Author: Richard A. O'Keefe <ok(at)cs(dot)otago(dot)ac(dot)nz>
Status: Draft
Type: Standards Track
Erlang-Version: R12B-4
Created: 14-Aug-2008
Post-History:

EEP 19: Comprehension multigenerators

Abstract

Add Clean-inspired multi-sequence generators to comprehensions, making code more intention-revealing and reducing the need to zip.

This is related to EEP 12, but is independent of it.

Specification

Currently, Erlang has

Pattern <- Expr

to enumerate over the elements of a single list and

Pattern <= Expr

to enumerate over a binary. EEP 12 adds

Pattern [<-] List
Pattern {<-} Tuple
Pattern <<<->> Binary

This proposal changes that to

generator: term_generator | binary_generator;
binary_generator: pattern '<=' expression;
term_generator: term_generator '&&' term_generator
              | pattern '<-' expression;

if we otherwise stick with current Erlang, or

generator: term_generator | binary_generator;
binary_generator: pattern '<=' expression
                | pattern '<<' '<-' '>>' expression;
term_generator: term_generator '&&' term_generator
              | pattern '<-' expression
              | pattern '[' '<-' ']' expression
              | pattern '{' '<-' '}' expression;

if we go with EEP 12.

Roughly speaking, ignoring errors and side effects, the effect of P1 <- E1 && ... Pn <- En is the effect of {P1,...,Pn} <- zip(E1, ..., En) where

zip([X1|Xs1], ..., [Xn|Xsn]) ->
    [{X1,...,Xn} | zip(Xs1, ..., Xsn)];
zip([], ..., []) ->
    [].

However, it is expected that there will NOT be any extra list or tuples created by the implementation; this specifies the effect but NOT how it is to be implemented.

The effect of a term generator using the new notations of EEP 12 is that which would be obtained by first replacing

P {<-} E   with   P <- tuple_to_list(E)
P [<-] E   with   P <- E

and then applying the translation above.

In the presence of errors, the behaviour of && is not precisely the same as using zip. We need to specify the actual behaviour more precisely. For brevity, I ignore binary enumeration. Both tuple enumeration and tuple comprehension are currently defined by rewriting to plain list comprehension, so that's all we need to worry about for now.

A list comprehension has the form [E || C1, ..., Cn] where each Ci is

  • a generator Pattern <- List_Expression
  • a binding Pattern = Any_Expression
  • a "guard" Other_Expression that should give true or false.

This acts like

R = [],
<| E || [C1, ..., Cn] |>(R),
reverse(R)

where

<| E || [] |>(R)
=>  R = [E | R]             % reassign R

<| E || [Pi <- Ei|Cs] |>(R)
=>  Ti = Ei
    Label: case Ti
             of [Pi|X] -> Ti = X % reassign Ti
                          <| E || Cs |>(R)
                          goto Label
              ; [_ |X] -> Ti = X % reassign Ti
                          goto Label
              ; []     -> ok                              
           end

<| E || [Pi = Ei|Cs] |>(R)
=>  case Ei
      of Pi -> <| E || Cs |>(R)
       ; _  -> ok
    end

<| E || [Ei|Cs] |>(R)
=>  case Ei
      of true  -> <| E || Cs |>(R)
       ; false -> ok
    end

In these translations, pattern matching syntax is used, with the intent that the variables which are unbound according to the normal rules of Erlang, and thus get bound by the Pi <- or Pi = matching, are treated as if unbound in the code to be generated, ignoring whatever values they might previous have had. That also applies when R or Ti appears on the left of a pattern match; the fact that the variable really was bound is ignored and a simple assignment is done.

This does involve (re-)assignment to local variables in the code to be generated, but it does NOT involve user-visible assignment and it does NOT involve mutable data structures. It is no more problematic for the language or the runtime system than reusing a dead register is.

Handling multi-list enumeration is a simple, albeit schematic, change to the rule for enumeration.

<| E || [Pi1 <- Ei1 && Pi2 <- Ei2 && ... && Pik <- Eik|Cs] |>(R)
=>  Ti1 = Ei1
    ...
    Tik = Eik
    Label: case {Ti1,...,Tik}
             of {[Pi1|X1], ..., [Pik,Xk]} ->
                Ti1 = X1    % reassign
                ...
                Tik = Xk    % reassign
                <| E || Cs |>(R)
                goto label
              ; {[_|X1], ..., [_|Xk]} ->
                Ti1 = X1    % reassign
                ...
                Tik = Xk    % reassign
              ; {[], ..., []} ->
                ok
           end

Note that the use of tuple syntax in the case expression and the case clauses does not imply the literal creation of a tuple in the generated code, only that k values are to be matched against k patterns in each case clause.

Motivation

"How do I iterate over several lists at once?" is a moderately common question from Erlang and Haskell beginners. The stock answer, "use zip", is almost tolerable for Haskell, where the the zipping family goes up to 7 lists and the compiler works hard to eliminate the intermediate data structures by using deforestation. For Erlang, where even zip4 is missing, and where the apparent cost of creating the unwanted list and tuples is all too real, the fact that the use of zips makes the code harder to read means that there is no good to outweigh the bad.

With the new notation,

zip4(As, Bs, Cs, Ds) ->
    [{A,B,C,D} || A <- As && B <- Bs && C <- Cs && D <- Ds].

zipwith4(F, As, Bs, Cs, Ds) ->
    [F(A,B,C,D) || A <- As && B <- Bs && C <- Cs && D <- Ds].

dot(Xs, Ys) ->
    sum([X*Y || X <- Xs && Y <- Ys]).

ifelse(Tests, Xs, Ys) -> % Simulate R's ifelse(,,)
    [  case T of true -> X ; false -> Y end
    || T <- Tests && X <- Xs && Y <- Ys
    ].

This code from module dialyzer_dep

merge_outs([#output{type=list, content=L1}|Left],
           #output{type=list, content=L2}) ->
  NewList = [merge_outs([X, Y]) || {X, Y} <- lists:zip(L1, L2)],
  merge_outs(Left, output(NewList));

would become

merge_outs([#output{type=list, content=L1}|Left],
            #output{type=list, content=L2]) ->
    merge_outs(Left, output(
        [merge_outs([X,Y]) || X <- L1 && Y <- L2]));

This code from forward_args/3 in module dialyzer_dataflow

NewArgTypes = [t_sup(X, Y) ||
               {X, Y} <- lists:zip(ArgTypes, OldArgTypes)],

would become

NewArgTypes = [t_sup(X, Y) || X <- ArgTypes && Y <- OldArgTypes],

Rationale

This is a case where no invention is required, really. Clean has

Qualifier = Generators {|Guard}
Generators = {Generator}-list
           | Generator {& Generator}
Generator = Selector <- ListExpr // lazy list
          | Selector <|- ListExpr // overloaded list
          | Selector <-: ArrayExpr //  array

All I have to do is bend this a little to fit it into Erlang syntax. Since we use "||" for list comprehensions, "&&" was the obvious spelling for generators that step together.

I do not yet understand in detail what the Erlang compiler does, but it seems to involve generating an auxiliary function. Let's take

[f(X) || X <- Xs, X > 0]

as an example. This seems to be compiled as

foo(Xs)

where

foo([X|Xs]) when X > 0 -> [f(X) | foo(Xs)];
foo([_|Xs]) -> foo(Xs);
foo([]) -> [].

With a multi-sequence generator, the translation is similar.

[g(X, Y) || X <- Xs && Y <- Ys, X > Y]

can be compiled as

bar(Xs, Ys)

where

bar([X|Xs], [Y|Ys]) when X > Y ->
    [g(X, Y) | bar(Xs, Ys)];
bar([_|Xs], [_|Ys]) -> bar(Xs, Ys);
bar([], []) -> [].

The specification above gives the kind of translation I would like to see; I do have an implementation in mind (based on Pop-2) that doesn't need the reversal but don't know how it would fit in BEAM.

One obvious question is whether we need this at all. Why not just get people to write calls to lists:zip and get the compiler to optimise them? One answer is that this notation is much clearer; the programmer's intent is to advance along two or more lists at the same time, not to create a list of pairs. When you want to create a list of pairs, lists:zip/2 is the perfect way to do it. A more important answer is that the proposed notation is NOT a simple optimisation of equivalent code using lists:zip/2.

[E || {P,Q} <- lists:zip(A, B)]    % "zip version"

fails at once if A and B are not proper lists of the same length.

[E || P <- A && Q <- B]            % "Clean version"

eventually fails if A and B are not proper lists of the same length, but may have evaluated E (which may have had side effects) many times before that. So an Erlang compiler would not be allowed to replace the "zip version" by the "Clean version" unless it could prove both that A and B were lists (which may be within the abilities of the Dialyzer) and that they were exactly the same length (which as far as I know isn't).

However, a multi-sequence generator and a single-sequence one using calls to lists:zip/2 are clearly similar, so they should eventually react to lists of different length the same way. In Haskell, zipping two lists of different length acts as if the longer were truncated to the length of the shorter. Since Haskell has lazy evaluation, lists may be infinite, so you can't afford to wait until the end to start a comprehension. Since Erlang is strict, and since mistakes are common, lists:zip/2 in Erlang makes sense as it is.

Backwards Compatibility

The "operator" '&&' is not legal syntax anywhere in Erlang at the moment, so no existing code can be affected.

Reference Implementation

None yet, but I'd like to do it when I can figure out how.

Copyright

This document has been placed in the public domain.

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