The Expression Problem solved,Finally!

FPSyd

Disclaimer

I had this problem before

Result

Failure Success Pending

Console Html

Screenshot?

Pdf?

The Expression Problem

Add(Lit(1), Lit(2))

The Expression Problem

The Expression Problem

Solved in Java?!?

Not a new problem

Once and for all

Encode

anything

Represent

datatypes

Once and for all

Typeclass

Mutually

recursive

Once and for all

Generic

function

Type constructors?

Encod

e

Count

Type constructors?

Typeclass

es

2 for 1!

Data types encodings

Recursive type

Natural

s

Church

encoding

Data types encodings

Fold-

Algebra

(T1 -> A, T2 -> A, …, Tn -> A)

F-Algebra

(T1 + T2 + … + Tn) -> A F[A] -> A

Data types encodings

Church

encoding

Extensibility

Extensibility

Encoder

Extensibility

Generic

functions for

lists

Better

encode

Troubl

eSolutio

n

Extensibility

Generic,

specialized

functions

Functions

Data Dispatchers

Main points

Data types as Folds (!= F-

Algebras)

Encoded as type-classes

Extensible and modular

“Finally tagless”

Finally tagless

Embedded DSLs“Initial

”“Final”

Extensibility “Initial”

Extensibility “Final”

Some other problems

• The tagging problem in the interpretation of typed higher-order languages

• The pattern-matching problem• Many others…

“The [deserialization] problem becomes much more frustrating, exhilarating, time

consuming and addictive in the general case of higher-order typed embedded languages”

- Oleg Kiselyov

The tagging problem

Higher-order

typed language

Does not

typecheck!

One approach

“tagged”

type

Partial

With GADTs

The “Symantics” approach

Synta

x

Semantic

s

Expressio

n

Pushing the negation down

“Initial”

neg (add 1 2) => add (neg 1) (neg 2)

Pushing the negation down “Final”

Bijection between and “Final”“Initial”

Advantages

Expressions are well-typed

Easily extensible

Less demanding of the type system

With OO

The Visitor solution

Data type

Visitor

Object algebra

Interface

Factory

Expressio

n

Pretty printer

Retroactive

Pretty printer

Direct

Extensions

For

booleans

Extensions

Booleans

Pretty-prin

ting

Multi-type

statement

s

Combining data

compositio

n

Combining operations

Banana-split!

Object algebras

Work with OO languages having generics

No visitor and “accept” method

Generic combinator classes?

Fold algebras

Conclusion

Easier on the type system

Extensibility

Shallow / Deep Embeddings – ICFP14

Fold algebras