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4年以上前 (2012/04/08)にアップロードinテクノロジー

The great attractiveness of purely functional languages is their ability to depart from sequentia...

The great attractiveness of purely functional languages is their ability to depart from sequential order of computation. Theoretically, it enables two important features of the compiler:

1) The ability to reorder computation flow, making the program implicitly parallelisable. Modern imperative language compilers, even using careful synchronization of concurrent code, still generate huge chunks of sequential instructions that need to be executed on a single processor core; a purely functional language compilers can dispatch very small chunks to many (hundreds and thousands) of cores, carefully eliminating as many execution path dependencies as possible.

2) As the compiler formalizes different types of side effects, it can detect a whole new class of program errors at compile time, including resource acquisition and releasing problems, concurrent access to shared resources, many types of deadlocks etc. It is not yet a full-fledged program verification, but it is a big step in that direction.

Scala is a semi-imperative language with strong support for functional programming and rich type system. One can isolate the purely functional core of the language which can be put on the firm mathematical foundation of dependent type theories. We argue that it is possible to treat Scala code as it’s written by now as an implicit do-notation which can be then reduced to a purely functional core by means of recently introduced Scala macros. The formalism of arrows and applicative contexts can bring Scala to a full glory of an implicitly parallelisable programming language, while still keeping its syntax mostly unchanged.

- Scala Days NYC 20166ヶ月前 by Martin Odersky
- Scala Days San Francisco1年以上前 by Martin Odersky
- Coding in Style3年以上前 by scalaconfjp

- Procedure Typing for Scala

Procedure Typing for Scala

Alexander Kuklev∗, Alexander Temerev‡

* Institute of Theoretical Physics, University of Göttingen

‡ Founder and CEO at Miriamlaurel Sàrl, Geneva

April 10, 2012 - Scala does not differentiate between them:

– both have types A => B .

Procedure Typing for Scala

Functions and procedures

In programming we have:

– pure functions;

– functions with side effects (AKA procedures). - Procedure Typing for Scala

Functions and procedures

In programming we have:

– pure functions;

– functions with side effects (AKA procedures).

Scala does not differentiate between them:

– both have types A => B . - – compile-time detection of a whole new class of problems:

(resource acquisition and releasing problems, race conditions,

deadlocks, etc.).

Static side effect tracking enables

– implicit parallelisability;

Procedure Typing for Scala

But it should! - – compile-time detection of a whole new class of problems:

(resource acquisition and releasing problems, race conditions,

deadlocks, etc.).

Procedure Typing for Scala

But it should!

Static side effect tracking enables

– implicit parallelisability; - Procedure Typing for Scala

But it should!

Static side effect tracking enables

– implicit parallelisability;

– compile-time detection of a whole new class of problems:

(resource acquisition and releasing problems, race conditions,

deadlocks, etc.). - Procedure Typing for Scala

Short list of applicable methodologies:

Kleisli Arrows of Outrageous Fortune (2011, C. McBride)

Capabilities for Uniqueness and Borrowing (2010, P. Haller, M. Odersky)

Static Detection of Race Conditions [..] (2010, M. Christakis, K. Sagonas)

Static Deadlock Detection [..] (2009, F. de Boer, I. Grabe,M. Steffen)

Complete Behavioural Testing of Object-Oriented Systems using

CCS-Augmented X-Machines (2002, M. Stannett, A. J. H. Simons)

An integration testing method that is proved to find all faults

(1997, F. Ipate, M. Holcombe) - Procedure Typing for Scala

Specifying procedure categories

We propose a new syntax

where a function definition may include a category it belongs to:

A =>[Pure] B – pure functions;

A =>[Proc] B – procedures. - Procedure Typing for Scala

Specifying procedure categories

There’s a lot more than Pure and Proc

There is a whole lattice of categories between Pure and Proc :

Logged: procedures with no side effects besides logging;

Throws[E]: no side effects besides throwing exceptions of type E ;

Reads(file): no side effects besides reading the file ;

etc. - equipped with some additional structure using an

associated type class.

Procedure Typing for Scala

Specifying procedure categories

Extensible approach

An effect system should be extensible.

⇒ We must provide a way to define procedure categories.

Procedure categories are binary types like Function[_,_] or

Logged[_,_] 1

1Definition of parameterized categories, e.g. Throws[E] or Reads(resource),

is also possible with the help of type lambdas and/or type providers. - Procedure Typing for Scala

Specifying procedure categories

Extensible approach

An effect system should be extensible.

⇒ We must provide a way to define procedure categories.

Procedure categories are binary types like Function[_,_] or

Logged[_,_] 1 equipped with some additional structure using an

associated type class.

1Definition of parameterized categories, e.g. Throws[E] or Reads(resource),

is also possible with the help of type lambdas and/or type providers. - Procedure Typing for Scala

Specifying procedure categories

Extensible approach

Syntax details

– A =>[R] B

R[A,B]

– A => B

Function[A,B] , i.e. type named “Function” from the

local context, not necessarily the Function from Predef2.

2 (A, B) should also mean Pair[A,B] from the local context, as they

must be consistent with functions: (A, B) => C ∼

= A => B => C . - Procedure Typing for Scala

Specifying procedure categories

Extensible approach

Proposed syntax for definitions

def process(d: Data):

=>[Throws[InterruptedException]] Int = { ...

// Procedure types can be dependent

def copy(src: File, dest: File):

=>[Reads(src), Writes(dest)] { ...

// Pre- and postconditions can be treated as effects too:

def open(file: File):

=>[Pre{file@Closed}, Post{file@Open}] { ...

Last two examples rely on recently added dependent method types.

(N.B. Such stunts are hard to implement using type-and-effect systems.) - Procedure Typing for Scala

Defining procedure categories

First of all, it should be a category in the usual mathematical sense,

i.e. we have to provide procedure composition and its neutral.

trait Category[Function[_,_]] {

def id[T]: T => T

def compose[A, B, C](f: B => C, g: A => B): A => C

} - Procedure Typing for Scala

Defining procedure categories

To give an example, let’s model logged functions on pure functions:

type Logged[A, B] = (A =>[Pure] (B, String))

object Logged extends Category[Logged] {

def id[T] = {x: T => (x, "")}

def compose[A, B, C](f: B => C, g: A => B) = {x: A =>

val (result1, logOutput1) = g(x)

val (result2, logOutput2) = f(result1)

(result2, logOutput1 + logOutput2)

}

}

Besides their results, logged functions produce log output of type

String. Composition of logged functions concatenates their logs. - Procedure Typing for Scala

Defining procedure categories

Linear functional composition is not enough.

We want to construct arbitrary circuits.

(This is the key step in enabling implicit parallelisability.) - Procedure Typing for Scala

Defining procedure categories

To make arbitrary circuits, we need just one additional operation

besides composition:

def affix[A, B, C, D](f: A => B, g: C => D): (A, C) => (B, D) - Procedure Typing for Scala

Defining procedure categories

In case of pure functions, affix is trivial:

– the execution of f and g is independent.

In case of procedures affix is not-so-trivial:

– have to pass the effects of f to the execution context of g ;

– execution order can be significant. - Procedure Typing for Scala

Defining procedure categories

Thus, procedures belong to a stronger structure than just a

category, namely a structure embracing the affix operation.

Such a structure is called circuitry. - Procedure Typing for Scala

Defining procedure categories

A circuitry is a closed monoidal category with respect to the affix

operation, where affix splits as follows:

trait Circuitry[F[_,_]] extends PairCategory[F] {

def passr[A, B, C](f: A => B): (A, C) => (B, C)

def passl[B, C, D](g: C => D): (B, C) => (B, D)

override def affix[A, B, C, D](f: A => B, g: C => D) = {

compose(passl(g), passr(f))

}

}

+

= - Don’t panic!

In most cases the default Pair and Unit work perfectly well.

⇒ No need to understand any of this, just use with Cartesian .

Procedure Typing for Scala

Defining procedure categories

For the mathematicians among us:

trait PairCategory[F[_,_]] extends Category[F] {

type Pair[A, B]

def assoc[X, Y, Z]: ((X, Y), Z) => (X, (Y, Z))

def unassoc[X, Y, Z]: (X, (Y, Z)) => ((X, Y), Z)

type Unit

def cancelr[X]: (X, Unit) => X

def cancell[X]: (Unit, X) => X

def uncancelr[X]: X => (X, Unit)

def uncancell[X]: X => (Unit, X)

def curry[A, B, C](f: (A, B) => C): A => B => C

def uncurry[A, B, C](f: A => B => C): (A, B) => C

def affix[A, B, C, D](f: A => B, g: C => D): (A, B) => (C, D)

} - In most cases the default Pair and Unit work perfectly well.

⇒ No need to understand any of this, just use with Cartesian .

Procedure Typing for Scala

Defining procedure categories

For the mathematicians among us:

trait PairCategory[F[_,_]] extends Category[F] {

type Pair[A, B]

def assoc[X, Y, Z]: ((X, Y), Z) => (X, (Y, Z))

def unassoc[X, Y, Z]: (X, (Y, Z)) => ((X, Y), Z)

type Unit

def cancelr[X]: (X, Unit) => X

def cancell[X]: (Unit, X) => X

def uncancelr[X]: X => (X, Unit)

def uncancell[X]: X => (Unit, X)

def curry[A, B, C](f: (A, B) => C): A => B => C

def uncurry[A, B, C](f: A => B => C): (A, B) => C

def affix[A, B, C, D](f: A => B, g: C => D): (A, B) => (C, D)

}

Don’t panic! - Procedure Typing for Scala

Defining procedure categories

For the mathematicians among us:

trait PairCategory[F[_,_]] extends Category[F] {

type Pair[A, B]

def assoc[X, Y, Z]: ((X, Y), Z) => (X, (Y, Z))

def unassoc[X, Y, Z]: (X, (Y, Z)) => ((X, Y), Z)

type Unit

def cancelr[X]: (X, Unit) => X

def cancell[X]: (Unit, X) => X

def uncancelr[X]: X => (X, Unit)

def uncancell[X]: X => (Unit, X)

def curry[A, B, C](f: (A, B) => C): A => B => C

def uncurry[A, B, C](f: A => B => C): (A, B) => C

def affix[A, B, C, D](f: A => B, g: C => D): (A, B) => (C, D)

}

Don’t panic!

In most cases the default Pair and Unit work perfectly well.

⇒ No need to understand any of this, just use with Cartesian . - Procedure Typing for Scala

Defining procedure categories

Elements of circuitries are called generalised arrows.

Besides procedures, circuitries provide a common formalism for:

– reversible quantum computations;

– electrical and logical circuits;

– linear and affine logic;

– actor model and other process calculi.

Circuitries provide the most general formalism for computations, see

“Multi-Level Languages are Generalized Arrows”, A. Megacz. - Procedure Typing for Scala

Defining procedure categories

We are talking mostly about procedure typing, so we are going to

consider some special cases:

Arrow circuitries3: circuitries generalising =>[Pure] .

Executable categories: categories generalising to =>[Proc] .

Procedure categories: executable cartesian4 procedure circuitries.

3AKA plain old “arrows” in Haskell and scalaz.

4i.e. having cartesian product types. - Procedure Typing for Scala

Defining procedure categories

trait ArrowCircuitry[F[_,_]] extends Circuitry[F] {

def reify[A, B](f: A =>[Pure] B): A => B

... // With reify we get id and passl for free

}

trait Executable extends Category[_] {

def eval[A, B](f: A => B): A =>[Proc] B

//

eval defines the execution strategy

}

trait ProcCategory[F[_,_]] extends ArrowCircuitry[F] with

Executable with Cartesian {

... // Some additional goodies

} - Wasn’t that easy?

Procedure Typing for Scala

Defining procedure categories

It’s time to give a full definition of =>[Logged] :

type Logged[A, B] = (A =>[Pure] (B, String))

object LoggedCircuitryImpl extends ProcCategory[Logged] {

def reify[A, B](f: A =>[Pure] B) = {x: A => (f(x), "")}

def compose[A, B, C](f: B => C, g: A => B) = {x: A =>

val (result1, logOutput1) = g(x)

val (result2, logOutput2) = f(result1)

(result2, logOutput1 + logOutput2)

}

def passr[A, B, C](f: A => B): = {x : (A, C) =>

val (result, log) = f(x._1)

((result, x._2), log)

}

def eval[A, B](p: A => B) = {x: A =>

val (result, log) = p(x)

println(log); result

}

} - Procedure Typing for Scala

Defining procedure categories

It’s time to give a full definition of =>[Logged] :

type Logged[A, B] = (A =>[Pure] (B, String))

object LoggedCircuitryImpl extends ProcCategory[Logged] {

def reify[A, B](f: A =>[Pure] B) = {x: A => (f(x), "")}

def compose[A, B, C](f: B => C, g: A => B) = {x: A =>

val (result1, logOutput1) = g(x)

val (result2, logOutput2) = f(result1)

(result2, logOutput1 + logOutput2)

}

def passr[A, B, C](f: A => B): = {x : (A, C) =>

val (result, log) = f(x._1)

((result, x._2), log)

}

def eval[A, B](p: A => B) = {x: A =>

val (result, log) = p(x)

println(log); result

}

}

Wasn’t that easy? - Procedure Typing for Scala

Defining procedure categories

Additionally we need a companion object for Logged[_,_] type.

That’s where circuitry-specific primitives should be defined.

object Logged {

val log: Logged[Unit, Unit] = {s: String => ((),s)}

} - Procedure Typing for Scala

Defining procedure categories

Other circuitry-specific primitives include:

– throw and catch for =>[Throws[E]]

– shift and reset for =>[Cont]

– match/case and if/else for =>[WithChoice]

– while and recursion for =>[WithLoops]

– etc.

Often they have to be implemented with Scala macros (available in

a next major Scala release near you). - Procedure Typing for Scala

Language purification by procedure typing

Note that impure code is localised to the eval method.

Thus, thorough usage of procedure typing localizes

impurities to well-controlled places in libraries.

Except for these, Scala becomes a clean multilevel language,

with effective type systems inside blocks being type-and-effect

systems internal to corresponding circuitries. - Informally, the work of A. Megacz provides an extension of it:

For arrow circuitries:

Internal logics = contextual logics

Internal languages = type-and-effect extended λ-calculi

Procedure Typing for Scala

Language purification by procedure typing

Curry-Howard-Lambek correspondence

relates type theories, logics and categories:

For cartesian closed categories:

Internal logic = constructive proposition logic

Internal language = simply-typed λ-calculus

For locally cartesian closed categories:

Internal logic = constructive predicate logic

Internal language = dependently-typed λ-calculus

... - Procedure Typing for Scala

Language purification by procedure typing

Curry-Howard-Lambek correspondence

relates type theories, logics and categories:

For cartesian closed categories:

Internal logic = constructive proposition logic

Internal language = simply-typed λ-calculus

For locally cartesian closed categories:

Internal logic = constructive predicate logic

Internal language = dependently-typed λ-calculus

...

Informally, the work of A. Megacz provides an extension of it:

For arrow circuitries:

Internal logics = contextual logics

Internal languages = type-and-effect extended λ-calculi - – Implement rules for lightweight effect polymorphism using a

system of implicits à la Rytz-Odersky-Haller (2012)

– Retrofit Akka with circuitries internalizing an appropriate actor

calculus + ownership/borrowing system (Haller, 2010).

Procedure Typing for Scala

Language purification by procedure typing

Scala purification/modularization programme

– Design a lattice of procedure categories between Pure and

Proc . In particular, reimplement flow control primitives as

macro5 methods in companion objects of respective categories.

5One reason for employing macros is to guarantee that scaffoldings will be

completely removed in compile time with no overhead on the bytecode level. - – Retrofit Akka with circuitries internalizing an appropriate actor

calculus + ownership/borrowing system (Haller, 2010).

Procedure Typing for Scala

Language purification by procedure typing

Scala purification/modularization programme

– Design a lattice of procedure categories between Pure and

Proc . In particular, reimplement flow control primitives as

macro5 methods in companion objects of respective categories.

– Implement rules for lightweight effect polymorphism using a

system of implicits à la Rytz-Odersky-Haller (2012)

5One reason for employing macros is to guarantee that scaffoldings will be

completely removed in compile time with no overhead on the bytecode level. - Procedure Typing for Scala

Language purification by procedure typing

Scala purification/modularization programme

– Design a lattice of procedure categories between Pure and

Proc . In particular, reimplement flow control primitives as

macro5 methods in companion objects of respective categories.

– Implement rules for lightweight effect polymorphism using a

system of implicits à la Rytz-Odersky-Haller (2012)

– Retrofit Akka with circuitries internalizing an appropriate actor

calculus + ownership/borrowing system (Haller, 2010).

5One reason for employing macros is to guarantee that scaffoldings will be

completely removed in compile time with no overhead on the bytecode level. - Procedure Typing for Scala

Comparing with other notions of computation

How do circuitries compare to

other notions of computation? - effects are specifiers as annotations for

“functions”; type system is extended with rules for “effects”.

Circuitry formalism is not an alternative, but an enclosure for

them.

Procedure Typing for Scala

Comparing with other notions of computation

Type-and-effect systems

Type-and-effect systems are the most well studied approach to

procedure typing: - Circuitry formalism is not an alternative, but an enclosure for

them.

Procedure Typing for Scala

Comparing with other notions of computation

Type-and-effect systems

Type-and-effect systems are the most well studied approach to

procedure typing: effects are specifiers as annotations for

“functions”; type system is extended with rules for “effects”. - Procedure Typing for Scala

Comparing with other notions of computation

Type-and-effect systems

Type-and-effect systems are the most well studied approach to

procedure typing: effects are specifiers as annotations for

“functions”; type system is extended with rules for “effects”.

Circuitry formalism is not an alternative, but an enclosure for

them. - Embedding effects into the type system by means of

the circuitry formalism resolves the issues above.

Procedure Typing for Scala

Comparing with other notions of computation

Type-and-effect systems

Direct implementation of type-and-effect systems

– is rigid (hardly extensible) and

– requires changes to the typechecker. - Procedure Typing for Scala

Comparing with other notions of computation

Type-and-effect systems

Direct implementation of type-and-effect systems

– is rigid (hardly extensible) and

– requires changes to the typechecker.

Embedding effects into the type system by means of

the circuitry formalism resolves the issues above. - Procedure Typing for Scala

Comparing with other notions of computation

Monads

Arrows generalise monads

In Haskell, monads are used as basis for imperative programming,

but they are often not general enough (see Hughes, 2000).

Monads are similar to cartesian arrow circuitries. The only

difference is that they are not equipped with non-linear composition. - Circuitries were invented to cure this.

Procedure Typing for Scala

Comparing with other notions of computation

Monads

Monads

– do not compose well,

– prescribe rigid execution order,

– are not general enough for concurrent computations. - Procedure Typing for Scala

Comparing with other notions of computation

Monads

Monads

– do not compose well,

– prescribe rigid execution order,

– are not general enough for concurrent computations.

Circuitries were invented to cure this. - Procedure Typing for Scala

Comparing with other notions of computation

Applicatives

Applicatives are a special case of arrows...

If procedures of type =>[A] never depend on effects of other

procedures of the same type, A is called essentially commutative.

Example

=>[Reads(config), Writes(log), Throws[NonBlockingException]]

Essentially commutative arrows arise from applicative functors.

They are flexible and easy to handle: you don’t have to propagate

effects, just accumulate them behind the scenes. - Procedure Typing for Scala

Comparing with other notions of computation

Applicatives

...but not a closed special case!

Composing applicatives may produce non-commutative circuitries

like =>[Reads(file), Writes(file)] .

Procedures of this type are no longer effect-independent: effect of

writes have to be passed to subsequent reads.

Besides these, there are also inherently non-commutative arrows

such as those arising from monads6, comonads and Hoare triples7.

6e.g. Tx = transaction monad, Cont = continuation passing monad.

7pre- and postconditioned arrows. - Any imperative code can be reduced to compose and affix.

The reduction process is known as variable elimination, it can be

understood as translation to a concatenative language like Forth.

(The concatenative languages’ juxtaposition is an overloaded operator reducing

to either compose or affix depending on how operands’ types match.)

But! Writing code this way can be quite cumbersome.

Procedure Typing for Scala

Comparing with other notions of computation

Traditional imperative approach

Can we do everything available in imperative

languages with arrows and circuitries? - The reduction process is known as variable elimination, it can be

understood as translation to a concatenative language like Forth.

(The concatenative languages’ juxtaposition is an overloaded operator reducing

to either compose or affix depending on how operands’ types match.)

But! Writing code this way can be quite cumbersome.

Procedure Typing for Scala

Comparing with other notions of computation

Traditional imperative approach

Can we do everything available in imperative

languages with arrows and circuitries?

Any imperative code can be reduced to compose and affix. - (The concatenative languages’ juxtaposition is an overloaded operator reducing

to either compose or affix depending on how operands’ types match.)

But! Writing code this way can be quite cumbersome.

Procedure Typing for Scala

Comparing with other notions of computation

Traditional imperative approach

Can we do everything available in imperative

languages with arrows and circuitries?

Any imperative code can be reduced to compose and affix.

The reduction process is known as variable elimination, it can be

understood as translation to a concatenative language like Forth. - But! Writing code this way can be quite cumbersome.

Procedure Typing for Scala

Comparing with other notions of computation

Traditional imperative approach

Can we do everything available in imperative

languages with arrows and circuitries?

Any imperative code can be reduced to compose and affix.

The reduction process is known as variable elimination, it can be

understood as translation to a concatenative language like Forth.

(The concatenative languages’ juxtaposition is an overloaded operator reducing

to either compose or affix depending on how operands’ types match.) - Procedure Typing for Scala

Comparing with other notions of computation

Traditional imperative approach

Can we do everything available in imperative

languages with arrows and circuitries?

Any imperative code can be reduced to compose and affix.

The reduction process is known as variable elimination, it can be

understood as translation to a concatenative language like Forth.

(The concatenative languages’ juxtaposition is an overloaded operator reducing

to either compose or affix depending on how operands’ types match.)

But! Writing code this way can be quite cumbersome. - Circuit notation for Scala is the topic of the part II...

Procedure Typing for Scala

Do-notation

Defining procedure categories is easy

enough. How about using them?

We develop a quasi-imperative notation8 and implement it using

macros.

Our notation shares syntax with usual Scala imperative code...

...but has different semantics: it compiles to a circuit of

appropriate type instead of being executed immediately.

8Akin to Haskell’s do-notation, but much easier to use. - Procedure Typing for Scala

Do-notation

Defining procedure categories is easy

enough. How about using them?

We develop a quasi-imperative notation8 and implement it using

macros.

Our notation shares syntax with usual Scala imperative code...

...but has different semantics: it compiles to a circuit of

appropriate type instead of being executed immediately.

Circuit notation for Scala is the topic of the part II...

8Akin to Haskell’s do-notation, but much easier to use. - Procedure Typing for Scala

Do-notation

Do-notation example

...but here’s a small example to keep your interest

Even pure functions have a side effect: they consume time.

=>[Future] is an example of a retrofitting procedure category9.

=>[Future] {

val a = alpha(x)

val b = beta(x)

after (a | b) {

Log.info("First one is completed")

}

after (a & b) {

Log.info("Both completed")

}

gamma(a, b)

}

9its reify is a macro, so any procedures can be retrofitted to be =>[Future]. - Procedure Typing for Scala

Do-notation

Literature:

– The marriage of effects and monads, P. Wadler, P. Thiemann

– Generalising monads to arrows, J. Hughes

– The Arrow Calculus, S. Lindley, P. Wadler, and J. Yallop

– Categorical semantics for arrows, B. Jacobs et al.

– What is a Categorical Model of Arrows?, R. Atkey

– Parameterized Notions of Computation, R. Atkey

– Multi-Level Languages are Generalized Arrows, A. Megacz - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

How do you use an arrow (say f: Logged[Int, String] ) in

present Scala code?

println(f(5)) seems to be the obvious way, but that’s

impossible, application is not defined for f.

To facilitate such natural notation, we need implicit unboxing. - A prototypical example where reify is a macro is Expr[T]. Example

with no macros involved is Future[T] (with await as eval).

Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Preliminaries

A wrapping is a type F[_] equipped with eval[T](v: F[T]): T

and reify[T](expr: => T): F[T] (reify often being a macro) so

that

eval(reify(x)) ≡ x and

reify(eval(x)) ≡ x for all x of the correct type. - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Preliminaries

A wrapping is a type F[_] equipped with eval[T](v: F[T]): T

and reify[T](expr: => T): F[T] (reify often being a macro) so

that

eval(reify(x)) ≡ x and

reify(eval(x)) ≡ x for all x of the correct type.

A prototypical example where reify is a macro is Expr[T]. Example

with no macros involved is Future[T] (with await as eval). - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Preliminaries

Implicit unboxing is this: whenever a value of the wrapping type

F[T] is found where a value of type T is accepted, its eval is called

implicitly.

In homoiconic languages (including Scala), all expressions can be

considered initially having the type Expr[T] and being unboxed into

T by an implicit unboxing rule Expr[T] => T . - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Syntax proposal

Let’s introduce an instruction implicit[F] enabling implicit

unboxing for F in its scope.

Implicit contexts can be implemented using macros:

– macro augments the relevant scope by F.reify as an implicit

conversion from F[T] to T;

– F.eval is applied to every occurrence of a symbol having or

returning type F[T] which is defined outside of its scope. - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Code that uses futures and promises can be made much more

readable by implicit unboxing.

An example: dataflows in Akka 2.0. Presently they look like this:

flow {

z << (x() + y())

if (v() > u) println("z = " + z())

} - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Now this can be recast without any unintuitive empty parentheses:

flow {

z << x + y

if (v > u) println("z = " + z)

} - Procedure Typing for Scala

Syntax for Circuitires

Implicit Unboxing

Back to our Logged example:

implicit[Logged]

def example(f: Int =>[Logged] String, n: Int): List[String] {

f(n).split(", ")

}

Which translates to:

def example(f: Int =>[Logged] String, n: Int): List[String] {

LoggedCircuitryImpl.eval(f)(n).split(", ")

} - Procedure Typing for Scala

Syntax for Circuitires

Purifying Scala

Now, which procedure category should example() belong to?

As it evaluates =>[Logged], it should be =>[Logged] itself. This

allows its reinterpretation without any usage of eval:

def example(f: Int =>[Logged] String, n: Int): List[String] = {

import LoggedCircuitryImpl._

reify{n} andThen f andThen reify{_.split(", ")}

}

This is now a pure code generating a new circuit of the type

=>[Logged] based on the existing one (f) and some pure functions. - Procedure Typing for Scala

Syntax for Circuitires

Purifying Scala

Purity Declaration

Let’s introduce @pure annotation which explicitly forbids calling

any functions with side effects and assignments of foreign variables.

This renders the code pure.

Procedure with side effects have to be composed by circuit

composition operations which are pure. The execution of

procedures, which is impure, always lies outside of the scope.

All code examples below are to be read as @pure . - Procedure Typing for Scala

Syntax for Circuitires

Purifying Scala

Inside of @pure implicit unboxing for arrows becomes

implicit circuit notation, which is operationally

indistinguishable, but semantically different. - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Circuit notation, general idea:

– write circuitry type like =>[X] in front of a braced code block;

– the code block will be reinterpreted as a circuitry of the given

type (via macros). - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Example:

=>[Logged] {

f(x) + g(x)

}

Result:

(reify{x} andThen reify(dup) andThen (f affix g) andThen reify{_ + _}) - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

In presence of implicit[X] every free braced block {...}

which uses external symbols of the type =>[X] should be

treated as =>[X] {...} , an implicit form of circuit syntax. - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

The desugaring rules producing operationally indistinguishable

circuits from imperative-style code blocks are quite complicated,

but certainly doable.

To make the other direction possible, we need an additional

operator: after . - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Consider two arrows f: Unit => Unit and g: Unit => Unit .

They can be composed in two ways: f affix g (out-of-order) and

f andThen g (in-order).

affix in circuit notation will obviously look like f; g , though for

andThen we need some new syntax:

=>[Future] {

val n = f

after(n) g

} - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Without after , =>[Future] and other similar circuitries respect

only dataflow ordering, but ignore the order of independent effects

(e.g. writing into a log).

By combining usual imperative notation and after ,

any possible circuit configurations can be achieved. - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Now the example stated above is fully understandable:

=>[Future] {

val a = alpha(x)

val b = beta(x)

after (a | b) {

Log.info("First one is completed")

}

after (a & b) {

Log.info("Both completed")

}

gamma(a, b)

}

( after trivially supports any combinations of ands and ors.) - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Blocks as Objects

For the sake of composability, blocks should be treated as

anonymous classes extending their arrow type:

=>[Future] {

val result = {

@expose val partialResult = compute1(x)

compute2(partialResult)

}

after (result.partialResult) {

Log.info("Partial result ready")

}

}

The result in the after context is not just =>[Future] Int , but

its anonymous descendant with a public member partialResult . - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

Of course, it should also work for named blocks:

def lengthyComputation(x: Double): Double = {

var _progress = 0.0

// goes from 0.0 to 1.0

@expose def progress = _progress // public getter

... // _progress is updated when necessary

}

val f = future someLengthyCalculation(x)

while (!f.isDone) {

Log.info("Progress: " + f.progress)

wait(500 ms)

}

(This is a perfect example of what can easily be done with macros.) - Procedure Typing for Scala

Syntax for Circuitires

Circuit notation

The exact desugaring rules are quite complex (but perfectly real).

We hope these examples gave you some insight how everything

might work.

Thank you!