Programs That Eat Programs

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Programs That Eat Programs Michael R. Bernstein February 24th, 2015 Software GR, Grand Rapids, MI w michaelrbernste.in t @mrb_bk

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I’m Obsessed

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I’m Obsessed

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I’m Obsessed

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I have a podcast

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Static analysis is my day job

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I live in College Park, Maryland

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Programs That Eat Programs

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Programs That Eat Programs

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What Is A Program?

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Programs

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Math

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Math is Cool

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“Introduction to Lattices and Order” Davey & Priestley

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“Ordered Sets and Complete Lattices: A Primer for Computer Science” Priestley

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A ______ is a _______ with a _______

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Partial Order

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Set Theory

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Partially Ordered Sets

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Lattices

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Monotonicity

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Galois Connections

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Very Cool Math

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“Principles of Program Analysis” Nielson, Nielson & Hankin

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What Is A Program?

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Programs That Eat Programs

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How Do You Eat One?

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Interpreters

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“Essentials of Programming Languages” Friedman & Wand

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“Abstracting Abstract Machines” Van Horn and Might

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From a concrete interpreter to an abstract interpreter

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type Σ = (Exp,Env,Store,Kont) type Env = Var :-> Addr data Storable = Clo (Lambda, Env) type Store = Addr :-> Storable data Kont = Mt | Ar (Exp,Env,Kont) | Fn (Lambda,Env,Kont) type Addr = Int

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step :: Σ -> Σ step (Ref x, ρ, σ, κ) = (Lam lam, ρ', σ, κ) where Clo (lam, ρ') = σ!(ρ!x) step (f :@ e, ρ, σ, κ) = (f, ρ, σ, Ar(e, ρ, κ)) step (Lam lam,ρ,σ,Ar(e, ρ', κ)) = (e, ρ', σ, Fn(lam, ρ, κ)) step (Lam lam,ρ,σ,Fn(x :=> e, ρ', κ)) = (e, ρ' // [x ==> a'], σ // [a' ==> Clo (lam, ρ)], κ) where a' = alloc(σ)

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Static Analysis

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As long as we’ve been writing programs, we’ve been writing programs to analyze our programs

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As long as we’ve been writing programs, we’ve been writing programs that eat programs

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What Do We Hope To Learn?

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State space exploration

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Soundness

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“In Defense of Soundiness: A Manifesto” Livshits, Sridharan,et. al.

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Soundiness

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Higher-Order PLs

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Practicality

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Semantics Matter!

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Brakeman - Rails Security Scanner

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The Future

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SMT Solvers

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Why write code and then generate proofs when you could write proofs and generate code?