Verifying the Composite Pattern using Separation Logic Bart Jacobs - - PowerPoint PPT Presentation

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verifying the composite pattern using separation logic

Verifying the Composite Pattern using Separation Logic Bart Jacobs - - PowerPoint PPT Presentation

Feb 17, 2023 335 likes •700 views

Verifying the Composite Pattern using Separation Logic Bart Jacobs Jan Smans Frank Piessens Katholieke Universiteit Leuven, Belgium Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic Overview

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Verifying the Composite Pattern using Separation Logic

Bart Jacobs Jan Smans Frank Piessens

Katholieke Universiteit Leuven, Belgium

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Overview

General Idea Example: Binary Tree

Interface Client Specification Client Proof Implementation and Implementation Proof Non-contiguous Focus Changes

Demonstration Conclusion

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

General Idea

Module Client Invariant

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Interface

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Client

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Specification

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Specification: Datatype tree

n0 n1 n2 n3 tree(n0, tree(n1, tree(n2, nil, nil), tree(n3, nil, nil)), nil)

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Pure function count

count(tree(n0, tree(n1, tree(n2, nil, nil), tree(n3, nil, nil)), nil)) = 4 n0 n1 n2 n3

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Datatype context

root n0 left_context(root, n0, nil) n0 n1 n2 right_context(left_context(root, n0, nil), n1, tree(n2, nil, nil))

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Predicate tree

n0 n1 n2 n3 memory region tree(n0, root, tree(n0, tree(n1, tree(n2, nil, nil), tree(n3, nil, nil)), nil)) focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Predicate tree

n0 n1 n2 n3 memory region tree(n1, left_context(root, n0, nil), tree(n1, tree(n2, nil, nil), tree(n3, nil, nil))) focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Predicate tree

n0 n1 n2 n3 memory region tree(n3, right_context( left_context(root, n0, nil), n1, tree(n2, nil, nil)), tree(n3, nil, nil)) focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Function create_tree

result focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

c

Example: Binary Tree Spec’n: Function tree_add_left

node r focus node c node r result focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

c

Example: Binary Tree Spec’n: Function tree_get_count

node t focus node c node t focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Function tree_get_parent

node t focus node pns r p node t pns r p focus node (case left_context)

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Spec’n: Function tree_dispose

node focus node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Client Proof

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Implementation: struct node

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Implementation: predicate tree

c node subtree focus node c node node subtree context(node, parent, count(subtree), c) subtree(node, parent, subtree)

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Implementation: predicate subtree

left left- Nodes right- Nodes node right node-> left | -> left node-> right | -> right node-> parent | -> parent node-> count | -> count(t) malloc_block_node(node) left left- Nodes right right- Nodes

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Implementation: predicate context

n pns r p right p-> left | -> n p-> right | -> right p-> parent | -> gp p-> count | -> pcount malloc_block_node(p) right r pns p

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Implementation: function create_tree

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Impl’n: function subtree_get_count

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Impl’n: function fixup_ancestors

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Impl’n: function tree_add_left

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Impl’n: function tree_get_count

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Example: Binary Tree Impl’n: function tree_get_parent

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Overview

General Idea Example: Binary Tree

Interface Client Specification Client Proof Implementation and Implementation Proof Non-contiguous Focus Changes

Demonstration Conclusion

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Non-contiguous Focus Changes Example Client Program

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Non-contiguous Focus Changes Additional Specification Elements

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Non-contiguous Focus Changes Proof of Example Client Program

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Non-contiguous Focus Changes Proof of lemma change_focus

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Overview

General Idea Example: Binary Tree

Interface Client Specification Client Proof Implementation and Implementation Proof Non-contiguous Focus Changes

Demonstration Conclusion

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Overview

General Idea Example: Binary Tree

Interface Client Specification Client Proof Implementation and Implementation Proof Non-contiguous Focus Changes

Demonstration Conclusion

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Bart Jacobs, Jan Smans, Frank Piessens - Verifying the Composite Pattern using Separation Logic

Conclusion

Approach:

Structure = 1 seplogic predicate In proof: Separate out focus node In client: Change focus node using

lemma

VeriFast:

www.cs.kuleuven.be/ ~ bartj/ verifast