Who’s afraid of Object Algebras? Tijs van der Storm @tvdstorm / [email protected]

Rascal _ Enso

Extensibility Language with addition Multiplication feature

abstract class Exp { } ! class Lit extends Exp { int value; Lit(this.value); } ! class Add extends Exp { Exp lhs, rhs; Add(this.lhs, this.rhs); } Abstract syntax 1 + 2 new Add(new Lit(1), new Lit(2))

Add Mul Lit ... Variants print check eval ... Operations

Evaluate operation Add Lit: 1 Lit: 2 eval( ) = 3

Print operation Add Lit: 1 Lit: 2 print( ) = “1 + 2”

Variants Operations OO languages FP languages

The Expression Problem ! Philip Wadler, 12 November 1998 ! The Expression Problem is a new name for an old problem. The goal is to define a datatype by cases, where one can add new cases to the datatype and new functions over the datatype, without recompiling existing code, and while retaining static type safety (e.g., no casts). For the concrete example, we take expressions as the data type, begin with one case (constants) and one function (evaluators), then add one more construct (plus) and one more function (conversion to a string). http://homepages.inf.ed.ac.uk/wadler/papers/expression/expression.txt

A design pattern inspired by abstract algebra to solve the expression problem without fancy language features Object Algebras

Plan •Let the expression problem happen before your eyes •Make it go away with Object Algebras

abstract class Exp { } ! class Lit extends Exp { int value; Lit(this.value); } ! class Add extends Exp { Exp lhs, rhs; Add(this.lhs, this.rhs); }

Standard OO style •+Natural encoding •+Easy to add variants •−Hard to add operations •−Scattering of operations

Visitor pattern

Visitor style •+Easy to add operations •+Operation-specific state •−Hard to add variants •−Double dispatch •−Breaks encapsulation

Decomposition print eval Lit Add

Object-oriented print eval Lit Add

Object-oriented print eval Lit Add

Visitor print eval Lit Add

Visitor print eval Lit Add

Variants Operations Variants Operations Standard style Visitor style

Solving the expression problem print eval Lit Add

Extensibility for the Masses Practical Extensibility with Object Algebras Bruno C. d. S. Oliveira1 and William R. Cook2 1National University of Singapore [email protected] 2 University of Texas, Austin [email protected] Abstract. This paper presents a new solution to the expression problem (EP) that works in OO languages with simple generics (including Java

Objects

Credit: Things Come Apart, by Todd McLellan

Multi-purpose objects Add print eval Lit: 1 print eval Lit: 2 print eval 1 + 2 =

Single purpose objects Add print Lit: 1 print Lit: 2 print printable 1 + 2 = Add eval Lit: 1 eval Lit: 2 eval evaluable 1 + 2 =

abstract class ExpFactory { Exp lit(int value); Exp add(Exp lhs, Exp rhs); } Abstract factory

Generic factory abstract class ExpFactory { E lit(int n); E add(E lhs, E rhs); }

The link with algebra An algebraic signature [17] defines the n perate over one or more abstract types, call f some primitive built-in sorts for integers a signature E lit: Int ⇥ E add: E E ⇥ E A general algebraic signature can contain he abstract set, as well as observations tha his paper we restrict signatures to only conta iven above. We call such signatures construc An -algebra is a set together with a co pecified in the signature . A given signat abstract class ExpAlg { E lit(int n); E add(E lhs, E rhs); } Guttag, J. V., Horning, J.J.: The algebraic specification of abstract datatypes. Acta Informatica (1978) Generic factory interfaces are algebraic signatures!

Extension! abstract class ExpAlg { E lit(int n); E add(E lhs, E rhs); } abstract class MulAlg extends ExpAlg { E mul(E lhs, E rhs); }

Object Algebra style

Object Algebras •Data type is a generic factory interface •Operation is a factory implementation •Easy to add variants (extend interface) •Easy to add operations (implement interface)

ExpAlg PrintExp MulAlg EvalExp PrintMul EvalMul ... ...

ExpAlg PrintExp MulAlg EvalExp PrintMul EvalMul Variants Operations ... ...

Extensibility print eval Lit Add Expression problem ExpAlg PrintExp MulAlg EvalExp PrintMul EvalMul . . Object Algebras

Object Algebras because extensibility