From Program Verification to Certified Binaries Angelos - PowerPoint PPT Presentation

From Program Verification to Certified Binaries Angelos Manousaridis Michalis A. Papakyriakou Nikolaos S. Papaspyrou National Technical University of Athens School of Electrical and Computer Engineering Software Engineering Laboratory {amanous, mpapakyr, nickie}@softlab.ntua.gr Logic and Theory of Algorithms 4th Conference on Computability in Europe Athens, Greece, June 18, 2008 A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 1 / 19

❖❱❊❘❆▲▲ ❘❆❚■◆●✿ ✲✹ ✭✉♥❛❝❝❡♣t❛❜❧❡ ❢♦r ♣r❡s❡♥t❛t✐♦♥✮ ❘❊❱■❊❲❊❘✬❙ ❈❖◆❋■❉❊◆❈❊✿ ✸ ✭❤✐❣❤✮ ✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✲ ❘❊❱■❊❲ ✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✲ ❚❤✐s s❤♦rt ♣❛♣❡r r❡♣❧❛②s t❤❡ ❞❡❝❛❞❡ ♦❧❞ ✈✐s✐♦♥ ♦❢ ♣r♦♦❢✲❝❛rr②✐♥❣ ❝♦❞❡✱ ❜✉t ❛✐♠✐♥❣ t♦ ✐♥❝r❡❛s❡ t❤❡ ❧❡✈❡❧ ♦❢ ❛♠❜✐t✐♦♥ ❢r♦♠ s✐♠♣❧❡ ♠❡♠♦r② ❛♥❞ ❝♦♥tr♦❧✲❢❧♦✇ ♣r♦♣❡rt✐❡s t♦ ❛r❜✐tr❛r② ♣r♦❣r❛♠ ♣r♦♣❡rt✐❡s✳ ■ ✇❛s ✉♥❛❜❧❡ t♦ s♣♦t ❛♥② r❡s❡❛r❝❤ ❝♦♥tr✐❜✉t✐♦♥s ♦r ♥♦✈❡❧t② ✐♥ t❤❡ ♣❛♣❡r✳ ■♥ s✉♠♠❛r②✱ t❤✐s ✇♦r❦ ✐s ♠✉❝❤ t♦♦ ♣r❡❧✐♠✐♥❛r② ❛♥❞ ✐s ✐♥ t❤❡ ❝✉rr❡♥t st❛t❡ ✉♥❛❝❝❡♣t❛❜❧❡ ❢♦r ♣r❡s❡♥t❛t✐♦♥✳ What is this about? A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 2 / 19

What is this about? ❖❱❊❘❆▲▲ ❘❆❚■◆●✿ ✲✹ ✭✉♥❛❝❝❡♣t❛❜❧❡ ❢♦r ♣r❡s❡♥t❛t✐♦♥✮ ❘❊❱■❊❲❊❘✬❙ ❈❖◆❋■❉❊◆❈❊✿ ✸ ✭❤✐❣❤✮ ✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✲ ❘❊❱■❊❲ ✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✕✲ ❚❤✐s s❤♦rt ♣❛♣❡r r❡♣❧❛②s t❤❡ ❞❡❝❛❞❡ ♦❧❞ ✈✐s✐♦♥ ♦❢ ♣r♦♦❢✲❝❛rr②✐♥❣ ❝♦❞❡✱ ❜✉t ❛✐♠✐♥❣ t♦ ✐♥❝r❡❛s❡ t❤❡ ❧❡✈❡❧ ♦❢ ❛♠❜✐t✐♦♥ ❢r♦♠ s✐♠♣❧❡ ♠❡♠♦r② ❛♥❞ ❝♦♥tr♦❧✲❢❧♦✇ ♣r♦♣❡rt✐❡s t♦ ❛r❜✐tr❛r② ♣r♦❣r❛♠ ♣r♦♣❡rt✐❡s✳ (snip) ■ ✇❛s ✉♥❛❜❧❡ t♦ s♣♦t ❛♥② r❡s❡❛r❝❤ ❝♦♥tr✐❜✉t✐♦♥s ♦r ♥♦✈❡❧t② ✐♥ t❤❡ ♣❛♣❡r✳ (snip) ■♥ s✉♠♠❛r②✱ t❤✐s ✇♦r❦ ✐s ♠✉❝❤ t♦♦ ♣r❡❧✐♠✐♥❛r② ❛♥❞ ✐s ✐♥ t❤❡ ❝✉rr❡♥t st❛t❡ ✉♥❛❝❝❡♣t❛❜❧❡ ❢♦r ♣r❡s❡♥t❛t✐♦♥✳ A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 2 / 19

So, what is this all about? ◮ A position paper, not much of a research paper ◮ Goal? the construction of certified software i.e. that provably satisfies its specifications ◮ Why? the Holy Grail of software engineering! ◮ How? by combining formal verification and proof-carrying code A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 3 / 19

Outline Introduction Program verification Proof-carrying code Motivation A Hybrid System A Motivating Example Proof-preserving Compilation Conclusion A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 4 / 19

Introduction (i) ◮ Program verification ◮ aims at formally proving program correctness ◮ given a formal specification or property ◮ long tradition (4 decades) ◮ several formal logics (e.g. Hoare Logic) ◮ at the source code level A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 5 / 19

Introduction (ii) ◮ Proof-carrying code (PCC) ◮ certified binary: a value together with a proof that the value satisfies a given specification ◮ relatively recent approach ( ∼ 10 years) ◮ essential in modern distributed computer systems ◮ executable code is transferred among devices that do not necessarily trust one another ◮ at a lower level (e.g. machine language) ◮ mainly interested in relatively simple properties: memory safety and control flow A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 6 / 19

Introduction (iii) ◮ Type-theoretic approaches to PCC e.g. Shao et al. , POPL 2002, TOPLAS 2005; Crary and Vanderwaart, ICFP 2002 ◮ arbitrary program properties ◮ embedding of logic “formulae as types” ◮ proof-preserving compilation ◮ makes the proof a part of the code ◮ type (proof) inference is undecidable A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 7 / 19

Motivation Program PCC verification programmer “friendly” high-level proofs end-user safety A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 8 / 19

Motivation Program PCC verification programmer “friendly” high-level proofs end-user safety A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 8 / 19

Motivation Program PCC verification programmer “friendly” high-level proofs end-user safety A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 8 / 19

Motivation Program PCC verification programmer “friendly” high-level proofs end-user safety A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 8 / 19

Motivation Program PCC verification programmer “friendly” high-level proofs end-user safety Can we write programs in a high-level language, provide correctness proofs for them and then compile them to provably correct executable code? A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 8 / 19

A hybrid system A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 9 / 19

✴✴❅ ✴✴❅ ✴✯❅ r❡q✉✐r❡s ❅ ❡♥s✉r❡s ❅✯✴ ✐♥t r♦♦t ✭✐♥t ♥✮ ④ ✐♥t ② ❂ ✵❀ ✴✴❅ ✇❤✐❧❡ ✭✭②✰✶✮✯✭②✰✶✮ ❁❂ ♥✮ ②✰✰❀ r❡t✉r♥ ②❀ ⑥ Integer square root (i) ◮ Given n ∈ N , find the greatest r ∈ N such that r 2 ≤ n A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 10 / 19

✴✴❅ ✴✴❅ ✴✯❅ r❡q✉✐r❡s ❅ ❡♥s✉r❡s ❅✯✴ ✴✴❅ Integer square root (i) ◮ Given n ∈ N , find the greatest r ∈ N such that r 2 ≤ n ✐♥t r♦♦t ✭✐♥t ♥✮ ④ ✐♥t ② ❂ ✵❀ ✇❤✐❧❡ ✭✭②✰✶✮✯✭②✰✶✮ ❁❂ ♥✮ ②✰✰❀ r❡t✉r♥ ②❀ ⑥ A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 10 / 19

✴✯❅ r❡q✉✐r❡s ❅ ❡♥s✉r❡s ❅✯✴ ✴✴❅ Integer square root (i) ◮ Given n ∈ N , find the greatest r ∈ N such that r 2 ≤ n ✴✴❅ predicate leRoot ( int r , int x ) { r ≥ 0 ∧ r 2 ≤ x } ✴✴❅ predicate isRoot ( int r , int x ) { leRoot ( r , x ) ∧ ( r + 1 ) 2 > x } ✐♥t r♦♦t ✭✐♥t ♥✮ ④ ✐♥t ② ❂ ✵❀ ✇❤✐❧❡ ✭✭②✰✶✮✯✭②✰✶✮ ❁❂ ♥✮ ②✰✰❀ r❡t✉r♥ ②❀ ⑥ A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 10 / 19

✴✴❅ Integer square root (i) ◮ Given n ∈ N , find the greatest r ∈ N such that r 2 ≤ n ✴✴❅ predicate leRoot ( int r , int x ) { r ≥ 0 ∧ r 2 ≤ x } ✴✴❅ predicate isRoot ( int r , int x ) { leRoot ( r , x ) ∧ ( r + 1 ) 2 > x } ✴✯❅ r❡q✉✐r❡s n ≥ 0 isRoot ( \ result , n ) ❅ ❡♥s✉r❡s ❅✯✴ ✐♥t r♦♦t ✭✐♥t ♥✮ ④ ✐♥t ② ❂ ✵❀ ✇❤✐❧❡ ✭✭②✰✶✮✯✭②✰✶✮ ❁❂ ♥✮ ②✰✰❀ r❡t✉r♥ ②❀ ⑥ A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 10 / 19

Integer square root (i) ◮ Given n ∈ N , find the greatest r ∈ N such that r 2 ≤ n ✴✴❅ predicate leRoot ( int r , int x ) { r ≥ 0 ∧ r 2 ≤ x } ✴✴❅ predicate isRoot ( int r , int x ) { leRoot ( r , x ) ∧ ( r + 1 ) 2 > x } ✴✯❅ r❡q✉✐r❡s n ≥ 0 isRoot ( \ result , n ) ❅ ❡♥s✉r❡s ❅✯✴ ✐♥t r♦♦t ✭✐♥t ♥✮ ④ ✐♥t ② ❂ ✵❀ ✴✴❅ invariant leRoot ( y , n ) ✇❤✐❧❡ ✭✭②✰✶✮✯✭②✰✶✮ ❁❂ ♥✮ ②✰✰❀ r❡t✉r♥ ②❀ ⑥ A. Manousaridis, M. A. Papakyriakou, N. S. Papaspyrou From Program Verification to Certified Binaries 10 / 19