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Points-to Analysis in Almost Linear Time

This paper, presented at the 23rd ACM Symposium on Principles of Programming Languages (POPL'96), explores an efficient algorithm for points-to analysis, addressing the challenges in static type systems. Authored by Bjarne Steensgaard, the research demonstrates a flow-insensitive and context-insensitive approach to interprocedural analysis through a novel type inference system. The talk covers essential concepts like the source language, typing rules, and efficiency comparisons with existing algorithms. With emphasis on practical examples, this work advances the understanding of type systems in programming languages.

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Points-to Analysis in Almost Linear Time

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  1. Points-to Analysis in Almost Linear Time paper by Bjarne Steensgaard 23rd ACM Symposium on Principles of Programming Languages (POPL'96) Microsoft Research Technical Report MSR-TR-95-08 presented by Jeff Blank CMSC 858Z Spring 2004

  2. Outline of Talk • Background • Source Language • Type System • Inference Algorithm • Examples

  3. Motivation • Why this paper? • and which paper, exactly? • What type of analysis? • flow-insensitive, context-insensitive, interprocedural

  4. Example: Factorial Source Language fact = fun(x)->(r) if lessthan(x 1) then r = 1 else xminusone = subtract(x 1) nextfac = fact(xminusone) r = multiply(x nextfac) fi result = fact(10) S ::= x = y | x = &y | x = *y | x = op(y1. . .yn) | x = allocate(y) | *x = y | x = fun(f1…fn)->(r1…rm) S* | x1…xm= p(y1…yn)

  5. Non-standard types  ::=  x   ::=  | ref()  ::=  | lam(1…n)(n+1…n+m)

  6. Typing Rules • “obvious” vs. with partial order • (review on sheet) _ = whatever!

  7. Type Inference System • imposing the rules = performing points-to analysis • Algorithm: • Initialization • assumptions • all variables set to different types • Inference • impose the rules, i.e. merge types as necessary • one pass

  8. a x,z b p y c Example Run a = &x b = &y if p then y = &z; else y = &x fi c = &y

  9. m i j n More Examplesoriginal algorithm m = 42 i = m j = m j = &n

  10. m i j n More Examplesimproved algorithm m = 42 i = m j = m j = &n

  11. m i j n More Examplesimproved algorithm (joining with pending set) m = 42 i = m j = m m = &n

  12. Efficiency of system • O(N(N,N)) •  is inverse Ackermann’s function, cost of find • Compared to others...

  13. Other comments • no support for separate types in a composite object (e.g. a struct) • is fast • even on mid-nineties computers • test data (show graph)

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