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Choice Calculus &Variational Programming

PNW PL/SE Meeting 2016

Eric Walkingshaw Oregon State University

PL Research @ OSU

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Lots of research related to variability:

• variational program analyses

• variational program execution

• variational data structures

• view-based editing of variational programs

Other active areas:

• language design & domain-specific languages

• functional programming

class Buffer { int buff = 0; #ifdef UndoOne int back = 0; #endif #ifdef UndoMany Stack stack = new Stack(); #endif int get() { return buff; } void set(int x) { #ifdef Logging log(buff+"->"+x); #endif #ifdef UndoOne back = buff; #endif #ifdef UndoMany stack.push(buff); #endif buff = x; }

#ifdef UndoOne void undo() { #ifdef Logging log(back+"<-"+bug); #endif buff = back; } #endif #ifdef UndoMany void undo() { #ifdef Logging log(stack.peek() +"<-"+buff); #endif buff = stack.pop(); } #endif }

class Buffer { int buff = 0; int get() { return buff; } void set(int x) { buff = x; } }

class Buffer { int buff = 0; int get() { return buff; } void set(int x) { log(buff+"->"+x); buff = x; } }

class Buffer { int buff = 0; int back = 0; int get() { return buff; } void set(int x) { back = buff; buff = x; } void undo() { buff = back; } }

class Buffer { int buff = 0; int back = 0; int get() { return buff; } void set(int x) { log(buff+"->"+x); back = buff; buff = x; } void undo() { log(back +"<-"+bug); buff = back; } }

class Buffer { int buff = 0; Stack stack = new Stack(); int get() { return buff; } void set(int x) { stack.push(buff); buff = x; } void undo() { buff = stack.pop(); } }

class Buffer { int buff = 0; Stack stack = new Stack(); int get() { return buff; } void set(int x) { log(buff+"->"+x); stack.push(buff); buff = x; } void undo() { log(stack.peek() +"<-"+buff); buff = stack.pop(); } }

software product line

Motivation: a problem from SPLs

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class Buffer { int buff = 0; int get() { return buff; } void set(int x) { buff = x; } }

✓program analysis

✓✓✓✘✓✓

Goal: apply thisto all of these

configure

Solution: analyze variational program

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class Buffer { int buff = 0; int get() { return buff; } void set(int x) { buff = x; } }

✓program analysis

variational program analysis

class Buffer { int buff = 0; #ifdef UndoOne int back = 0; #endif #ifdef UndoMany Stack stack = new Stack(); #endif int get() { return buff; } void set(int x) { #ifdef Logging log(buff+"->"+x); #endif #ifdef UndoOne back = buff; #endif #ifdef UndoMany stack.push(buff); #endif buff = x; }

#ifdef UndoOne void undo() { #ifdef Logging log(back+"<-"+bug); #endif buff = back; } #endif #ifdef UndoMany void undo() { #ifdef Logging log(stack.peek() +"<-"+buff); #endif buff = stack.pop(); } #endif }

✓✘✓✓✓

confi

gure

confi

gure

implementing these things = research

variational programvariational result

• Intro and motivation

• Choice calculus

• Variational type inference + applications

• Brief note on variational data structures

Outline

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Choice calculus

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e ::= a{e,...,e} | D⟨e,e⟩

A⟨2,3⟩ + B⟨4,A⟨5,6⟩⟩

2 + B⟨4,5⟩ 3 + B⟨4,6⟩

3 + 4 3 + 62 + 4 2 + 5

{A} {¬A}

{A,B} {A,¬B} {¬A,¬B}{¬A,B}

object language AST

choice between two alternatives synchronized by a dimension

A core metalanguage for describing variation

Martin Erwig

Equivalence laws

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D⟨e,e⟩ ≡ e idempotency

D⟨e1,D⟨e2,e3⟩⟩ ≡ D⟨e1,e3⟩ domination

D1⟨D2⟨e1,e2⟩,D2⟨e3,e4⟩⟩ ≡ D2⟨D1⟨e1,e3⟩,D1⟨e2,e4⟩⟩

distribution

D⟨a{e1,e2},a{e3,e4}⟩ ≡ a{D⟨e1,e3⟩,D⟨e2,e4⟩}

factoring

Instantiating the choice calculus

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e ::= c | x | λx.e | e e | D⟨e,e⟩

variational lambda calculus

T ::= κ | a | T -> T | D⟨T,T⟩

variational types

D⟨T1 -> T2, T3 -> T4⟩ ≡ D⟨T1,T3⟩ -> D⟨T2,T4⟩

can instantiate theequivalence laws too:

• Intro and motivation

• Choice calculus

• Variational type inference + applications

• Brief note on variational data structures

Outline

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Variational type inference

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Hindley-Milner

confi

gure

confi

gure

variational type

inference

variational lambda calculus

variational type

lambda calculus type

Variational unification

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Goal: find a mapping so that�= {a ⇥� T } TL�� TR�

AhInt,ai ¥? Aha,Booli

Int¥? a a ¥?Bool

stuck!

decompose byalternatives

�= {a ⇥� A⇤Int,Bool⌅ }

Variational unification

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A�Int,aA⇥ ⇤? A�aA ,Bool⇥

AhInt,ai ¥? Aha,Booli

1. Qualification

aA ¥?BoolInt¥? aA 2. Solve qualified problem

3. Completion

{aA ⇥� Int,aA ⇥� Bool }

{a ⇥� A⇤Int,Bool⌅ }

Variational unification

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AhBhInt,Booli,aAi ¥? BhaB,Booli

AhBhInt,Booli,ai ¥? Bha,Booli

Goal: transformso we candecomposeby alternatives

1. Qualification

BhAhInt,aABi, AhBool,aABii ¥? BhaB,Booliswap

2. Solve qualified problem

C-C-SWAP1D0hDhT1,T2i,T3i ¥ DhD0hT1,T3i,D0hT2,T3ii

Variational unification

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AhBhInt,Booli,aAi ¥? BhaB,Booli

AhBhInt,Booli,ai ¥? Bha,Booli

1. Qualification

BhAhInt,aABi, AhBool,aABii ¥? BhaB,Booliswap

AhInt,aABi ¥? aB

Bool¥?Bool aAB ¥?

Bool

AhBool,aABi ¥?Bool

3. Completion

2. Solve qualified problem

C-IDEMPT1 ¥ T T2 ¥ T

DhT1,T2i ¥ T

{aB ⇥� A⇤Int,aAB⌅, aAB ⇥� Bool }

{a ⇥� B⇤A⇤Int, c⌅, A⇤d,Bool⌅⌅ }

Important results

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O(l2r+ lr2)

Extending Type Inference to Variational ProgramsTOPLAS, 2014

Variational unification is:

• sound, complete, and most general

• polynomially bounded:

Variational type inference is sound, complete, and principal

Surprising applications

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Sheng Chen @ Lafayette• Improving error location in plain Haskell

Counter-Factual Typing for Debugging Type ErrorsPOPL, 2014

• Improving precision of type inference for GADTs

Principal Type Inference for GADTsPOPL, 2016

• Intro and motivation

• Choice calculus

• Variational type inference + applications

• Brief note on variational data structures

Outline

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Variational analysis strike force

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Christian KästnerCarnegie Mellon

Sven ApelPassau

Martin ErwigOregon State

Eric BoddenDarmstadt

Variational . . .• parsing in TypeChef• type checking in TypeChef & FFJPL

• type inference in VLC

• data-flow analysis in SPLLIFT

• execution in a Haskell DSL• test execution in VarEx(J)

When implementing variational analyses … the variation gets everywhere!

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Must manage variation in …

• lists – token streams, TLDs

• trees – ASTs, types

• maps – symbol tables

• graphs – data-flow, control-flow

• and all kinds of intermediate values

so far we’ve dealt with this in an ad hoc way …

Variational execution and data structures

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Needed: foundational work

• deal with variation systematically

• solve problems by considering tradeoffs among well-understood, general-purpose variational data structures

support reuse (libraries) and intentional design decisions

Variational Data Structures: Exploring Tradeoffs in Computing with Variability Onward!, 2014

Beyond variational program analyses

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evaluation w/ multiple privacy policies

Austin et al. (PLAS'13)

encoding lists in symbolic execution Torlak & Bodik (PLDI'14)

Car BikeWalkBus

PDX, Portland, OR

Starting Location(s)

OSU, Corvallis, OR

Ending Location(s)

Fillmore Inn, Corvallis, OR

Silver Falls, Marion, OR

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