exists i... |
136 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_week10_BoundedQueue_01.dfy | class BoundedQueue<T(0)>
{
// abstract state
ghost var contents: seq<T> // the contents of the bounded queue
ghost var N: nat // the (maximum) size of the bounded queue
ghost var Repr: set<object>
// concrete state
var data: array<T>
var wr: nat
var rd: nat
ghost predicate Valid()
reads this, Repr
ensures... | class BoundedQueue<T(0)>
{
// abstract state
ghost var contents: seq<T> // the contents of the bounded queue
ghost var N: nat // the (maximum) size of the bounded queue
ghost var Repr: set<object>
// concrete state
var data: array<T>
var wr: nat
var rd: nat
ghost predicate Valid()
reads this, Repr
ensures... |
137 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_week10_ExtensibleArray.dfy | class ExtensibleArray<T(0)> {
// abstract state
ghost var Elements: seq<T>
ghost var Repr: set<object>
//concrete state
var front: array?<T>
var depot: ExtensibleArray?<array<T>>
var length: int // number of elements
var M: int // number of elements in depot
ghost predicate Valid()
decreases ... | class ExtensibleArray<T(0)> {
// abstract state
ghost var Elements: seq<T>
ghost var Repr: set<object>
//concrete state
var front: array?<T>
var depot: ExtensibleArray?<array<T>>
var length: int // number of elements
var M: int // number of elements in depot
ghost predicate Valid()
reads this... |
138 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_week8_CheckSumCalculator.dfy | ghost function Hash(s:string):int {
SumChars(s) % 137
}
ghost function SumChars(s: string):int {
if |s| == 0 then 0 else
s[|s| - 1] as int + SumChars(s[..|s| -1])
}
class CheckSumCalculator{
var data: string
var cs:int
ghost predicate Valid()
reads this
{
cs == Hash(da... | ghost function Hash(s:string):int {
SumChars(s) % 137
}
ghost function SumChars(s: string):int {
if |s| == 0 then 0 else
s[|s| - 1] as int + SumChars(s[..|s| -1])
}
class CheckSumCalculator{
var data: string
var cs:int
ghost predicate Valid()
reads this
{
cs == Hash(da... |
139 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_week8_CoffeeMaker2.dfy | class Grinder {
ghost var hasBeans: bool
ghost var Repr: set<object>
ghost predicate Valid()
reads this, Repr
ensures Valid() ==> this in Repr
constructor()
ensures Valid() && fresh(Repr) && !hasBeans
function Ready(): bool
requires Valid()
reads Repr
ensures Ready() == hasBeans ... | class Grinder {
ghost var hasBeans: bool
ghost var Repr: set<object>
ghost predicate Valid()
reads this, Repr
ensures Valid() ==> this in Repr
constructor()
ensures Valid() && fresh(Repr) && !hasBeans
function Ready(): bool
requires Valid()
reads Repr
ensures Ready() == hasBeans ... |
140 | Dafny_Learning_Experience_tmp_tmpuxvcet_u_week8_12_week9_lemma.dfy | method AssignmentsToMark(students:int, tutors: int) returns (r:int)
requires students > 0 && tutors > 1
ensures r < students
{
assert students > 0 && tutors > 1;
assert students > 0 && tutors > 1 && true;
assert students > 0 && tutors > 1 && students/tutors < students ==> students/tutors < students;... | method AssignmentsToMark(students:int, tutors: int) returns (r:int)
requires students > 0 && tutors > 1
ensures r < students
{
DivisionLemma(students,tutors);
r:= students/tutors;
calc {
//true;
1/tutors < 1;
students/tutors < students;
}
}
lemma DivisionLemma(n:int,d:i... |
141 | Dafny_ProgrammingLanguages_tmp_tmp82_e0kji_ExtraCredit.dfy | datatype Exp = Const(int) | Var(string) | Plus(Exp, Exp) | Mult(Exp, Exp)
function eval(e:Exp, store:map<string, int>):int
{
match(e)
case Const(n) => n
case Var(s) => if(s in store) then store[s] else -1
case Plus(e1, e2) => eval(e1, store) + eval(e2, store)
case Mult(e1, e2) => eval(e1, store) * eval(e2, s... | datatype Exp = Const(int) | Var(string) | Plus(Exp, Exp) | Mult(Exp, Exp)
function eval(e:Exp, store:map<string, int>):int
{
match(e)
case Const(n) => n
case Var(s) => if(s in store) then store[s] else -1
case Plus(e1, e2) => eval(e1, store) + eval(e2, store)
case Mult(e1, e2) => eval(e1, store) * eval(e2, s... |
142 | Dafny_Programs_tmp_tmp99966ew4_binary_search.dfy | predicate sorted(a: array<int>)
requires a != null
reads a
{
forall j, k :: 0 <= j < k < a.Length ==> a[j] <= a[k]
}
method BinarySearch(a: array<int>, value: int) returns (index: int)
requires a != null && 0 <= a.Length && sorted(a)
ensures 0 <= index ==> index < a.Length && a[index] == value
ensures... | predicate sorted(a: array<int>)
requires a != null
reads a
{
forall j, k :: 0 <= j < k < a.Length ==> a[j] <= a[k]
}
method BinarySearch(a: array<int>, value: int) returns (index: int)
requires a != null && 0 <= a.Length && sorted(a)
ensures 0 <= index ==> index < a.Length && a[index] == value
ensures... |
143 | Dafny_Programs_tmp_tmp99966ew4_lemma.dfy | lemma SkippingLemma(a : array<int>, j : int)
requires a != null
requires forall i :: 0 <= i < a.Length ==> 0 <= a[i]
requires forall i :: 0 < i < a.Length ==> a[i-1]-1 <= a[i]
requires 0 <= j < a.Length
ensures forall k :: j <= k < j + a[j] && k < a.Length ==> a[k] != 0
{
var i := j;
while i < j + ... | lemma SkippingLemma(a : array<int>, j : int)
requires a != null
requires forall i :: 0 <= i < a.Length ==> 0 <= a[i]
requires forall i :: 0 < i < a.Length ==> a[i-1]-1 <= a[i]
requires 0 <= j < a.Length
ensures forall k :: j <= k < j + a[j] && k < a.Length ==> a[k] != 0
{
var i := j;
while i < j + ... |
144 | Dafny_Programs_tmp_tmp99966ew4_mymax.dfy | method Max(a: int, b:int) returns (c: int)
ensures c >= a && c>= b
{
if (a < b)
{ c := b; }
else
{ c := a; }
assert a <= c && b <= c;
}
method Testing()
{
var v := Max(2, 3);
assert v >= 3;
}
| method Max(a: int, b:int) returns (c: int)
ensures c >= a && c>= b
{
if (a < b)
{ c := b; }
else
{ c := a; }
}
method Testing()
{
var v := Max(2, 3);
}
|
145 | Dafny_Programs_tmp_tmp99966ew4_trig.dfy | predicate P(x: int)
predicate Q(x: int)
method test()
requires forall x {:trigger P(x)} :: P(x) && Q(x)
ensures Q(0)
{
assert P(0);
}
| predicate P(x: int)
predicate Q(x: int)
method test()
requires forall x {:trigger P(x)} :: P(x) && Q(x)
ensures Q(0)
{
}
|
146 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_validation_examples.dfy | function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(N: int) returns (y: nat) requires N >= 0
ensures y == Power(N)
{
y := 1;
var x := 0;
while x != N
invariant 0 <= x <= N
invariant y == Power(x)
decreases N - x
{
x, y :=... | function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(N: int) returns (y: nat) requires N >= 0
ensures y == Power(N)
{
y := 1;
var x := 0;
while x != N
{
x, y := x + 1, y + y;
}
}
// Original davinci-003 completion:
// method ComputePower1(N:... |
147 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_ComputePower.dfy | function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(N: int) returns (y: nat) requires N >= 0
ensures y == Power(N)
{
y := 1;
var x := 0;
while x != N
invariant 0 <= x <= N
invariant y == Power(x)
decreases N - x
{
x, y :=... | function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(N: int) returns (y: nat) requires N >= 0
ensures y == Power(N)
{
y := 1;
var x := 0;
while x != N
{
x, y := x + 1, y + y;
}
}
|
148 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_CopyMatrix.dfy | method CopyMatrix(src: array2, dst: array2)
requires src.Length0 == dst.Length0 && src.Length1 == dst.Length1
modifies dst
ensures forall i, j :: 0 <= i < src.Length0 && 0 <= j < src.Length1 ==> dst[i,j] == old(src[i,j])
{
var m := 0;
while m != src.Length0
invariant 0 <= m <= src.Length0
... | method CopyMatrix(src: array2, dst: array2)
requires src.Length0 == dst.Length0 && src.Length1 == dst.Length1
modifies dst
ensures forall i, j :: 0 <= i < src.Length0 && 0 <= j < src.Length1 ==> dst[i,j] == old(src[i,j])
{
var m := 0;
while m != src.Length0
{
var n := 0;
while n... |
149 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_Cube.dfy | method Cube(n: nat) returns (c: nat)
ensures c == n * n * n
{
c := 0;
var i := 0;
var k := 1;
var m := 6;
while i != n
invariant 0 <= i <= n
invariant c == i * i * i
invariant k == 3*i*i + 3*i + 1
invariant m == 6 * i + 6
{
c, k, m := c + k, k + m, ... | method Cube(n: nat) returns (c: nat)
ensures c == n * n * n
{
c := 0;
var i := 0;
var k := 1;
var m := 6;
while i != n
{
c, k, m := c + k, k + m, m + 6;
i := i + 1;
}
}
|
150 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_DoubleArray.dfy | method DoubleArray(src: array<int>, dst: array<int>)
requires src.Length == dst.Length
modifies dst
ensures forall i :: 0 <= i < src.Length ==> dst[i] == 2 * old(src[i])
{
var n := 0;
while n != src.Length
invariant 0 <= n <= src.Length
invariant forall i :: 0 <= i < n ==> dst[i] == 2 * old(... | method DoubleArray(src: array<int>, dst: array<int>)
requires src.Length == dst.Length
modifies dst
ensures forall i :: 0 <= i < src.Length ==> dst[i] == 2 * old(src[i])
{
var n := 0;
while n != src.Length
{
dst[n] := 2 * src[n]; n := n + 1;
}
}
|
151 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_IncrementMatrix.dfy | method IncrementMatrix(a: array2<int>)
modifies a
ensures forall i, j :: 0 <= i < a.Length0 && 0 <= j < a.Length1 ==> a[i,j] == old(a[i,j]) + 1
{
var m := 0;
while m != a.Length0
invariant 0 <= m <= a.Length0
invariant forall i, j :: 0 <= i < m && 0 <= j < a.Length1 ==> a[i,j] == old(a[i... | method IncrementMatrix(a: array2<int>)
modifies a
ensures forall i, j :: 0 <= i < a.Length0 && 0 <= j < a.Length1 ==> a[i,j] == old(a[i,j]) + 1
{
var m := 0;
while m != a.Length0
{
var n := 0;
while n != a.Length1
{
a[m,n] := a[m,n] + 1;
n := n + 1;
... |
152 | Dafny_Verify_tmp_tmphq7j0row_AI_agent_verify_examples_RotateRight.dfy | method RotateRight(a: array)
requires a.Length > 0
modifies a
ensures forall i :: 1<= i < a.Length ==> a[i] == old(a[(i-1)])
ensures a[0] == old(a[a.Length-1])
{
var n := 1;
while n != a.Length
invariant 1 <= n <= a.Length
invariant forall i :: 1 <= i < n ==> a[i] == old(a[i-1])... | method RotateRight(a: array)
requires a.Length > 0
modifies a
ensures forall i :: 1<= i < a.Length ==> a[i] == old(a[(i-1)])
ensures a[0] == old(a[a.Length-1])
{
var n := 1;
while n != a.Length
{
a[0], a[n] := a[n], a[0]; n := n + 1;
}
}
|
153 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_28.dfy | method main(x: int, y: int) returns (x_out: int, y_out: int, n: int)
requires x >= 0
requires y >= 0
requires x == y
ensures y_out == n
{
x_out := x;
y_out := y;
n := 0;
while (x_out != n)
invariant x_out >= 0
invariant x_out == y_out
{
x_out := x_out - 1;
y_out := y... | method main(x: int, y: int) returns (x_out: int, y_out: int, n: int)
requires x >= 0
requires y >= 0
requires x == y
ensures y_out == n
{
x_out := x;
y_out := y;
n := 0;
while (x_out != n)
{
x_out := x_out - 1;
y_out := y_out - 1;
}
}
|
154 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_37.dfy | method main(n: int) returns(x: int, m: int)
requires n > 0
ensures (n <= 0) || (0 <= m && m < n)
{
x := 0;
m := 0;
while(x < n)
invariant 0 <= x <= n
invariant 0 <= m < n
{
if(*)
{
m := x;
}
else{}
x := x + 1;
}
}
| method main(n: int) returns(x: int, m: int)
requires n > 0
ensures (n <= 0) || (0 <= m && m < n)
{
x := 0;
m := 0;
while(x < n)
{
if(*)
{
m := x;
}
else{}
x := x + 1;
}
}
|
155 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_38.dfy | method main(n : int) returns (i: int, x: int, y:int)
requires n >= 0
ensures (i % 2 != 0) || (x == 2 * y)
{
i := 0;
x := 0;
y := 0;
while (i < n)
invariant 0 <= i <= n
invariant x == i
invariant y == i / 2
{
i := i + 1;
x := x + 1;
if (i % 2 == 0)
... | method main(n : int) returns (i: int, x: int, y:int)
requires n >= 0
ensures (i % 2 != 0) || (x == 2 * y)
{
i := 0;
x := 0;
y := 0;
while (i < n)
{
i := i + 1;
x := x + 1;
if (i % 2 == 0)
{
y := y + 1;
}
else
{}
}
}
|
156 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_41.dfy | method main(n: int, k: int) returns (i :int, j: int)
requires n >= 0
requires k == 1 || k >= 0
ensures k + i + j >= 2 * n
{
i := 0;
j := 0;
while(i < n)
invariant 0 <= i <= n
invariant j == i * (i + 1) / 2
{
i := i + 1;
j := j + i;
}
}
| method main(n: int, k: int) returns (i :int, j: int)
requires n >= 0
requires k == 1 || k >= 0
ensures k + i + j >= 2 * n
{
i := 0;
j := 0;
while(i < n)
{
i := i + 1;
j := j + i;
}
}
|
157 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_BinarySearch.dfy | method BinarySearch(a: array<int>, key: int) returns (n: int)
requires forall i, j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
ensures 0 <= n <= a.Length
ensures forall i :: 0 <= i < n ==> a[i] < key
ensures forall i :: n <= i < a.Length ==> key <= a[i]
{
var lo, hi := 0, a.Length;
while lo < hi
... | method BinarySearch(a: array<int>, key: int) returns (n: int)
requires forall i, j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
ensures 0 <= n <= a.Length
ensures forall i :: 0 <= i < n ==> a[i] < key
ensures forall i :: n <= i < a.Length ==> key <= a[i]
{
var lo, hi := 0, a.Length;
while lo < hi
... |
158 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_50_examples_SumArray.dfy | function Sum(arr: array<int>, len: int): int
reads arr
requires arr.Length > 0 && 0 <= len <= arr.Length
{
if len == 0 then 0 else arr[len-1] + Sum(arr, len-1)
}
method SumArray(arr: array<int>) returns (sum: int)
requires arr.Length > 0
ensures sum == Sum(arr, arr.Length)
{
sum := 0;
var i... | function Sum(arr: array<int>, len: int): int
reads arr
requires arr.Length > 0 && 0 <= len <= arr.Length
{
if len == 0 then 0 else arr[len-1] + Sum(arr, len-1)
}
method SumArray(arr: array<int>) returns (sum: int)
requires arr.Length > 0
ensures sum == Sum(arr, arr.Length)
{
sum := 0;
var i... |
159 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_error_data_completion_06_n.dfy | method Main() returns (x: int, y: int)
ensures x == y;
{
x := 0;
y := 0;
var w := 1;
var z := 0;
var turn := 0;
while(x != y)
invariant x == y ==> !(0 <= -z*2/2 && 1 <= -(w-1)*2/2)
invariant !((x != y && x - y <= -1) || (x - y >= 1 && -z*2/2 <= 0 && (w-1)*2/2 <= 1))
invariant !(w*2/2 <= 0 && ((x != y ... | method Main() returns (x: int, y: int)
ensures x == y;
{
x := 0;
y := 0;
var w := 1;
var z := 0;
var turn := 0;
while(x != y)
{
if(turn == 0){
turn := 1;
}
if(turn == 1){
if(w % 2 == 1){
x := x + 1;
}
if(z % 2 == 0){
y := y + 1;
}
turn := 1;
}
else{
if(turn == 2){
... |
160 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_error_data_completion_07.dfy | method main(n: int) returns (a: int, b: int)
requires n >= 0
ensures a + b == 3 * n
{
var i: int := 0;
a := 0;
b := 0;
while(i < n)
invariant 0 <= i <= n
invariant a + b == 3 * i
{
if(*)
{
a := a + 1;
b := b + 2;
}
else... | method main(n: int) returns (a: int, b: int)
requires n >= 0
ensures a + b == 3 * n
{
var i: int := 0;
a := 0;
b := 0;
while(i < n)
{
if(*)
{
a := a + 1;
b := b + 2;
}
else
{
a := a + 2;
b := b + 1;
... |
161 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_error_data_completion_11.dfy | method main(x :int) returns (j :int, i :int)
requires x > 0
ensures j == 2 * x
{
i := 0;
j := 0;
while i < x
invariant 0 <= i <= x
invariant j == 2 * i
{
j := j + 2;
i := i + 1;
}
}
| method main(x :int) returns (j :int, i :int)
requires x > 0
ensures j == 2 * x
{
i := 0;
j := 0;
while i < x
{
j := j + 2;
i := i + 1;
}
}
|
162 | Dafny_Verify_tmp_tmphq7j0row_Fine_Tune_Examples_normal_data_completion_MaxPerdV2.dfy | function contains(v: int, a: array<int>, n: int): bool
reads a
requires n <= a.Length
{
exists j :: 0 <= j < n && a[j] == v
}
function upper_bound(v: int, a: array<int>, n: int): bool
reads a
requires n <= a.Length
{
forall j :: 0 <= j < n ==> a[j] <= v
}
function is_max(m: int, a: array<int>, n: int): bool
r... | function contains(v: int, a: array<int>, n: int): bool
reads a
requires n <= a.Length
{
exists j :: 0 <= j < n && a[j] == v
}
function upper_bound(v: int, a: array<int>, n: int): bool
reads a
requires n <= a.Length
{
forall j :: 0 <= j < n ==> a[j] <= v
}
function is_max(m: int, a: array<int>, n: int): bool
r... |
163 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_15.dfy | method main(n: int, k: int) returns (k_out: int)
requires n > 0;
requires k > n;
ensures k_out >= 0;
{
k_out := k;
var j: int := 0;
while(j < n)
invariant 0 <= j <= n;
invariant k_out == k - j;
{
j := j + 1;
k_out := k_out - 1;
}
}
| method main(n: int, k: int) returns (k_out: int)
requires n > 0;
requires k > n;
ensures k_out >= 0;
{
k_out := k;
var j: int := 0;
while(j < n)
{
j := j + 1;
k_out := k_out - 1;
}
}
|
164 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_ComputePower.dfy | function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(n: nat) returns (p: nat)
ensures p == Power(n)
{
p := 1;
var i := 0;
while i != n
invariant 0 <= i <= n && p == Power(i)
{
i := i + 1;
p := p * 2;
}
}
| function Power(n: nat): nat {
if n == 0 then 1 else 2 * Power(n - 1)
}
method ComputePower(n: nat) returns (p: nat)
ensures p == Power(n)
{
p := 1;
var i := 0;
while i != n
{
i := i + 1;
p := p * 2;
}
}
|
165 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_Count.dfy | function has_count(v: int, a: array<int>, n: int): int
reads a // This allows the function to read from array 'a'
requires n >= 0 && n <= a.Length
{
if n == 0 then 0 else
(if a[n-1] == v then has_count(v, a, n-1) + 1 else has_count(v, a, n-1))
}
method count (v: int, a: array<int>, n: int) returns (r... | function has_count(v: int, a: array<int>, n: int): int
reads a // This allows the function to read from array 'a'
requires n >= 0 && n <= a.Length
{
if n == 0 then 0 else
(if a[n-1] == v then has_count(v, a, n-1) + 1 else has_count(v, a, n-1))
}
method count (v: int, a: array<int>, n: int) returns (r... |
166 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_LinearSearch.dfy | method LinearSearch<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures 0 <= n <= a.Length
ensures n == a.Length || P(a[n])
ensures forall i :: 0 <= i < n ==> !P(a[i])
{
n := 0;
while n != a.Length
invariant 0 <= n <= a.Length
invariant forall i :: 0 <= i < n ==> !P(a[i])
{
... | method LinearSearch<T>(a: array<T>, P: T -> bool) returns (n: int)
ensures 0 <= n <= a.Length
ensures n == a.Length || P(a[n])
ensures forall i :: 0 <= i < n ==> !P(a[i])
{
n := 0;
while n != a.Length
{
if P(a[n]) {
return;
}
n := n + 1;
}
}
|
167 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_Minimum.dfy | method Minimum(a: array<int>) returns (m: int)
requires a.Length > 0
ensures exists i :: 0 <= i < a.Length && m == a[i]
ensures forall i :: 0 <= i < a.Length ==> m <= a[i]
{
var n := 0;
m := a[0];
while n != a.Length
invariant 0 <= n <= a.Length
invariant exists i :: 0 <= i < a.Length && m == a[i]
invarian... | method Minimum(a: array<int>) returns (m: int)
requires a.Length > 0
ensures exists i :: 0 <= i < a.Length && m == a[i]
ensures forall i :: 0 <= i < a.Length ==> m <= a[i]
{
var n := 0;
m := a[0];
while n != a.Length
{
if a[n] < m {
m := a[n];
}
n := n + 1;
}
}
|
168 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_Mult.dfy | method mult(a:int, b:int) returns (x:int)
requires a >= 0 && b >= 0
ensures x == a * b
{
x := 0;
var y := a;
while y > 0
invariant x == (a - y) * b
{
x := x + b;
y := y - 1;
}
}
| method mult(a:int, b:int) returns (x:int)
requires a >= 0 && b >= 0
ensures x == a * b
{
x := 0;
var y := a;
while y > 0
{
x := x + b;
y := y - 1;
}
}
|
169 | Dafny_Verify_tmp_tmphq7j0row_Generated_Code_rand.dfy | method Main(xInit: int, y: int) returns (z: int)
requires xInit >= 0
requires y >= 0
ensures z == 0
{
var x := xInit;
z := x * y;
while x > 0
invariant x >= 0
invariant z == x * y
decreases x
{
x := x - 1;
z := z - y;
}
}
| method Main(xInit: int, y: int) returns (z: int)
requires xInit >= 0
requires y >= 0
ensures z == 0
{
var x := xInit;
z := x * y;
while x > 0
{
x := x - 1;
z := z - y;
}
}
|
170 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_Function.dfy | function Average (a: int, b: int): int
{
(a + b) / 2
}
method TripleConditions(x: int) returns (r: int)
ensures r == 3 * x
{
r := 3 * x;
assert r == 3 * x;
}
method Triple' (x: int) returns (r: int)
ensures Average(r, 3 * x) == 3 * x
ensures r == 3 * x
{
r:= 3 * x;
}
method ProveSpecif... | function Average (a: int, b: int): int
{
(a + b) / 2
}
method TripleConditions(x: int) returns (r: int)
ensures r == 3 * x
{
r := 3 * x;
}
method Triple' (x: int) returns (r: int)
ensures Average(r, 3 * x) == 3 * x
ensures r == 3 * x
{
r:= 3 * x;
}
method ProveSpecificationsEquivalent(x: i... |
171 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_Ghost.dfy | function Average(a: int, b: int): int
{
(a + b) / 2
}
ghost method Triple(x: int) returns (r: int)
ensures r == 3 * x
{
r := Average(2 * x, 4 * x);
}
method Triple1(x: int) returns (r: int)
ensures r == 3 * x
{
var y := 2 * x;
r := x + y;
ghost var a, b := DoubleQuadruple(x);
assert ... | function Average(a: int, b: int): int
{
(a + b) / 2
}
ghost method Triple(x: int) returns (r: int)
ensures r == 3 * x
{
r := Average(2 * x, 4 * x);
}
method Triple1(x: int) returns (r: int)
ensures r == 3 * x
{
var y := 2 * x;
r := x + y;
ghost var a, b := DoubleQuadruple(x);
}
ghost me... |
172 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_Index.dfy | method Index(n: int) returns (i: int)
requires 1 <= n
ensures 0 <= i < n
{
i := n/2;
}
method Min(x: int, y: int) returns (m: int)
ensures m <= x && m <= y
ensures m == x || m == y
{
if (x >= y) {
m := y;
} else {
m := x;
}
assert m <= x && m <= y;
}
method Max(x: int, y: int) re... | method Index(n: int) returns (i: int)
requires 1 <= n
ensures 0 <= i < n
{
i := n/2;
}
method Min(x: int, y: int) returns (m: int)
ensures m <= x && m <= y
ensures m == x || m == y
{
if (x >= y) {
m := y;
} else {
m := x;
}
}
method Max(x: int, y: int) returns (m: int) {
if (x >=... |
173 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_LoopInvariant.dfy | method UpWhileLess(N: int) returns (i: int)
requires 0 <= N
ensures i == N
{
i := 0;
while i < N
invariant 0 <= i <= N
decreases N - i
{
i := i + 1;
}
}
method UpWhileNotEqual(N: int) returns (i: int)
requires 0 <= N
ensures i == N
{
i := 0;
while i != N
invariant 0 <= i <... | method UpWhileLess(N: int) returns (i: int)
requires 0 <= N
ensures i == N
{
i := 0;
while i < N
{
i := i + 1;
}
}
method UpWhileNotEqual(N: int) returns (i: int)
requires 0 <= N
ensures i == N
{
i := 0;
while i != N
{
i := i + 1;
}
}
method DownWhileNotEqual(N: int)... |
174 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_Triple.dfy | method Triple(x: int) returns (r: int)
{
var y := 2 * x;
r := x + y;
assert r == 3 * x;
}
method TripleIf(x: int) returns (r: int) {
if (x == 0) {
r := 0;
} else {
var y := 2 * x;
r := x + y;
}
assert r == 3 * x;
}
method TripleOver(x: int) returns (r: int) {
if... | method Triple(x: int) returns (r: int)
{
var y := 2 * x;
r := x + y;
}
method TripleIf(x: int) returns (r: int) {
if (x == 0) {
r := 0;
} else {
var y := 2 * x;
r := x + y;
}
}
method TripleOver(x: int) returns (r: int) {
if {
case x < 18 =>
var a, b := ... |
175 | Dafny_Verify_tmp_tmphq7j0row_Test_Cases_solved_1_select.dfy | method SelectionSort(a: array<int>)
modifies a
ensures forall i,j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
ensures multiset(a[..]) == old(multiset(a[..]))
{
var n := 0;
while n != a.Length
invariant 0 <= n <= a.Length
invariant forall i,j :: 0 <= i < j < a.Length && j < n ==> a[i] <= a[j]
invaria... | method SelectionSort(a: array<int>)
modifies a
ensures forall i,j :: 0 <= i < j < a.Length ==> a[i] <= a[j]
ensures multiset(a[..]) == old(multiset(a[..]))
{
var n := 0;
while n != a.Length
{
var mindex, m := n, n;
while m != a.Length
{
if a[m] < a[mindex] {
mindex := m;
}
... |
176 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_01.dfy | method main() returns (t1: int, t2: int, x: int, y: int)
ensures y >= 1
{
x := 1;
y := 1;
t1 := 0;
t2 := 0;
while(x <= 100000)
invariant x == y;
{
t1 := x;
t2 := y;
x := t1 + t2;
y := t1 + t2;
}
}
| method main() returns (t1: int, t2: int, x: int, y: int)
ensures y >= 1
{
x := 1;
y := 1;
t1 := 0;
t2 := 0;
while(x <= 100000)
{
t1 := x;
t2 := y;
x := t1 + t2;
y := t1 + t2;
}
}
|
177 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_06_n.dfy | // MODULE main
// int x;
// int y;
// int w;
// int z;
// int turn;
// assume(x == 0);
// assume(y == 0);
// assume(z == 0);
// assume(w == 1);
// assume(turn == 0);
// while(*){
// if(turn == 0){
// if(*){
// turn = 1;
// }
// else{
// turn = 2;
// }
// }
// else{
// skip;
//... | // MODULE main
// int x;
// int y;
// int w;
// int z;
// int turn;
// assume(x == 0);
// assume(y == 0);
// assume(z == 0);
// assume(w == 1);
// assume(turn == 0);
// while(*){
// if(turn == 0){
// if(*){
// turn = 1;
// }
// else{
// turn = 2;
// }
// }
// else{
// skip;
//... |
178 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_07.dfy | // MODULE main
// int i;
// int n;
// int a;
// int b;
// assume(i == 0);
// assume(a == 0);
// assume(b == 0);
// assume(n >= 0);
// while(i < n){
// if(*) {
// a = a+1;
// b = b+2;
// }
// else {
// a = a+2;
// b = b+1;
// }
// i = i+1;
// }
// assert(a + b ... | // MODULE main
// int i;
// int n;
// int a;
// int b;
// assume(i == 0);
// assume(a == 0);
// assume(b == 0);
// assume(n >= 0);
// while(i < n){
// if(*) {
// a = a+1;
// b = b+2;
// }
// else {
// a = a+2;
// b = b+1;
// }
// i = i+1;
// }
// assert(a + b ... |
179 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_11.dfy | method main(x :int) returns (j :int, i :int)
requires x > 0
ensures j == 2 * x
{
i := 0;
j := 0;
while i < x
invariant 0 <= i <= x
invariant j == 2 * i
{
j := j + 2;
i := i + 1;
}
}
// MODULE main
// int i;
// int j;
// int x;
// assume(j == 0);
// assume(x >... | method main(x :int) returns (j :int, i :int)
requires x > 0
ensures j == 2 * x
{
i := 0;
j := 0;
while i < x
{
j := j + 2;
i := i + 1;
}
}
// MODULE main
// int i;
// int j;
// int x;
// assume(j == 0);
// assume(x > 0);
// assume(i == 0);
// while(i < x){
// j = j + 2;... |
180 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_15.dfy | method main(n: int, k: int) returns (k_out: int)
requires n > 0;
requires k > n;
ensures k_out >= 0;
{
k_out := k;
var j: int := 0;
while(j < n)
invariant 0 <= j <= n;
invariant j + k_out == k;
{
j := j + 1;
k_out := k_out - 1;
}
}
// C code:
// MODULE main
// int i;
// in... | method main(n: int, k: int) returns (k_out: int)
requires n > 0;
requires k > n;
ensures k_out >= 0;
{
k_out := k;
var j: int := 0;
while(j < n)
{
j := j + 1;
k_out := k_out - 1;
}
}
// C code:
// MODULE main
// int i;
// int n;
// int j;
// int k;
// assume(n > 0);
// as... |
181 | Dafny_Verify_tmp_tmphq7j0row_dataset_C_convert_examples_23_x.dfy | method main(n: int) returns (sum: int, i: int)
requires n >= 0
{
sum := 0;
i := 0;
while(i < n)
invariant sum >= 0
invariant 0 <= i <= n
{
sum := sum + i;
i := i + 1;
}
}
// MODULE main
// int i;
// int sum;
// int n;
// assume(sum == 0);
// assume(n >= 0);
/... | method main(n: int) returns (sum: int, i: int)
requires n >= 0
{
sum := 0;
i := 0;
while(i < n)
{
sum := sum + i;
i := i + 1;
}
}
// MODULE main
// int i;
// int sum;
// int n;
// assume(sum == 0);
// assume(n >= 0);
// assume(i == 0);
// while(i < n){
// sum = sum + i;... |
182 | Dafny_Verify_tmp_tmphq7j0row_dataset_bql_exampls_Min.dfy | method min(a: array<int>, n : int) returns (min : int)
requires 0 < n <= a.Length;
ensures (exists i : int :: 0 <= i && i < n && a[i] == min);
ensures (forall i : int :: 0 <= i && i < n ==> a[i] >= min);
{
var i : int;
min := a[0];
i := 1;
while (i < n)
invariant i <= n;
invariant (exists j : int :: 0 <... | method min(a: array<int>, n : int) returns (min : int)
requires 0 < n <= a.Length;
ensures (exists i : int :: 0 <= i && i < n && a[i] == min);
ensures (forall i : int :: 0 <= i && i < n ==> a[i] >= min);
{
var i : int;
min := a[0];
i := 1;
while (i < n)
{
if (a[i] < min) {
min := a[i];
}
i := i + ... |
183 | Dafny_Verify_tmp_tmphq7j0row_dataset_bql_exampls_SmallNum.dfy | method add_small_numbers (a: array<int>, n: int, max: int) returns (r: int)
requires n > 0;
requires n <= a.Length;
requires (forall i: int :: 0 <= i && i < n ==> a[i] <= max);
ensures r <= max * n;
{
var i: int;
i := 0;
r := 0;
while (i < n)
invariant i <= n;
invariant r <= max * i;
{
r := r + a[i... | method add_small_numbers (a: array<int>, n: int, max: int) returns (r: int)
requires n > 0;
requires n <= a.Length;
requires (forall i: int :: 0 <= i && i < n ==> a[i] <= max);
ensures r <= max * n;
{
var i: int;
i := 0;
r := 0;
while (i < n)
{
r := r + a[i];
i := i + 1;
}
}
|
184 | Dafny_Verify_tmp_tmphq7j0row_dataset_bql_exampls_Square.dfy | method square (n: int) returns (r: int)
requires 0 <= n;
ensures r == n*n;
{
var x: int;
var i: int;
r := 0;
i := 0;
x := 1;
while (i < n)
invariant i <= n;
invariant r == i*i;
invariant x == 2*i + 1;
{
r := r + x;
x := x + 2;
i := i + 1;
}
}
| method square (n: int) returns (r: int)
requires 0 <= n;
ensures r == n*n;
{
var x: int;
var i: int;
r := 0;
i := 0;
x := 1;
while (i < n)
{
r := r + x;
x := x + 2;
i := i + 1;
}
}
|
185 | Dafny_Verify_tmp_tmphq7j0row_dataset_detailed_examples_SelectionSort.dfy | // Works by dividing the input list into two parts: sorted and unsorted. At the beginning,
// the sorted part is empty and the unsorted part contains all the elements.
method SelectionSort(a: array<int>)
modifies a
// Ensures the final array is sorted in ascending order
ensures forall i,j :: 0 <= i < j < a.Lengt... | // Works by dividing the input list into two parts: sorted and unsorted. At the beginning,
// the sorted part is empty and the unsorted part contains all the elements.
method SelectionSort(a: array<int>)
modifies a
// Ensures the final array is sorted in ascending order
ensures forall i,j :: 0 <= i < j < a.Lengt... |
186 | Dafny_Verify_tmp_tmphq7j0row_dataset_error_data_real_error_IsEven_success_1.dfy | function even(n: int): bool
requires n >= 0
{
if n == 0 then true else !even(n-1)
}
method is_even(n: int) returns (r: bool)
requires n >= 0;
ensures r <==> even(n);
{
var i: int := 0;
r := true;
while i < n
invariant 0 <= i <= n;
invariant r <==> even(i);
{
r := !r;
i := i + 1;
}
}
| function even(n: int): bool
requires n >= 0
{
if n == 0 then true else !even(n-1)
}
method is_even(n: int) returns (r: bool)
requires n >= 0;
ensures r <==> even(n);
{
var i: int := 0;
r := true;
while i < n
{
r := !r;
i := i + 1;
}
}
|
187 | Dafny_tmp_tmp0wu8wmfr_Heimaverkefni 1_LinearSearch.dfy | // Author of question: Snorri Agnarsson
// Permalink of question: https://rise4fun.com/Dafny/0HRr
// Author of solution: Alexander Guðmundsson
// Permalink of solution: https://rise4fun.com/Dafny/8pxWd
// Use the command
// dafny LinearSearch-skeleton.dfy
// or
// compile LinearSearch-skeleton.dfy
// to compil... | // Author of question: Snorri Agnarsson
// Permalink of question: https://rise4fun.com/Dafny/0HRr
// Author of solution: Alexander Guðmundsson
// Permalink of solution: https://rise4fun.com/Dafny/8pxWd
// Use the command
// dafny LinearSearch-skeleton.dfy
// or
// compile LinearSearch-skeleton.dfy
// to compil... |
188 | Dafny_tmp_tmp0wu8wmfr_Heimaverkefni 2_BinarySearchDec.dfy | // Author of question: Snorri Agnarsson
// Permalink of question: https://rise4fun.com/Dafny/CGB1z
// Authors of solution: Alexander Guðmundsson
// Permalink of solution: https://rise4fun.com/Dafny/VnB5
// Use the command
// dafny H2-skeleton.dfy
// or
// compile H2-skeleton.dfy
// to compile the file.
// Or us... | // Author of question: Snorri Agnarsson
// Permalink of question: https://rise4fun.com/Dafny/CGB1z
// Authors of solution: Alexander Guðmundsson
// Permalink of solution: https://rise4fun.com/Dafny/VnB5
// Use the command
// dafny H2-skeleton.dfy
// or
// compile H2-skeleton.dfy
// to compile the file.
// Or us... |
189 | Dafny_tmp_tmp0wu8wmfr_Heimaverkefni 3_InsertionSortMultiset.dfy | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/G4sc3
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://rise4fun.com/Dafny/nujsu
// Insertion sort með hjálp helmingunarleitar.
method Search( s: seq<int>, x: int ) returns ( k: i... | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/G4sc3
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://rise4fun.com/Dafny/nujsu
// Insertion sort með hjálp helmingunarleitar.
method Search( s: seq<int>, x: int ) returns ( k: i... |
190 | Dafny_tmp_tmp0wu8wmfr_Heimaverkefni 3_SelectionSortMultiset.dfy | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/dtcnY
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://rise4fun.com/Dafny/ybUCz
///////////////////////////////////////////////////////////////
// Hér byrjar óbreytanlegi hluti sk... | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/dtcnY
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://rise4fun.com/Dafny/ybUCz
///////////////////////////////////////////////////////////////
// Hér byrjar óbreytanlegi hluti sk... |
191 | Dafny_tmp_tmp0wu8wmfr_Heimaverkefni 8_H8.dfy | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/GW7a
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://www.rise4fun.com/Dafny/JPGct
// Klárið að forrita föllin tvö.
method Partition( m: multiset<int> )
returns( pre: mul... | // Höfundur spurningar: Snorri Agnarsson, snorri@hi.is
// Permalink spurningar: https://rise4fun.com/Dafny/GW7a
// Höfundur lausnar: Alexander Guðmundsson
// Permalink lausnar: https://www.rise4fun.com/Dafny/JPGct
// Klárið að forrita föllin tvö.
method Partition( m: multiset<int> )
returns( pre: mul... |
192 | Dafny_tmp_tmp0wu8wmfr_tests_F1a.dfy | method F() returns ( r: int)
ensures r <= 0
{
r := 0;
}
method Main()
{
var x := F();
assert x <= 0;
x := x-1;
assert x <= -1;
print x;
}
method Mid( p: int, q: int) returns ( m: int )
// | ... | ??? | ... |
// p m q
requires p <= q;
ensures p<= m <= q;
ensur... | method F() returns ( r: int)
ensures r <= 0
{
r := 0;
}
method Main()
{
var x := F();
x := x-1;
print x;
}
method Mid( p: int, q: int) returns ( m: int )
// | ... | ??? | ... |
// p m q
requires p <= q;
ensures p<= m <= q;
ensures m-p <= q-m;
ensures 0 <= (q-m)-(... |
193 | Dafny_tmp_tmp0wu8wmfr_tests_InsertionSortSeq.dfy | // Insertion sort.
//
// Author: Snorri Agnarsson, snorri@hi.is
predicate IsSorted( s: seq<int> )
{
forall p,q | 0<=p<q<|s| :: s[p]<=s[q]
}
method InsertionSort( s: seq<int> ) returns ( r: seq<int> )
ensures multiset(r) == multiset(s);
ensures IsSorted(r);
{
r := [];
var rest := s;
while rest ... | // Insertion sort.
//
// Author: Snorri Agnarsson, snorri@hi.is
predicate IsSorted( s: seq<int> )
{
forall p,q | 0<=p<q<|s| :: s[p]<=s[q]
}
method InsertionSort( s: seq<int> ) returns ( r: seq<int> )
ensures multiset(r) == multiset(s);
ensures IsSorted(r);
{
r := [];
var rest := s;
while rest ... |
194 | Dafny_tmp_tmp0wu8wmfr_tests_Search1000.dfy | // Author: Snorri Agnarsson, snorri@hi.is
// Search1000 is a Dafny version of a function shown
// by Jon Bentley in his old Programming Pearls
// column in CACM. Surprisingly Dafny needs no help
// to verify the function.
method Search1000( a: array<int>, x: int ) returns ( k: int )
requires a.Length >= 1000;
... | // Author: Snorri Agnarsson, snorri@hi.is
// Search1000 is a Dafny version of a function shown
// by Jon Bentley in his old Programming Pearls
// column in CACM. Surprisingly Dafny needs no help
// to verify the function.
method Search1000( a: array<int>, x: int ) returns ( k: int )
requires a.Length >= 1000;
... |
195 | Dafny_tmp_tmp0wu8wmfr_tests_SumIntsLoop.dfy | function sumInts( n: int ): int
requires n >= 0;
{
if n == 0 then
0
else
sumInts(n-1)+n
}
method SumIntsLoop( n: int ) returns ( s: int )
requires n >= 0;
ensures s == sumInts(n)
ensures s == n*(n+1)/2;
{
s := 0;
var k := 0;
while k != n
decreases n-k;
... | function sumInts( n: int ): int
requires n >= 0;
{
if n == 0 then
0
else
sumInts(n-1)+n
}
method SumIntsLoop( n: int ) returns ( s: int )
requires n >= 0;
ensures s == sumInts(n)
ensures s == n*(n+1)/2;
{
s := 0;
var k := 0;
while k != n
{
k := k+1;
... |
196 | Dafny_tmp_tmpj88zq5zt_2-Kontrakte_max.dfy | method max(a: array<int>, b: array<int>, i: int, j: int)
returns (m: int)
requires 0 <= i < a.Length
requires 0 <= j < b.Length
ensures a[i] > b[j] ==> m == a[i]
ensures a[i] <= b[j] ==> m == b[j]
{
if a[i] > b[j] {
m := a[i];
} else {
m := b[j];
}
}
method testMax(a:array<int>, b:array<int>... | method max(a: array<int>, b: array<int>, i: int, j: int)
returns (m: int)
requires 0 <= i < a.Length
requires 0 <= j < b.Length
ensures a[i] > b[j] ==> m == a[i]
ensures a[i] <= b[j] ==> m == b[j]
{
if a[i] > b[j] {
m := a[i];
} else {
m := b[j];
}
}
method testMax(a:array<int>, b:array<int>... |
197 | Dafny_tmp_tmpj88zq5zt_2-Kontrakte_reverse3.dfy | method swap3(a: array<int>, h: int, i: int, j: int)
modifies a
requires 0 <= h < a.Length
requires 0 <= i < a.Length
requires 0 <= j < a.Length
requires i != j && j != h && h != i;
ensures a[h] == old(a[i]);
ensures a[j] == old(a[h]);
ensures a[i] == old(a[j]);
ensures forall k: int :: 0 <= k < a.Leng... | method swap3(a: array<int>, h: int, i: int, j: int)
modifies a
requires 0 <= h < a.Length
requires 0 <= i < a.Length
requires 0 <= j < a.Length
requires i != j && j != h && h != i;
ensures a[h] == old(a[i]);
ensures a[j] == old(a[h]);
ensures a[i] == old(a[j]);
ensures forall k: int :: 0 <= k < a.Leng... |
198 | Dafny_tmp_tmpmvs2dmry_SlowMax.dfy | function max(x:nat, y:nat) : nat
{
if (x < y) then y else x
}
method slow_max(a: nat, b: nat) returns (z: nat)
ensures z == max(a, b)
{
z := 0;
var x := a;
var y := b;
while (z < x && z < y)
invariant x >=0;
invariant y >=0;
invariant z == a - x && z == b - y;
invariant a-x == b-y
decr... | function max(x:nat, y:nat) : nat
{
if (x < y) then y else x
}
method slow_max(a: nat, b: nat) returns (z: nat)
ensures z == max(a, b)
{
z := 0;
var x := a;
var y := b;
while (z < x && z < y)
{
z := z + 1;
x := x - 1;
y := y - 1;
}
if (x <= y) { return b; }
else { return a;}
}
|
199 | Dafny_tmp_tmpmvs2dmry_examples1.dfy | method Abs(x:int) returns (y:int)
ensures y>=0;
ensures x>=0 ==> x == y;
ensures x<0 ==> -x == y;
ensures y == abs(x); // use this instead of line 3,4
{
if(x<0)
{
return -x;
}
else{
return x;
}
}
function abs(x: int): int{
if x>0 then x else -x
}
method Testing(){
var v:= Ab... | method Abs(x:int) returns (y:int)
ensures y>=0;
ensures x>=0 ==> x == y;
ensures x<0 ==> -x == y;
ensures y == abs(x); // use this instead of line 3,4
{
if(x<0)
{
return -x;
}
else{
return x;
}
}
function abs(x: int): int{
if x>0 then x else -x
}
method Testing(){
var v:= Ab... |
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