Re: [isabelle] Hoare-Logic-bubble_Sort

```Dear lyj238,

```
if you didn't find any techniques how to handle functions, then you didn't look very far. Most of today's theorem proving work with Isabelle/HOL is based on some kind of function definitions (just definitions without recursion, primitive recursive functions, and more general recursive functions whose termination has to be proved).
```
```
But I reckon that instead of "function" as I understand it, you might mean something like "side-effects" and thus functions that are allowed to modify some kind of state. If that is the case (and also for arrays) you might want to have a look at Imperative_HOL (which is a theory based on standard Isabelle/HOL).
```
The sources can be found in the subdirectory

src/HOL/Imperative_HOL/Imperative_HOL.thy

of the Isabelle distribution. And a paper about it is available, e.g., here:

http://www4.in.tum.de/~krauss/imperative/imperative.pdf

cheers

chris

On 12/01/2014 05:22 AM, lyj238 wrote:
```
```Yes, I have a similar question.

In a real-world program verification, functions （or procedures) and array are used frequently, without techniques to handle these features, it is too diffcult to apply theorem proving tehnique.

But I really coudl not find techniques to handle functions and arrays in Isabelle src directory or any public source after many searchings.

Best regard!

lyj238

From: mahmoud abdelazim
Date: 2014-11-28 17:39
To: cl-isabelle-users
Subject: [isabelle] Hoare-Logic-bubble_Sort
Hi
i want to proof the correctness of the bubble Sort algoritmo
procedure BubbleSort( A : lista degli elementi da ordinare )
scambio ← true
while scambio
scambio ← false
for i ← 0 to length(A)-2  do
if A[i] > A[i+1] then
swap( A[i], A[i+1] )
scambio ← true
There exists any Hoare Logic theory in Isabelle that can i use to proof that algorithm (In particular a Hoare Logic theory in Isabelle that implement Arrays too )

Thanks

```
```

```

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