test_ID stringlengths 3 3 | test_file stringlengths 14 119 | ground_truth stringlengths 70 28.7k | hints_removed stringlengths 58 28.7k |
|---|---|---|---|
700 | ironsync-osdi2023_tmp_tmpx80antoe_lib_Math_div_def.dfy | //- 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;
decreases... | //- 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;
{
if x < ... |
701 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_arrays.dfy | // 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>)
ensures a != n... | // 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>)
ensures a != n... |
702 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_maps.dfy | // 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 *** !!!!\n";
... | // 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 *** !!!!\n";
... |
703 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_c++_sets.dfy | // 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)
method Test1(t0:... | // 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)
method Test1(t0:... |
704 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-1158.dfy | // 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
ensures i in ... | // 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)];
forall i
ensures i in a.Keys <==> i in b.Keys
{
calc {
i in a.Keys;
... |
705 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-283.dfy | // 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: %dif... | // 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: %dif... |
706 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-506.dfy | // 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 index := 6;
... | // 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 index := 6;
... |
707 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_Test_git-issues_git-issue-975.dfy | // 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
}
| // 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
0
}
|
708 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old.dfy | 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; // j is local and ... | 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:
// value is this.value; 'this' is the same
// same reference in current and pre state but the
// v... |
709 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old2.dfy | 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(); // Line X
label N... | 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(); // Line X
label N... |
710 | ironsync-osdi2023_tmp_tmpx80antoe_linear-dafny_docs_DafnyRef_examples_Example-Old3.dfy | 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 value z2
z... | 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;
a := z2;
z2[0] := 27;
// z2; in pre-state z2[0] == 17
/... |
711 | laboratory_tmp_tmps8ws6mu2_dafny-tutorial_exercise12.dfy | 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 INDEX ... | 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 INDEX ... |
712 | laboratory_tmp_tmps8ws6mu2_dafny-tutorial_exercise9.dfy | 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 need to cha... | 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 need to cha... |
713 | lets-prove-blocking-queue_tmp_tmptd_aws1k_dafny_prod-cons.dfy | /**
* 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 defined).
t... | /**
* 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 defined).
t... |
714 | libraries_tmp_tmp9gegwhqj_examples_MutableMap_MutableMapDafny.dfy | /*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
// RUN: %verify "%s"
/**
* Implements mutable maps in Dafny to g... | /*******************************************************************************
* Copyright by the contributors to the Dafny Project
* SPDX-License-Identifier: MIT
*******************************************************************************/
// RUN: %verify "%s"
/**
* Implements mutable maps in Dafny to g... |
715 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_0.dfy | 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
ensures res... | 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
ensures res... |
716 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_160.dfy | 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)
requires oper... | function pow(base: int, exponent: int): int
requires exponent >= 0
{
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)
requires operators != [] && operan... |
717 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_161.dfy | 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 if c >= 'A' && ... | 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 if c >= 'A' && ... |
718 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_3.dfy | 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: bool)
ensure... | 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: bool)
ensure... |
719 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_5.dfy | 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 < |inte... | 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 < |inte... |
720 | llm-verified-eval_tmp_tmpd2deqn_i_dafny_9.dfy | 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 isMax(result, n... | 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|
{
if numbers[i] >... |
721 | metodosFormais_tmp_tmp4q2kmya4_T1-MetodosFormais_examples_ex1.dfy | /*
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 - r
invariant... | /*
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
{
if a[r] == x
{
... |
722 | metodosFormais_tmp_tmp4q2kmya4_T1-MetodosFormais_examples_somatoriov2.dfy | 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(a,i)
{
... | 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
{
s := s + a[i];
}
}
|
723 | nitwit_tmp_tmplm098gxz_nit.dfy | // Liam Wynn, 3/13/2021, CS 510p
/*
In this program, I'm hoping to define
N's complement: a generalized form of 2's complement.
I ran across this idea back in ECE 341, when I asked
the professor about a crackpot theoretical "ternary machine".
Looking into it, I came across a general form of 2's complement.
... | // Liam Wynn, 3/13/2021, CS 510p
/*
In this program, I'm hoping to define
N's complement: a generalized form of 2's complement.
I ran across this idea back in ECE 341, when I asked
the professor about a crackpot theoretical "ternary machine".
Looking into it, I came across a general form of 2's complement.
... |
724 | paxos_proof_tmp_tmpxpmiksmt_triggers.dfy | // predicate P(x:int)
// predicate Q(x:int)
lemma M(a: seq<int>, m: map<bool,int>)
requires 2 <= |a|
requires false in m && true in m
{
assume forall i {:trigger a[i]} :: 0 <= i < |a|-1 ==> a[i] <= a[i+1];
var x :| 0 <= x <= |a|-2;
assert a[x] <= a[x+1];
}
| // predicate P(x:int)
// predicate Q(x:int)
lemma M(a: seq<int>, m: map<bool,int>)
requires 2 <= |a|
requires false in m && true in m
{
assume forall i {:trigger a[i]} :: 0 <= i < |a|-1 ==> a[i] <= a[i+1];
var x :| 0 <= x <= |a|-2;
}
|
725 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch01_fast_exp.dfy | function exp(b: nat, n: nat): nat {
if n == 0 then 1
else b * exp(b, n-1)
}
lemma exp_sum(b: nat, n1: nat, n2: nat)
ensures exp(b, n1 + n2) == exp(b, n1) * exp(b, n2)
{
if n1 == 0 {
return;
}
exp_sum(b, n1-1, n2);
}
// this "auto" version of exp_sum is convenient when we want to let Z3 figure
// out h... | function exp(b: nat, n: nat): nat {
if n == 0 then 1
else b * exp(b, n-1)
}
lemma exp_sum(b: nat, n1: nat, n2: nat)
ensures exp(b, n1 + n2) == exp(b, n1) * exp(b, n2)
{
if n1 == 0 {
return;
}
exp_sum(b, n1-1, n2);
}
// this "auto" version of exp_sum is convenient when we want to let Z3 figure
// out h... |
726 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch03_nim_v3.dfy | // Nim version 3: fix the bug and demonstrate a behavior.
//
// In this version, we've fixed the bug by actually flipping whose turn it is in
// each transition.
datatype Player = P1 | P2
{
function Other(): Player {
if this == P1 then P2 else P1
}
}
datatype Variables = Variables(piles: seq<nat>, turn: Player... | // Nim version 3: fix the bug and demonstrate a behavior.
//
// In this version, we've fixed the bug by actually flipping whose turn it is in
// each transition.
datatype Player = P1 | P2
{
function Other(): Player {
if this == P1 then P2 else P1
}
}
datatype Variables = Variables(piles: seq<nat>, turn: Player... |
727 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch04_inductive_chain.dfy | module Ex {
// This simple example illustrates what the process of looking for an
// inductive invariant might look like.
datatype Variables = Variables(p1: bool, p2: bool, p3: bool, p4: bool)
ghost predicate Init(v: Variables) {
&& !v.p1
&& !v.p2
&& !v.p3
&& !v.p4
}
// The state machine ... | module Ex {
// This simple example illustrates what the process of looking for an
// inductive invariant might look like.
datatype Variables = Variables(p1: bool, p2: bool, p3: bool, p4: bool)
ghost predicate Init(v: Variables) {
&& !v.p1
&& !v.p2
&& !v.p3
&& !v.p4
}
// The state machine ... |
728 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch04_invariant_proof.dfy | /* These three declarations are _abstract_ - we declare a state machine, but
* don't actually give a definition. Dafny will assume nothing about them, so our
* proofs below will be true for an abitrary state machine. */
type Variables
predicate Init(v: Variables)
predicate Next(v: Variables, v': Variables)
/* We'll... | /* These three declarations are _abstract_ - we declare a state machine, but
* don't actually give a definition. Dafny will assume nothing about them, so our
* proofs below will be true for an abitrary state machine. */
type Variables
predicate Init(v: Variables)
predicate Next(v: Variables, v': Variables)
/* We'll... |
729 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch04_leader_election.dfy | // We'll define "Between" to capture how the ring wraps around.
// SOLUTION
ghost predicate Between(start: nat, i: nat, end: nat)
{
if start < end then start < i < end
else i < end || start < i
}
lemma BetweenTests()
{
assert Between(3, 4, 5);
assert !Between(3, 2, 4);
// when start >= end, behavior is a bi... | // We'll define "Between" to capture how the ring wraps around.
// SOLUTION
ghost predicate Between(start: nat, i: nat, end: nat)
{
if start < end then start < i < end
else i < end || start < i
}
lemma BetweenTests()
{
// when start >= end, behavior is a bit tricker
// before end
// after start
// not in ... |
730 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch04_toy_consensus.dfy | // Ported from ivy/examples/ivy/toy_consensus.ivy.
// Ivy only supports first-order logic, which is limited (perhaps in surprising
// ways). In this model of consensus, we use some tricks to model quorums in
// first-order logic without getting into the arithmetic of why sets of n/2+1
// nodes intersect.
type Node(==... | // Ported from ivy/examples/ivy/toy_consensus.ivy.
// Ivy only supports first-order logic, which is limited (perhaps in surprising
// ways). In this model of consensus, we use some tricks to model quorums in
// first-order logic without getting into the arithmetic of why sets of n/2+1
// nodes intersect.
type Node(==... |
731 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_ch06_refinement_proof.dfy | // Analogous to ch04/invariant_proof.dfy, we show what the conditions on a
// refinement (an abstraction function, invariant, an initial condition, and an
// inductive property)
module Types {
type Event(==, 0, !new)
}
import opened Types
module Code {
import opened Types
type Variables(==, 0, !new)
ghost pr... | // Analogous to ch04/invariant_proof.dfy, we show what the conditions on a
// refinement (an abstraction function, invariant, an initial condition, and an
// inductive property)
module Types {
type Event(==, 0, !new)
}
import opened Types
module Code {
import opened Types
type Variables(==, 0, !new)
ghost pr... |
732 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_dafny-internals_02-triggers_triggers2.dfy | function f(x: int): int
function ff(x: int): int
lemma {:axiom} ff_eq()
ensures forall x {:trigger ff(x)} :: ff(x) == f(f(x))
lemma {:axiom} ff_eq2()
ensures forall x {:trigger f(f(x))} :: ff(x) == f(f(x))
lemma {:axiom} ff_eq_bad()
// dafny ignores this trigger because it's an obvious loop
ensures forall x... | function f(x: int): int
function ff(x: int): int
lemma {:axiom} ff_eq()
ensures forall x {:trigger ff(x)} :: ff(x) == f(f(x))
lemma {:axiom} ff_eq2()
ensures forall x {:trigger f(f(x))} :: ff(x) == f(f(x))
lemma {:axiom} ff_eq_bad()
// dafny ignores this trigger because it's an obvious loop
ensures forall x... |
733 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_dafny-internals_03-encoding_lemma_call.dfy | function f(x: int): int
lemma {:axiom} f_positive(x: int)
requires x >= 0
ensures f(x) >= 0
lemma f_2_pos()
ensures f(2) >= 0
{
f_positive(2);
}
lemma f_1_1_pos()
ensures f(1 + 1) >= 0
{
f_2_pos();
assert 1 + 1 == 2;
}
| function f(x: int): int
lemma {:axiom} f_positive(x: int)
requires x >= 0
ensures f(x) >= 0
lemma f_2_pos()
ensures f(2) >= 0
{
f_positive(2);
}
lemma f_1_1_pos()
ensures f(1 + 1) >= 0
{
f_2_pos();
}
|
734 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_demos_dafny-internals_03-encoding_pair.dfy | // based on https://ethz.ch/content/dam/ethz/special-interest/infk/chair-program-method/pm/documents/Education/Courses/SS2019/Program%20Verification/05-EncodingToSMT.pdf
module DafnyVersion {
datatype Pair = Pair(x: int, y: int)
function pair_x(p: Pair): int {
p.x
}
function pair_y(p: Pair): int {
p.... | // based on https://ethz.ch/content/dam/ethz/special-interest/infk/chair-program-method/pm/documents/Education/Courses/SS2019/Program%20Verification/05-EncodingToSMT.pdf
module DafnyVersion {
datatype Pair = Pair(x: int, y: int)
function pair_x(p: Pair): int {
p.x
}
function pair_y(p: Pair): int {
p.... |
735 | protocol-verification-fa2023_tmp_tmpw6hy3mjp_exercises_chapter04-invariants_ch03exercise03.dfy |
// Model a lock service that consists of a single server and an
// arbitrary number of clients.
//
// The state of the system includes the server's state (whether the server
// knows that some client holds the lock, and if so which one)
// and the clients' states (for each client, whether that client knows
// it holds... |
// Model a lock service that consists of a single server and an
// arbitrary number of clients.
//
// The state of the system includes the server's state (whether the server
// knows that some client holds the lock, and if so which one)
// and the clients' states (for each client, whether that client knows
// it holds... |
736 | pucrs-metodos-formais-t1_tmp_tmp7gvq3cw4_fila.dfy | /*
OK fila de tamanho ilimitado com arrays circulares
OK representação ghost: coleção de elementos da fila e qualquer outra informação necessária
OK predicate: invariante da representação abstrata associada à coleção do tipo fila
Operações
- OK construtor inicia fila fazia
- OK adic... | /*
OK fila de tamanho ilimitado com arrays circulares
OK representação ghost: coleção de elementos da fila e qualquer outra informação necessária
OK predicate: invariante da representação abstrata associada à coleção do tipo fila
Operações
- OK construtor inicia fila fazia
- OK adic... |
737 | repo-8967-Ironclad_tmp_tmp4q25en_1_ironclad-apps_src_Dafny_Libraries_Util_seqs_simple.dfy | static lemma lemma_vacuous_statement_about_a_sequence(intseq:seq<int>, j:int)
requires 0<=j<|intseq|;
ensures intseq[0..j]==intseq[..j];
{
}
static lemma lemma_painful_statement_about_a_sequence(intseq:seq<int>)
ensures intseq==intseq[..|intseq|];
{
}
static lemma lemma_obvious_statement_about_a_sequence(... | static lemma lemma_vacuous_statement_about_a_sequence(intseq:seq<int>, j:int)
requires 0<=j<|intseq|;
ensures intseq[0..j]==intseq[..j];
{
}
static lemma lemma_painful_statement_about_a_sequence(intseq:seq<int>)
ensures intseq==intseq[..|intseq|];
{
}
static lemma lemma_obvious_statement_about_a_sequence(... |
738 | sat_dfy_tmp_tmpfcyj8am9_dfy_Seq.dfy | module Seq {
function seq_sum(s: seq<int>) : (sum: int)
{
if s == [] then
0
else
var x := s[0];
var remaining := s[1..];
x + seq_sum(remaining)
}
lemma SeqPartsSameSum(s: seq<int>, s1: seq<int>, s2: seq<int>)
requires s == s1 + s2
... | module Seq {
function seq_sum(s: seq<int>) : (sum: int)
{
if s == [] then
0
else
var x := s[0];
var remaining := s[1..];
x + seq_sum(remaining)
}
lemma SeqPartsSameSum(s: seq<int>, s1: seq<int>, s2: seq<int>)
requires s == s1 + s2
... |
739 | se2011_tmp_tmp71eb82zt_ass1_ex4.dfy | method Eval(x:int) returns (r:int) // do not change
requires x >= 0
ensures r == x*x
{ // do not change
var y:int := x; // do not change
var z:int := 0; // do not change
while y>0 // do not change
invariant 0 <= y <= x && z == x*(x-y)
decreases y
{ // do not change
z := z + x; ... | method Eval(x:int) returns (r:int) // do not change
requires x >= 0
ensures r == x*x
{ // do not change
var y:int := x; // do not change
var z:int := 0; // do not change
while y>0 // do not change
{ // do not change
z := z + x; // do not change
y := y - 1; // do no... |
740 | se2011_tmp_tmp71eb82zt_ass1_ex6.dfy | method Ceiling7(n:nat) returns (k:nat)
requires n >= 0
ensures k == n-(n%7)
{
k := n-(n%7);
}
method test7() {
var k: nat;
k := Ceiling7(43);
assert k == 42;
k := Ceiling7(6);
assert k == 0;
k := Ceiling7(1000);
assert k == 994;
k := Ceiling7(7);
assert k == 7;
k := Ceiling7(70);
assert k == 70;
}
| method Ceiling7(n:nat) returns (k:nat)
requires n >= 0
ensures k == n-(n%7)
{
k := n-(n%7);
}
method test7() {
var k: nat;
k := Ceiling7(43);
k := Ceiling7(6);
k := Ceiling7(1000);
k := Ceiling7(7);
k := Ceiling7(70);
}
|
741 | se2011_tmp_tmp71eb82zt_ass2_ex2.dfy | // ex2
// this was me playing around to try and get an ensures for the method
/*predicate method check(a: array<int>, seclar:int)
requires a.Length > 0
reads a
{ ensures exists i :: 0 <= i < a.Length && forall j :: (0 <= j < a.Length && j != i) ==> (a[i] >= a[j]) && (seclar <= a[i]) && ( if a[j] != a[i] then seclar >... | // ex2
// this was me playing around to try and get an ensures for the method
/*predicate method check(a: array<int>, seclar:int)
requires a.Length > 0
reads a
{ ensures exists i :: 0 <= i < a.Length && forall j :: (0 <= j < a.Length && j != i) ==> (a[i] >= a[j]) && (seclar <= a[i]) && ( if a[j] != a[i] then seclar >... |
742 | software-specification-p1_tmp_tmpz9x6mpxb_BoilerPlate_Ex1.dfy | datatype Tree<V> = Leaf(V) | SingleNode(V, Tree<V>) | DoubleNode(V, Tree<V>, Tree<V>)
datatype Code<V> = CLf(V) | CSNd(V) | CDNd(V)
function serialise<V>(t : Tree<V>) : seq<Code<V>>
decreases t
{
match t {
case Leaf(v) => [ CLf(v) ]
case SingleNode(v, t) => serialise(t) + [ CSNd(v) ]
case DoubleNode... | datatype Tree<V> = Leaf(V) | SingleNode(V, Tree<V>) | DoubleNode(V, Tree<V>, Tree<V>)
datatype Code<V> = CLf(V) | CSNd(V) | CDNd(V)
function serialise<V>(t : Tree<V>) : seq<Code<V>>
{
match t {
case Leaf(v) => [ CLf(v) ]
case SingleNode(v, t) => serialise(t) + [ CSNd(v) ]
case DoubleNode(v, t1, t2) => ... |
743 | software_analysis_tmp_tmpmt6bo9sf_ss.dfy | method find_min_index(a : array<int>, s: int, e: int) returns (min_i: int)
requires a.Length > 0
requires 0 <= s < a.Length
requires e <= a.Length
requires e > s
ensures min_i >= s
ensures min_i < e
ensures forall k: int :: s <= k < e ==> a[min_i] <= a[k]
{
min_i := s;
var i : int := s;
while i < e
... | method find_min_index(a : array<int>, s: int, e: int) returns (min_i: int)
requires a.Length > 0
requires 0 <= s < a.Length
requires e <= a.Length
requires e > s
ensures min_i >= s
ensures min_i < e
ensures forall k: int :: s <= k < e ==> a[min_i] <= a[k]
{
min_i := s;
var i : int := s;
while i < e
... |
744 | specTesting_tmp_tmpueam35lx_examples_binary_search_binary_search_specs.dfy | lemma BinarySearch(intSeq:seq<int>, key:int) returns (r:int)
// original
requires forall i,j | 0 <= i <= j < |intSeq| :: intSeq[i] <= intSeq[j]
ensures r >= 0 ==> r < |intSeq| && intSeq[r] == key
ensures r < 0 ==> forall i:nat | i < |intSeq| :: intSeq[i] != key
{
var lo:nat := 0;
var hi:nat :=... | lemma BinarySearch(intSeq:seq<int>, key:int) returns (r:int)
// original
requires forall i,j | 0 <= i <= j < |intSeq| :: intSeq[i] <= intSeq[j]
ensures r >= 0 ==> r < |intSeq| && intSeq[r] == key
ensures r < 0 ==> forall i:nat | i < |intSeq| :: intSeq[i] != key
{
var lo:nat := 0;
var hi:nat :=... |
745 | specTesting_tmp_tmpueam35lx_examples_increment_decrement_spec.dfy | module OneSpec {
datatype Variables = Variables(value: int)
predicate Init(v: Variables)
{
v.value == 0
}
predicate IncrementOp(v: Variables, v': Variables)
{
&& v'.value == v.value + 1
}
predicate DecrementOp(v: Variables, v': Variables)
{
&& v'.value == v... | module OneSpec {
datatype Variables = Variables(value: int)
predicate Init(v: Variables)
{
v.value == 0
}
predicate IncrementOp(v: Variables, v': Variables)
{
&& v'.value == v.value + 1
}
predicate DecrementOp(v: Variables, v': Variables)
{
&& v'.value == v... |
746 | specTesting_tmp_tmpueam35lx_examples_max_max.dfy | lemma max(a:int, b:int) returns (m:int)
ensures m >= a
ensures m >= b
ensures m == a || m == b
{
if (a > b) {
m := a;
} else {
m := b;
}
}
predicate post_max(a:int, b:int, m:int)
{
&& m >= a
&& m >= b
&& (m == a || m == b)
}
// to check if it is functioning: postcon... | lemma max(a:int, b:int) returns (m:int)
ensures m >= a
ensures m >= b
ensures m == a || m == b
{
if (a > b) {
m := a;
} else {
m := b;
}
}
predicate post_max(a:int, b:int, m:int)
{
&& m >= a
&& m >= b
&& (m == a || m == b)
}
// to check if it is functioning: postcon... |
747 | specTesting_tmp_tmpueam35lx_examples_sort_sort.dfy | method quickSort(intSeq:array<int>)
modifies intSeq
ensures forall i:nat, j:nat | 0 <= i <= j < intSeq.Length :: intSeq[i] <= intSeq[j]
// ensures multiset(intSeq[..]) == multiset(old(intSeq[..]))
lemma sort(prevSeq:seq<int>) returns (curSeq:seq<int>)
ensures (forall i:nat, j:nat | 0 <= i <= j < |curS... | method quickSort(intSeq:array<int>)
modifies intSeq
ensures forall i:nat, j:nat | 0 <= i <= j < intSeq.Length :: intSeq[i] <= intSeq[j]
// ensures multiset(intSeq[..]) == multiset(old(intSeq[..]))
lemma sort(prevSeq:seq<int>) returns (curSeq:seq<int>)
ensures (forall i:nat, j:nat | 0 <= i <= j < |curS... |
748 | stunning-palm-tree_tmp_tmpr84c2iwh_ch1.dfy | // Ex 1.3
method Triple (x: int) returns (r: int)
ensures r == 3*x {
var y := 2*x;
r := y + x;
assert r == 3*x;
}
method Caller() {
var t := Triple(18);
assert t < 100;
}
// Ex 1.6
method MinUnderSpec (x: int, y: int) returns (r: int)
ensures r <= x && r <= y {
if x <= y {
r := x - 1;
} else {
... | // Ex 1.3
method Triple (x: int) returns (r: int)
ensures r == 3*x {
var y := 2*x;
r := y + x;
}
method Caller() {
var t := Triple(18);
}
// Ex 1.6
method MinUnderSpec (x: int, y: int) returns (r: int)
ensures r <= x && r <= y {
if x <= y {
r := x - 1;
} else {
r := y - 1;
}
}
method Min (x: ... |
749 | stunning-palm-tree_tmp_tmpr84c2iwh_ch10.dfy | // Ch. 10: Datatype Invariants
module PQueue {
export
// Impl
provides PQueue
provides Empty, IsEmpty, Insert, RemoveMin
// Spec
provides Valid, Elements, EmptyCorrect, IsEmptyCorrect
provides InsertCorrect, RemoveMinCorrect
reveals IsMin
// Implementati... | // Ch. 10: Datatype Invariants
module PQueue {
export
// Impl
provides PQueue
provides Empty, IsEmpty, Insert, RemoveMin
// Spec
provides Valid, Elements, EmptyCorrect, IsEmptyCorrect
provides InsertCorrect, RemoveMinCorrect
reveals IsMin
// Implementati... |
750 | stunning-palm-tree_tmp_tmpr84c2iwh_ch5.dfy | function More(x: int): int {
if x <= 0 then 1 else More(x - 2) + 3
}
lemma {:induction false} Increasing(x: int)
ensures x < More(x)
{
if x <= 0 {}
else {
// x < More(x) <=> x < More(x - 2) + 3
// <=> x - 3 < More(x - 2)
// Increasing(x - 2) ==> x - 2 < More(x - 2)
// ... | function More(x: int): int {
if x <= 0 then 1 else More(x - 2) + 3
}
lemma {:induction false} Increasing(x: int)
ensures x < More(x)
{
if x <= 0 {}
else {
// x < More(x) <=> x < More(x - 2) + 3
// <=> x - 3 < More(x - 2)
// Increasing(x - 2) ==> x - 2 < More(x - 2)
// ... |
751 | stunning-palm-tree_tmp_tmpr84c2iwh_ch8.dfy | // Ch. 8: Sorting
datatype List<T> = Nil | Cons(head: T, tail: List<T>)
function Length<T>(xs: List<T>): int
ensures Length(xs) >= 0
{
match xs
case Nil => 0
case Cons(_, tl) => 1 + Length(tl)
}
function At<T>(xs: List, i: nat): T
requires i < Length(xs)
{
if i == 0 then xs.head else At(xs.tail, ... | // Ch. 8: Sorting
datatype List<T> = Nil | Cons(head: T, tail: List<T>)
function Length<T>(xs: List<T>): int
ensures Length(xs) >= 0
{
match xs
case Nil => 0
case Cons(_, tl) => 1 + Length(tl)
}
function At<T>(xs: List, i: nat): T
requires i < Length(xs)
{
if i == 0 then xs.head else At(xs.tail, ... |
752 | summer-school-2020_tmp_tmpn8nf7zf0_chapter01_solutions_exercise04_solution.dfy | // Predicates
// A common thing you'll want is a function with a boolean result.
function AtLeastTwiceAsBigFunction(a:int, b:int) : bool
{
a >= 2*b
}
// It's so fantastically common that there's a shorthand for it: `predicate`.
predicate AtLeastTwiceAsBigPredicate(a:int, b:int)
{
a >= 2*b
}
function Double(a:int... | // Predicates
// A common thing you'll want is a function with a boolean result.
function AtLeastTwiceAsBigFunction(a:int, b:int) : bool
{
a >= 2*b
}
// It's so fantastically common that there's a shorthand for it: `predicate`.
predicate AtLeastTwiceAsBigPredicate(a:int, b:int)
{
a >= 2*b
}
function Double(a:int... |
753 | summer-school-2020_tmp_tmpn8nf7zf0_chapter01_solutions_exercise11_solution.dfy | // Algebraic datatypes in their full glory. The include statement.
// A struct is a product:
// There are 3 HAlign instances, and 3 VAlign instances;
// so there are 9 TextAlign instances (all combinations).
// Note that it's okay to omit the parens for zero-element constructors.
datatype HAlign = Left | Center | Righ... | // Algebraic datatypes in their full glory. The include statement.
// A struct is a product:
// There are 3 HAlign instances, and 3 VAlign instances;
// so there are 9 TextAlign instances (all combinations).
// Note that it's okay to omit the parens for zero-element constructors.
datatype HAlign = Left | Center | Righ... |
754 | summer-school-2020_tmp_tmpn8nf7zf0_chapter02_solutions_exercise01_solution.dfy | predicate divides(f:nat, i:nat)
requires 1<=f
{
i % f == 0
}
predicate IsPrime(i:nat)
{
&& 1 < i
&& forall f :: 1 < f < i ==> !divides(f, i)
}
method Main()
{
assert !IsPrime(0);
assert !IsPrime(1);
assert IsPrime(2);
assert IsPrime(3);
assert divides(2, 6);
assert !IsPrime(6);
assert IsPrime(7)... | predicate divides(f:nat, i:nat)
requires 1<=f
{
i % f == 0
}
predicate IsPrime(i:nat)
{
&& 1 < i
&& forall f :: 1 < f < i ==> !divides(f, i)
}
method Main()
{
}
|
755 | summer-school-2020_tmp_tmpn8nf7zf0_chapter02_solutions_exercise02_solution.dfy | predicate divides(f:nat, i:nat)
requires 1<=f
{
i % f == 0
}
predicate IsPrime(i:nat)
{
&& 1<i
&& ( forall f :: 1 < f < i ==> !divides(f, i) )
}
// Convincing the proof to go through requires adding
// a loop invariant and a triggering assert.
method test_prime(i:nat) returns (result:bool)
requires 1<i
en... | predicate divides(f:nat, i:nat)
requires 1<=f
{
i % f == 0
}
predicate IsPrime(i:nat)
{
&& 1<i
&& ( forall f :: 1 < f < i ==> !divides(f, i) )
}
// Convincing the proof to go through requires adding
// a loop invariant and a triggering assert.
method test_prime(i:nat) returns (result:bool)
requires 1<i
en... |
756 | summer-school-2020_tmp_tmpn8nf7zf0_chapter02_solutions_exercise03_solution.dfy | predicate IsSorted(s:seq<int>)
{
forall i :: 0 <= i < |s|-1 ==> s[i] <= s[i+1]
}
predicate SortSpec(input:seq<int>, output:seq<int>)
{
&& IsSorted(output)
&& multiset(output) == multiset(input)
}
//lemma SequenceConcat(s:seq<int>, pivot:int)
// requires 0<=pivot<|s|
// ensures s[..pivot] + s[pivot..] == s
//{... | predicate IsSorted(s:seq<int>)
{
forall i :: 0 <= i < |s|-1 ==> s[i] <= s[i+1]
}
predicate SortSpec(input:seq<int>, output:seq<int>)
{
&& IsSorted(output)
&& multiset(output) == multiset(input)
}
//lemma SequenceConcat(s:seq<int>, pivot:int)
// requires 0<=pivot<|s|
// ensures s[..pivot] + s[pivot..] == s
//{... |
757 | t1_MF_tmp_tmpi_sqie4j_exemplos_classes_parte1_contadorV1b.dfy | class Contador
{
var valor: int;
//construtor anônimo
constructor ()
ensures valor == 0
{
valor := 0;
}
//construtor com nome
constructor Init(v:int)
ensures valor == v
{
valor := v;
}
method Incrementa()
modifies this
ensures valor == o... | class Contador
{
var valor: int;
//construtor anônimo
constructor ()
ensures valor == 0
{
valor := 0;
}
//construtor com nome
constructor Init(v:int)
ensures valor == v
{
valor := v;
}
method Incrementa()
modifies this
ensures valor == o... |
758 | t1_MF_tmp_tmpi_sqie4j_exemplos_colecoes_arrays_ex4.dfy | function SomaAte(a:array<nat>, i:nat):nat
requires 0 <= i <= a.Length
reads a
{
if i == 0
then 0
else a[i-1] + SomaAte(a,i-1)
}
method Somatorio(a:array<nat>) returns (s:nat)
ensures s == SomaAte(a,a.Length)
{
var i := 0;
s := 0;
while i < a.Length
invariant 0 <= i && i <= a.Length
... | function SomaAte(a:array<nat>, i:nat):nat
requires 0 <= i <= a.Length
reads a
{
if i == 0
then 0
else a[i-1] + SomaAte(a,i-1)
}
method Somatorio(a:array<nat>) returns (s:nat)
ensures s == SomaAte(a,a.Length)
{
var i := 0;
s := 0;
while i < a.Length
{
s := s + a[i];
i :... |
759 | t1_MF_tmp_tmpi_sqie4j_exemplos_colecoes_arrays_ex5.dfy | method Busca<T(==)>(a:array<T>, x:T) returns (r:int)
ensures 0 <= r ==> r < a.Length && a[r] == x
ensures r < 0 ==> forall i :: 0 <= i < a.Length ==> a[i] != x
{
r :=0;
while r < a.Length
invariant 0 <= r <= a.Length
invariant forall i :: 0 <= i < r ==> a[i] != x
{
if a[r]==x
... | method Busca<T(==)>(a:array<T>, x:T) returns (r:int)
ensures 0 <= r ==> r < a.Length && a[r] == x
ensures r < 0 ==> forall i :: 0 <= i < a.Length ==> a[i] != x
{
r :=0;
while r < a.Length
{
if a[r]==x
{
return;
}
r := r + 1;
}
r := -1;
}
|
760 | t1_MF_tmp_tmpi_sqie4j_exemplos_colecoes_conjuntos_ex5.dfy | function to_seq<T>(a: array<T>, i: int) : (res: seq<T>)
requires 0 <= i <= a.Length
ensures res == a[i..]
reads a
decreases a.Length-i
{
if i == a.Length
then []
else [a[i]] + to_seq(a, i + 1)
}
method Main() {
var a: array<int> := new int[2];
a[0] := 2;
a[1] := 3;
var ms: multiset<int> := multiset(a[..... | function to_seq<T>(a: array<T>, i: int) : (res: seq<T>)
requires 0 <= i <= a.Length
ensures res == a[i..]
reads a
{
if i == a.Length
then []
else [a[i]] + to_seq(a, i + 1)
}
method Main() {
var a: array<int> := new int[2];
a[0] := 2;
a[1] := 3;
var ms: multiset<int> := multiset(a[..]);
}
|
761 | t1_MF_tmp_tmpi_sqie4j_exemplos_colecoes_sequences_ex3.dfy | // line contém uma string de tamanho l
// remover p caracteres a partir da posição at
method Delete(line:array<char>, l:nat, at:nat, p:nat)
requires l <= line.Length
requires at+p <= l
modifies line
ensures line[..at] == old(line[..at])
ensures line[at..l-p] == old(line[at+p..l])
{
var i:nat := 0;
whi... | // line contém uma string de tamanho l
// remover p caracteres a partir da posição at
method Delete(line:array<char>, l:nat, at:nat, p:nat)
requires l <= line.Length
requires at+p <= l
modifies line
ensures line[..at] == old(line[..at])
ensures line[at..l-p] == old(line[at+p..l])
{
var i:nat := 0;
whi... |
762 | t1_MF_tmp_tmpi_sqie4j_exemplos_introducao_ex4.dfy | function Fat(n: nat): nat
{
if n == 0 then 1 else n * Fat(n-1)
}
method Fatorial(n:nat) returns (r:nat)
ensures r == Fat(n)
{
r := 1;
var i := 0;
while i < n
invariant 0 <= i <= n
invariant r == Fat(i)
{
i := i + 1;
r := r * i;
}
}
| function Fat(n: nat): nat
{
if n == 0 then 1 else n * Fat(n-1)
}
method Fatorial(n:nat) returns (r:nat)
ensures r == Fat(n)
{
r := 1;
var i := 0;
while i < n
{
i := i + 1;
r := r * i;
}
}
|
763 | tangent-finder_tmp_tmpgyzf44ve_circles.dfy | method Tangent(r: array<int>, x: array<int>) returns (b: bool)
requires forall i, j :: 0 <= i <= j < x.Length ==> x[i] <= x[j] // values in x will be in ascending order or empty
requires forall i, j :: (0 <= i < r.Length && 0 <= j < x.Length) ==> (r[i] >= 0 && x[j] >= 0) // x and r will contain no negativ... | method Tangent(r: array<int>, x: array<int>) returns (b: bool)
requires forall i, j :: 0 <= i <= j < x.Length ==> x[i] <= x[j] // values in x will be in ascending order or empty
requires forall i, j :: (0 <= i < r.Length && 0 <= j < x.Length) ==> (r[i] >= 0 && x[j] >= 0) // x and r will contain no negativ... |
764 | test-generation-examples_tmp_tmptwyqofrp_IntegerSet_dafny_IntegerSet.dfy | module IntegerSet {
class Set {
var elements: seq<int>;
constructor Set0()
ensures this.elements == []
ensures |this.elements| == 0
{
this.elements := [];
}
constructor Set(elements: seq<int>)
requires forall i, j | 0 <= i < |elements|... | module IntegerSet {
class Set {
var elements: seq<int>;
constructor Set0()
ensures this.elements == []
ensures |this.elements| == 0
{
this.elements := [];
}
constructor Set(elements: seq<int>)
requires forall i, j | 0 <= i < |elements|... |
765 | test-generation-examples_tmp_tmptwyqofrp_IntegerSet_dafny_Utils.dfy | module Utils {
class Assertions<T> {
static method {:extern} assertEquals(expected : T, actual : T)
requires expected == actual
static method {:extern} expectEquals(expected : T, actual : T)
ensures expected == actual
static method {:extern} assertTrue(condition : bool)
requires condition
... | module Utils {
class Assertions<T> {
static method {:extern} assertEquals(expected : T, actual : T)
requires expected == actual
static method {:extern} expectEquals(expected : T, actual : T)
ensures expected == actual
static method {:extern} assertTrue(condition : bool)
requires condition
... |
766 | test-generation-examples_tmp_tmptwyqofrp_ParamTests_dafny_Utils.dfy | module Utils {
export
reveals Assertions
provides Assertions.assertEquals
class Assertions {
static method {:axiom} assertEquals<T>(left : T, right : T)
requires left == right
/*
public static void assertEquals<T>(T a, T b) {
Xunit.Assert.Equal(a, b);
}
... | module Utils {
export
reveals Assertions
provides Assertions.assertEquals
class Assertions {
static method {:axiom} assertEquals<T>(left : T, right : T)
requires left == right
/*
public static void assertEquals<T>(T a, T b) {
Xunit.Assert.Equal(a, b);
}
... |
767 | test-generation-examples_tmp_tmptwyqofrp_RussianMultiplication_dafny_RussianMultiplication.dfy | module RussianMultiplication {
export provides mult
method mult(n0 : int, m0 : int) returns (res : int)
ensures res == (n0 * m0);
{
var n, m : int;
res := 0;
if (n0 >= 0) {
n,m := n0, m0;
}
else {
n,m := -n0, -m0;
}
w... | module RussianMultiplication {
export provides mult
method mult(n0 : int, m0 : int) returns (res : int)
ensures res == (n0 * m0);
{
var n, m : int;
res := 0;
if (n0 >= 0) {
n,m := n0, m0;
}
else {
n,m := -n0, -m0;
}
w... |
768 | type-definition_tmp_tmp71kdzz3p_final.dfy | // -------------------------------------------------------------
// 1. Implementing type inference
// -------------------------------------------------------------
// Syntax:
//
// τ := Int | Bool | τ1->τ2
// e ::= x | λx : τ.e | true| false| e1 e2 | if e then e1 else e2
// v ::= true | false | λx : τ.e
// E ::= [·] |... | // -------------------------------------------------------------
// 1. Implementing type inference
// -------------------------------------------------------------
// Syntax:
//
// τ := Int | Bool | τ1->τ2
// e ::= x | λx : τ.e | true| false| e1 e2 | if e then e1 else e2
// v ::= true | false | λx : τ.e
// E ::= [·] |... |
769 | veri-sparse_tmp_tmp15fywna6_dafny_concurrent_poc_6.dfy | class Process {
var row: nat;
var curColumn: nat;
var opsLeft: nat;
constructor (init_row: nat, initOpsLeft: nat)
ensures row == init_row
ensures opsLeft == initOpsLeft
ensures curColumn == 0
{
row := init_row;
curColumn := 0;
opsLeft := initOpsLeft;... | class Process {
var row: nat;
var curColumn: nat;
var opsLeft: nat;
constructor (init_row: nat, initOpsLeft: nat)
ensures row == init_row
ensures opsLeft == initOpsLeft
ensures curColumn == 0
{
row := init_row;
curColumn := 0;
opsLeft := initOpsLeft;... |
770 | veri-sparse_tmp_tmp15fywna6_dafny_dspmspv.dfy | function sum(X_val : array<int>, X_crd : array<nat>,
v_val : array<int>, v_crd : array<nat>, kX : nat, kV : nat, pX_end : nat, pV_end : nat) : (s : int)
reads X_val, X_crd
requires X_val.Length == X_crd.Length
requires pX_end <= X_crd.Length
requires 0 <= kX <= X_crd.Length
reads v_crd, v_val
... | function sum(X_val : array<int>, X_crd : array<nat>,
v_val : array<int>, v_crd : array<nat>, kX : nat, kV : nat, pX_end : nat, pV_end : nat) : (s : int)
reads X_val, X_crd
requires X_val.Length == X_crd.Length
requires pX_end <= X_crd.Length
requires 0 <= kX <= X_crd.Length
reads v_crd, v_val
... |
771 | veri-sparse_tmp_tmp15fywna6_dafny_spmv.dfy | function sum(X_val: array<int>, X_crd: array<nat>, v : array<int>, b : int, k : int) : (s : int)
reads X_val, X_crd, v
requires X_val.Length >= b >= 0
requires k <= X_val.Length
requires X_val.Length == X_crd.Length
requires forall i :: 0 <= i < X_crd.Length ==> 0 <= X_crd[i] < v.Length
decreases k - b
{
... | function sum(X_val: array<int>, X_crd: array<nat>, v : array<int>, b : int, k : int) : (s : int)
reads X_val, X_crd, v
requires X_val.Length >= b >= 0
requires k <= X_val.Length
requires X_val.Length == X_crd.Length
requires forall i :: 0 <= i < X_crd.Length ==> 0 <= X_crd[i] < v.Length
{
if k <= b then... |
772 | veri-titan_tmp_tmpbg2iy0kf_spec_crypto_fntt512.dfy | // include "ct_std2rev_model.dfy"
// abstract module ntt_impl {
// import opened Seq
// import opened Power
// import opened Power2
// import opened DivMod
// import opened Mul
// import opened pows_of_2
// import opened ntt_index
// import opened ntt_512_params
// import o... | // include "ct_std2rev_model.dfy"
// abstract module ntt_impl {
// import opened Seq
// import opened Power
// import opened Power2
// import opened DivMod
// import opened Mul
// import opened pows_of_2
// import opened ntt_index
// import opened ntt_512_params
// import o... |
773 | veribetrkv-osdi2020_tmp_tmpra431m8q_docker-hdd_src_veribetrkv-linear_lib_Base_SetBijectivity.dfy | module SetBijectivity {
lemma BijectivityImpliesEqualCardinality<A, B>(setA: set<A>, setB: set<B>, relation: iset<(A, B)>)
requires forall a :: a in setA ==> exists b :: b in setB && (a, b) in relation
requires forall a1, a2, b :: a1 in setA && a2 in setA && b in setB && (a1, b) in relation && (a2, b) in rela... | module SetBijectivity {
lemma BijectivityImpliesEqualCardinality<A, B>(setA: set<A>, setB: set<B>, relation: iset<(A, B)>)
requires forall a :: a in setA ==> exists b :: b in setB && (a, b) in relation
requires forall a1, a2, b :: a1 in setA && a2 in setA && b in setB && (a1, b) in relation && (a2, b) in rela... |
774 | veribetrkv-osdi2020_tmp_tmpra431m8q_docker-hdd_src_veribetrkv-linear_lib_Base_Sets.dfy | module Sets {
lemma {:opaque} ProperSubsetImpliesSmallerCardinality<T>(a: set<T>, b: set<T>)
requires a < b
ensures |a| < |b|
{
assert |b| == |a| + |b-a|;
}
lemma {:opaque} SetInclusionImpliesSmallerCardinality<T>(a: set<T>, b: set<T>)
requires a <= b
ensures |a| <= |b|
{
assert b ==... | module Sets {
lemma {:opaque} ProperSubsetImpliesSmallerCardinality<T>(a: set<T>, b: set<T>)
requires a < b
ensures |a| < |b|
{
}
lemma {:opaque} SetInclusionImpliesSmallerCardinality<T>(a: set<T>, b: set<T>)
requires a <= b
ensures |a| <= |b|
{
}
lemma {:opaque} SetInclusionImpliesStri... |
775 | verification-class_tmp_tmpz9ik148s_2022_chapter05-distributed-state-machines_exercises_UtilitiesLibrary.dfy | module UtilitiesLibrary {
function DropLast<T>(theSeq: seq<T>) : seq<T>
requires 0 < |theSeq|
{
theSeq[..|theSeq|-1]
}
function Last<T>(theSeq: seq<T>) : T
requires 0 < |theSeq|
{
theSeq[|theSeq|-1]
}
function UnionSeqOfSets<T>(theSets: seq<set<T>>) : set<T>
{
if |theSets| == 0 the... | module UtilitiesLibrary {
function DropLast<T>(theSeq: seq<T>) : seq<T>
requires 0 < |theSeq|
{
theSeq[..|theSeq|-1]
}
function Last<T>(theSeq: seq<T>) : T
requires 0 < |theSeq|
{
theSeq[|theSeq|-1]
}
function UnionSeqOfSets<T>(theSets: seq<set<T>>) : set<T>
{
if |theSets| == 0 the... |
776 | verified-isort_tmp_tmp7hhb8ei__dafny_isort.dfy | // Dafny is designed to be familiar to those programming in an OOP language like
// Java, so, we have plain old ordinary mutable arrays rather than the functional
// list data structures that we saw in Coq. This means that unlike our Coq
// and Python examples, we can sort our array in-place and avoid needing a whole
... | // Dafny is designed to be familiar to those programming in an OOP language like
// Java, so, we have plain old ordinary mutable arrays rather than the functional
// list data structures that we saw in Coq. This means that unlike our Coq
// and Python examples, we can sort our array in-place and avoid needing a whole
... |
777 | verified-using-dafny_tmp_tmp7jatpjyn_longestZero.dfy | function getSize(i: int, j:int) : int
{
j - i + 1
}
// For a given integer array, let's find the longest subesquence of 0s.
// sz: size, pos: position. a[pos..(pos+sz)] will be all zeros
method longestZero(a: array<int>) returns (sz:int, pos:int)
requires 1 <= a.Length
ensures 0 <= sz <= a.Length
... | function getSize(i: int, j:int) : int
{
j - i + 1
}
// For a given integer array, let's find the longest subesquence of 0s.
// sz: size, pos: position. a[pos..(pos+sz)] will be all zeros
method longestZero(a: array<int>) returns (sz:int, pos:int)
requires 1 <= a.Length
ensures 0 <= sz <= a.Length
... |
778 | vfag_tmp_tmpc29dxm1j_Verificacion_torneo.dfy | method torneo(Valores : array?<real>, i : int, j : int, k : int) returns (pos_padre : int, pos_madre : int)
requires Valores != null && Valores.Length >= 20 && Valores.Length < 50 && i >= 0 && j >= 0 && k >= 0
requires i < Valores.Length && j < Valores.Length && k < Valores.Length && i != j && j != k && k != i... | method torneo(Valores : array?<real>, i : int, j : int, k : int) returns (pos_padre : int, pos_madre : int)
requires Valores != null && Valores.Length >= 20 && Valores.Length < 50 && i >= 0 && j >= 0 && k >= 0
requires i < Valores.Length && j < Valores.Length && k < Valores.Length && i != j && j != k && k != i... |
779 | vfag_tmp_tmpc29dxm1j_mergesort.dfy | method ordenar_mergesort(V : array?<int>)
requires V != null
modifies V
{
mergesort(V, 0, V.Length - 1) ;
}
method mergesort(V : array?<int>, c : int, f : int)
requires V != null
requires c >= 0 && f <= V.Length
decreases f - c
modifies V
{
if c < f {
... | method ordenar_mergesort(V : array?<int>)
requires V != null
modifies V
{
mergesort(V, 0, V.Length - 1) ;
}
method mergesort(V : array?<int>, c : int, f : int)
requires V != null
requires c >= 0 && f <= V.Length
modifies V
{
if c < f {
var m... |
780 | vfag_tmp_tmpc29dxm1j_sumar_componentes.dfy | method suma_componentes(V : array?<int>) returns (suma : int)
requires V != null
ensures suma == suma_aux(V, 0) // x = V[0] + V[1] + ... + V[N - 1]
{
var n : int ;
assert V != null ; // P
assert 0 <= V.Length <= V.Length && 0 == suma_aux(V, V.Length) ; // P ==> pmd(n := V.Length ; x := ... | method suma_componentes(V : array?<int>) returns (suma : int)
requires V != null
ensures suma == suma_aux(V, 0) // x = V[0] + V[1] + ... + V[N - 1]
{
var n : int ;
n := V.Length ; // n := N
suma := 0 ;
while n != 0
{
suma := suma + V[n - 1] ;
n := n - 1 ;
}
... |
781 | vmware-verification-2023_tmp_tmpoou5u54i_demos_leader_election.dfy | // Each node's identifier (address)
datatype Constants = Constants(ids: seq<nat>) {
predicate ValidIdx(i: int) {
0<=i<|ids|
}
ghost predicate UniqueIds() {
(forall i, j | ValidIdx(i) && ValidIdx(j) && ids[i]==ids[j] :: i == j)
}
ghost predicate WF() {
&& 0 < |ids|
&& UniqueIds()
}
}
// Th... | // Each node's identifier (address)
datatype Constants = Constants(ids: seq<nat>) {
predicate ValidIdx(i: int) {
0<=i<|ids|
}
ghost predicate UniqueIds() {
(forall i, j | ValidIdx(i) && ValidIdx(j) && ids[i]==ids[j] :: i == j)
}
ghost predicate WF() {
&& 0 < |ids|
&& UniqueIds()
}
}
// Th... |
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