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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 Outline of Talk • • • • Background Source Language Type System Inference Algorithm – Examples Motivation • Why this paper? – and which paper, exactly? • What type of analysis? – flow-insensitive, context-insensitive, interprocedural 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) Non-standard types ::= x ::= | ref() ::= | lam(1…n)(n+1…n+m) Typing Rules • “obvious” vs. with partial order • (review on sheet) _ = whatever! 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 Example Run a a = &x b = &y if p then y = &z; else y = &x fi c = &y x,z b p y c More Examples original algorithm m i j j = = = = 42 m m &n m i j n More Examples improved algorithm m i j j = = = = 42 m m &n m i j n More Examples improved algorithm (joining with pending set) m i j m = = = = 42 m m &n m i j n Efficiency of system • O(N(N,N)) – is inverse Ackermann’s function, cost of find • Compared to others... 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)