Formal methods Project Report for the support of slides uploaded
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This report details a formal methods project that finds the index of the last zero in an integer array. It outlines the challenge of only passing the array as input and describes the implementation of two functions, 'exist_zero' and 'last_zero', used to achieve the objective. The report also provides test cases to demonstrate that the functions work correctly, confirming the proof statuses for each test.
![6/8/2015
2
EXIST_ZERO function:
val EXIST_ZERO_DEF= Define
` (EXISTS [] = F) /
( EXISTS (h::t) = if (h=0) then T else EXISTS t)`;
Secondly we have made the function "last_zero" which in turn uses the
"EXIST_ZERO" function and returns the index of the last zero in the array
passed to it.
last_zero function:
val last_zero = Define
`( zero [] = 0 ) /
(zero (h::t) =
if (EXISTS (h::t))
then 1+ zero t
else
0
)`;
Some test cases to verify:
We verified the test cases using "e(RW_TAC
std_ss[last_zero,EXIST_ZERO_DEF]);" after setting goals.
Goals/Test Cases:
1: g`zero[]=0`;
Expected output: 0
Output:
> val it =](https://image.slidesharecdn.com/formalmethods-150609200950-lva1-app6892/85/Formal-methods-Project-Report-for-the-support-of-slides-uploaded-3-320.jpg)
![6/8/2015
3
Initial goal proved.
|- zero [] = 0 : proof
Status: Passed
2: g`zero[1;2;0;4]=3`;
Expected output: 3
Output:
> val it =
Initial goal proved.
|- zero [1; 2; 0; 4] = 3 : proof
Status: Passed
3: g`zero[0;0]=2`;
Expected output: 2
Output:
> val it =
Initial goal proved.
|- zero [0; 0] = 2 : proof
Status: Passed
4: g`zero[0;0;0;0]=zero[1;2;3;0]`;
Expected output: zero [0; 0; 0; 0] = zero [1; 2; 3; 0]
Output:
> val it =
Initial goal proved.
|- zero [0; 0; 0; 0] = zero [1; 2; 3; 0] : proof
Status: Passed](https://image.slidesharecdn.com/formalmethods-150609200950-lva1-app6892/85/Formal-methods-Project-Report-for-the-support-of-slides-uploaded-4-320.jpg)
![6/8/2015
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5: g`zero[1;2;0;4]=2`;
Expected output: F
Output: > val it =
F
Status: Passed](https://image.slidesharecdn.com/formalmethods-150609200950-lva1-app6892/85/Formal-methods-Project-Report-for-the-support-of-slides-uploaded-5-320.jpg)
Formal methods Project Report for the support of slides uploaded
- 1. FORMAL METHODS Project Report The purpose of this report is to demonstrate our end semester project for “Formal Methods” that Find the index of the last 0 in an array program. Submitted by : Shoaib Haseeb
- 2. 6/8/2015 1 FORMAL METHODS Project Report Title: Find the index of the last 0 in an array program Input: An array of integers. Expected Output: Index of the last zero in that array. Pseudo code: Summary: In this project we were asked to find the index of the last zero in array. The challenge which we faced was that we had the restriction of passing only the array as an input. We couldn't pass another variable with that. So for this purpose we made a function named "EXIST_ZERO" in which an array is passed and we have used a built-in function of "EXISTS" in it which is checking the existence of zero in the array.
- 3. 6/8/2015 2 EXIST_ZERO function: val EXIST_ZERO_DEF= Define ` (EXISTS [] = F) / ( EXISTS (h::t) = if (h=0) then T else EXISTS t)`; Secondly we have made the function "last_zero" which in turn uses the "EXIST_ZERO" function and returns the index of the last zero in the array passed to it. last_zero function: val last_zero = Define `( zero [] = 0 ) / (zero (h::t) = if (EXISTS (h::t)) then 1+ zero t else 0 )`; Some test cases to verify: We verified the test cases using "e(RW_TAC std_ss[last_zero,EXIST_ZERO_DEF]);" after setting goals. Goals/Test Cases: 1: g`zero[]=0`; Expected output: 0 Output: > val it =
- 4. 6/8/2015 3 Initial goal proved. |- zero [] = 0 : proof Status: Passed 2: g`zero[1;2;0;4]=3`; Expected output: 3 Output: > val it = Initial goal proved. |- zero [1; 2; 0; 4] = 3 : proof Status: Passed 3: g`zero[0;0]=2`; Expected output: 2 Output: > val it = Initial goal proved. |- zero [0; 0] = 2 : proof Status: Passed 4: g`zero[0;0;0;0]=zero[1;2;3;0]`; Expected output: zero [0; 0; 0; 0] = zero [1; 2; 3; 0] Output: > val it = Initial goal proved. |- zero [0; 0; 0; 0] = zero [1; 2; 3; 0] : proof Status: Passed
- 5. 6/8/2015 4 5: g`zero[1;2;0;4]=2`; Expected output: F Output: > val it = F Status: Passed