Technologies for finding errors in object-oriented software

Technologies for finding errorsin object-oriented software K. Rustan M. LeinoMicrosoft Research, Redmond, WA Lecture 0Summer school on Formal Models of Software1 Sep 2003, Tunis, Tunisia

Motivation

Software development problem • Software construction and maintenance are expensive • Reliability is costly and difficult to achieve

Vision • Increased programmer productivity and program reliability through increased rigor Record design decisions + Utilize automatic checking= Detect errors and improve maintainability

User's view Error messages Program with specifications Program checker public class Bag { private /*@non_null*/ int[] a; private int n; //@ invariant 0 <= n && n <= a.length; public Bag(/*@non_null*/ int[] initialElements) { n = initialElements.length; a = new int[n]; System.arraycopy(initialElements, 0, a, 0, n); } public void add(int x) { if (n == a.length) { int[] b = new int[2*(a.length+1)]; System.arraycopy(a, 0, b, 0, n); a = b; } a[n] = x; n++; } public int extractMin() { int m = Integer.MAX_VALUE; int mindex = 0; for (int i = 0; i < n; i++) { if (a[i] < m) { mindex = i; m = a[i]; } } if (0 < n) { n--; a[mindex] = a[n]; } return m; } // The program text continues down here, but if you’re // reading this, you probably aren’t paying attention to // the talk. Bag.java:18: Array index possibly too large

Extended Static Checker for Java (ESC/Java) • Built at Compaq SRC • Input: Java + user-supplied annotations • Annotation language captures programmer design decisions • Powered by program semantics and automatic theorem proving • Performs modular checking

ESC/Java demo

Program checker design tradeoffs • Missed errors • Spurious warnings • Annotation overhead • Performance

Tool architecture Annotated Java program Translator Verification condition Valid Automatic theorem prover Resource exhausted Counterexample context Post processor Warning messages

Tool architecture, detail Annotated Java program Sugared command Translator Primitive command Passive command Verification condition Automatic theorem prover Counterexample context Post processor Warning messages

Annotated Java program Annotated Java program Sugared command Sugared command Primitive command Translator Translator Primitive command Passive command Passive command Verification condition Verification condition Automatictheorem prover Automatic theorem prover Counterexample context Counterexample context Post processor Post processor Warning messages Warning messages Tool architecture, detail

Annotation language Annotated Java program • Simple • non_null • Method annotations • requires E; • modifies w; • ensures E; • exsures (T x) E; • Object invariants • invariantE; Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Annotation language Annotated Java program • Specification expressions • side-effect free Java expressions • no ++, no method calls • result, old(E) • ensuresresult == old(x); • ==> • (forall T x; E), (exists T x; E) • (forallint j; 0 <= j && j < n ==> a[j] > 0); • typeof(E), type(T), <: • requirestypeof(x) == typeof(this); Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Annotation language Annotated Java program • Concurrency • monitored_by lock • /*@ monitored_bythis */ long x; • lockset[lock] • requireslockset[this]; • lock0 < lock1 • max(lockset) • requiresmax(lockset) < this; Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Annotation language Annotated Java program • Ghost variables • ghostpublic T x; • ghostpublicint objectState; • ghostpublicTYPE elementType; • set x = E; • set objectState = Open; • set elementType = type(T); Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Annotation language Annotated Java program • Miscellaneous • assert E; • assume E; • assume x >= 0; // because x == y*y • nowarn • x = a[j]; //@ nowarn • axiom E; • axiom (forallint x; x ≫ 2 >= 0); Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Sugared commands Annotated Java program • S,T ::= assert E | assume E | x = E | raise | S ; T | S ! T | S [] T | loop {inv E} S  T end | call x = t.m(E) | … Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Sugared commands Annotated Java program • x = t.f.g; assert t ≠ null; tmp = select(f, t); assert tmp ≠ null; x = select(g, tmp) • if (x < 0) { x = -x; }/*@ assert x >= 0; */ ( assume x < 0; x = -x [] assume￢(x < 0) ); assert x >= 0 Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Sugared commands Annotated Java program • x = t.f.g; assert lblneg(“Null@58.9”, t ≠ null); tmp = select(f, t); assert lblneg(“Null@58.11”, tmp ≠ null); x = select(g, tmp) • if (x < 0) { x = -x; }/*@ assert x >= 0; */ ( assume x < 0;assume lblpos(“Then^280:7”, true); x = -x [] assume ￢ (x < 0);assume lblpos(“Else^280:7”, true) ); assert x >= 0 Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Primitive commands Annotated Java program • S,T ::= assert E | assume E | x = E | raise | S ; T | S ! T | S [] T | loop {inv E} S  T end | call x = t.m(E) | … Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Primitive commands Annotated Java program • //@ requires Pre; modifies w; ensures Post;X m(U u); • call x = t.m(E) var u in u = E; assert Pre; var w0in w0 = w; havoc w; assume Post; x = result end end Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

| raise | S ; T | S ! T | S [] T Passive commands Annotated Java program • S,T ::= assert E | assume E | x = E Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Passive commands Annotated Java program • if (x < 0) { x= -x; }/*@ assert x >= 0; */ ( assume x0 < 0; x1 = -x0;x2 = x1 [] assume ￢(x0 < 0);x2 = x0 ); assert x2 >= 0 Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Passive commands Annotated Java program • if (x < 0) { x= -x; }/*@ assert x >= 0; */ ( assume x0 < 0; assume x1 == -x0;assume x2 == x1 [] assume ￢(x0 < 0);assume x2 == x0 ); assert x2 >= 0 Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Weakest preconditions Annotated Java program • A Hoare triple{P}S{Q}says that if command S is started in a state satisfying P, then S terminates without error in a state satisfying Q • The weakest precondition of a command S with respect to a postcondition Q, written wp(S,Q), is the weakest P such that{P}S{Q} Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Weakest preconditions Annotated Java program • wp(assert E, Q) = E && Q • wp(assume E, Q) = E ==> Q • wp(S;T, Q) = wp(S, wp(T,Q)) • wp(S [] T, Q) = wp(S, Q) && wp(T, Q) • wp(S, Q) = wp(S, true) && wlp(S, Q) • wlp(S, Q) = wlp(S, false) || Q Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Verification condition Annotated Java program • Universal background predicate • (∀t ･ t <: t) • Type-specific background predicate • Bag <: java.lang.Object • Verification condition:BPUniv && BPT ==> VCmethod Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

(BG_PUSH (AND (<: T_T |T_java.lang.Object|) (EQ T_T (asChild T_T |T_java.lang.Object|)) (DISTINCT arrayType |T_boolean| |T_char| |T_byte| |T_short| |T_int| |T_long| |T_float| |T_double| |T_.TYPE| T_T |T_java.lang.Object|))) (EXPLIES (LBLNEG |vc.T.abs.2.2| (IMPLIES (AND (EQ |elems@pre| elems) (EQ elems (asElems elems)) (< (eClosedTime elems) alloc) (EQ LS (asLockSet LS)) (EQ |alloc@pre| alloc)) (NOT (AND (EQ |@true| (is |x:2.21| T_int)) (OR (AND (OR (AND (< |x:2.21| 0) (LBLPOS |trace.Then^0,3.15| (EQ |@true| |@true|)) (EQ |x:3.17| (- 0 |x:2.21|)) (EQ |x:2.21<1>| |x:3.17|)) (AND (NOT (< |x:2.21| 0)) (LBLPOS |trace.Else^1,3.4| (EQ |@true| |@true|)) (EQ |x:2.21<1>| |x:2.21|))) (NOT (LBLNEG |Assert@4.8| (>= |x:2.21<1>| 0)))) (AND (OR (AND (< |x:2.21| 0) (LBLPOS |trace.Then^0,3.15| (EQ |@true| |@true|)) (EQ |x:3.17| (- 0 |x:2.21|)) (EQ |x:2.21<1>| |x:3.17|)) (AND (NOT (< |x:2.21| 0)) (LBLPOS |trace.Else^1,3.4| (EQ |@true| |@true|)) (EQ |x:2.21<1>| |x:2.21|))) (LBLNEG |Assert@4.8| (>= |x:2.21<1>| 0)) (NOT (LBLNEG |Exception@5.2| (EQ |ecReturn| |ecReturn|))))))))) (AND (DISTINCT |ecReturn|))) Verification condition Annotated Java program • class T { staticint abs(int x) { if (x < 0) { x = -x; } //@ assert x >= 0; } } Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Theorem prover: “Simplify” Annotated Java program • Nelson-Oppen cooperating decision procedures • conguence closure • linear arithmetic • partial orders • quantifiers • Key features: • automatic: no user interaction • refutation based: searches for counterexamples • heuristics tuned for program checking • labels • time limit Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Counterexamples and warnings Annotated Java program • Counterexample: labels: (|IndexTooBig@26.5| |vc.Bag.add.20.2| |trace.Then^0,21.23|) context: (AND (NEQ |tmp1!a:23.23| null) (NEQ this null) (EQ |alloc@pre| alloc) (EQ |tmp4!n:26.6| 0) … (<= alloc (vAllocTime |tmp3!a:26.4|)) ) • Bag: add(int) ...-----------------------------------------------------------Bag.java:26: Warning: Array index possibly too large (IndexTooBig) a[n] = x;^Execution trace information: Executed then branch in "Bag.java", line 21, col 23.----------------------------------------------------------- Sugared command Primitive command Translator Passive command Verification condition Automatictheorem prover Counterexample context Post processor Warning messages

Experience: annotations • Capture common design decisions • Suggested immediately by warnings • Overhead: 4-10% of source code • ～1 annotation per field or parameter • Most common annotations: • non_null • container element types

Experience: performance • 50% of all methods: < 0.5 s • 80% of all methods: < 1 s • time limit: 300 s • total time for Javafe (～40kloc): 65 min.

Related work • ESC/Modula-3 • Full functional specification and verification • JML, LOOP, B, Penelope, ... • Languages and language features • Euclid, Eiffel, Escher, Guava, Vault, Cqual, ... • LCLint, refinement types, Types against races, ... • Other checking techniques • Abstract interpretation, PREfix, SLAM, Bandera,Java PathFinder 2, Canvas, ESP, AST Toolkit, Metal,…

Conclusions • Using program semantics and automatic decision procedures for program analysis works! • Cost effective?

What's needed? • Semantics of programming language • Specification language • Programming methodology and disciplines • Decision procedures • Property inference Download ESC/Java (tool, documentation, sources):http://research.compaq.com/SRC/esc http://research.compaq.com

Technologies for finding errors in object-oriented software