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fact_run_after_ppo_opt0.txt
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TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function factorial(n: int) returns (res: int)
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function factorial(n: int) returns (res: int)
requires n >=
SCORE
-1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n ==
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n -
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) >
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n ==
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n -
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
}
SCORE
None
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
}
}
SCORE
1.0
TEXT
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
}
}
```
SCORE
1.0
CHOSEN SOLUTION
### Spec: In Dafny, write a factorial function and prove that the factorial is always strictly positive.
### Hint: Use a plain function, NOT a function method.
### Dafny:Here is a Dafny specification for a factorial function, proving that the factorial is always strictly positive.
```dafny
function Factorial(n: nat): nat {
if n == 0 then 1 else n * Factorial(n - 1)
}
lemma {:induction} FactorialPositive(n: nat)
ensures Factorial(n) > 0
{
if n == 0 {
} else {
FactorialPositive(n - 1);
}
}
```