Introduction to Our Research on Certifying Compiler

1. Introduction to Our Research on Certifying Compiler Zhaopeng Li (In Chinese: 李兆鹏) Email: zpli@mail.ustc.edu.cn Certifying Compiler Group USTC-Yale Joint Research Center September 4, 2009

2. Outline Motivation Previous Work On-going Work Demonstration

3. Goal of Our Center Building Certified System Software • Verification Framework • Language: x86/MIPS assembly Lang. • Logic: domain-specific logics • Proof: developed in Coq manually Methodology! Shortcoming: Development under this framework is costly.

4. Motivation Lift the verification framework to source-level. ★ productivity ★ user-friendly Generate proof by automated theorem prover.★ automation★ support proof-carrying code

5. Motivation (cont.) Specifications C Code Proof Compcert Specifications Assembly Code Proof Compcert [Xavier Leroy et al.]★ a Certified C Compiler ★ Realistic (Optimization) Difference from a certified compiler?

6. Previous Work Lang.:Subset of C Logic : Pointer Logic Annotated C Code Manual Proof in Coq Pointer Logic Certifying Compiler Pointer Logic Certifying Compiler Front-end Back-end VCGen Proof-Gen VC Proof Proof assistant Coq Annotatedx86 Assembly Code Proof

7. Previous Work (cont.) • Prototype I : a Certifying Compiler • Language: PointerC(subset of C) • Logic: Pointer Logic (long access path, alias inference) • Supported data structures • (circular) singly-linked list • (circular) doubly-linked list • tree

8. On-going Work overview List_create: push ebp mov esp, ebp sub esp, 8 jmp L0 L0 : … L1 : /*n>0 | emp*/ struct list* list_create(int n) { … while(n>0) /*n>=0 | list(p)*/ {… } return p; } /* true | list(res)*/ Lemma wf_L0: … Lemma wf_L1: … Lemma … CComp Compiler SCAP Framework C-like language + Separation Logic

9. On-going Work (cont.) • Prototype II : CComp • Language: C-like(subset of C) • Logic: Separation Logic (fragment) • Build-in automated theorem provers • Support data structures: list/tree

10. On-going Work (cont.) Lang.:Subset of C Logic : Separation Logic Annotated C Code Build-in Automated Theorem Prover CComp Certifying Compiler Front-end Back-end VCGen Proof-Gen VC Proof ATP Annotatedx86 Assembly Code Proof

11. Automated Theorem Prover Prover for fragment of Separation Logic Linear integer Arithmetic Prover Formulas Proof (Proof Term Checkable by Coq) Other Domain-Specific Provers (list, and etc.) Proof Tree Proof Output Automated Theorem Prover Fragment of Separation Logic : separation star / emp / p|->_ Build-in Predicates : list/lseg/dlist/dlseg/tree…

12. Automated Theorem Prover (cont.) • Prover for linear integer arithmetic • Based on Simplex decision procedure • Output coq-compatible proof term • Build using coq libraries (ZArith … ) • Check using coqc • Provide interfaces to VCGen & other provers

13. Automated Theorem Prover (cont.) • Prover for separation logic • Support a fragment (star/ |->/list/lseg/dlist/dlseg/tree) • Using linear integer arithmetic prover to prove equality • Output coq-compatible proof term (on-going work) • More powerful than Smallfoot

14. Demonstration • Simin Yang • Automated linear integer arithmetic prover • Test cases on integer arithmetic • Zhong Zhuang • Automated prover for fragment of separation logic • Test cases manipulating on linked list

15. Thanks!