enumerators 0.4.0

A small DSL for writing enumerators of Dart datatypes, inspired by http://hackage.haskell.org/package/testing-feat

Random Access Enumerations

A library which allows for randomized or exhaustive testing of Dart functions by providing random access enumerations of Dart datatypes. It is heavily inspired by Jonas Duregård's testing-feat.

Put simply, it allows to test things like reverse(reverse(list)) == list by picking, say, 100 random lists of booleans for list (quickcheck style), or by enumerating all the lists of booleans up to a certain depth (smallcheck style). It is however up to the user to provide the glorified while loops that constitute the "quickcheck" and "smallcheck" functions of these libraries. The propcheck library just does that.

Simple Usage

The combinators.dart library provides a predefined set of combinators for the most common use cases:

import 'package:enumerators/combinators.dart' as 'c';

main() {
  // c.strings is an enumeration: a infinite list of finite parts
  // part 0 contains the strings of size 0, part 1 the strings of size 1,
  // etc.
  final strings20 = c.strings.parts[20];

  // we have fast access to the cardinal of a part
  final n = (strings20.length * 0.123).toInt();

  // as well as fast access to the nth element of a part
  print("the ${n}th string of size 20: ${strings20[n]}");

  // we quickly access the nth element of an enumeration seen as the
  // concatenation of its parts
  print("the 71468th string: ${c.strings[71468]}");

  // we can also print a part as a whole, but it might be huge
  print("the ints of size 200: ${c.ints.parts[200]}");

  // setsOf is a combinator: it takes an Enumeration and returns an
  // Enumeration
  print("a set of strings: ${c.setsOf(c.strings)[123456789]}");

  // we can arbitrarily nest combinators
  print("a map from nats to lists of ints: "
        "${c.mapsOf(c.nats, c.listsOf(c.ints))[123456789]}");
}

Output:

the 2451162314110757454221410304th string of size 20: dfdwbglqwbgmgvzcwrqm
the 71468th string: dart
the ints of size 200: {200, -200}
a set of strings: {e, , n, m, v, ab, u, ac, f, t}
a map from nats to lists of ints: {1: [], 4: [0, 0, 0, -1, 1, 0], 5: [], 6: [-1]}

Advanced Usage

The enumerators.dart library provides lower-level primitives for building enumerations of user-defined datatypes.

import 'package:enumerators/enumerators.dart';

// we define linked lists as "Nil" and "Cons", as well as two curryfied
// shorthands "nil" and "cons" for their constructors

class LList {}
class Nil extends LList {
  toString() => "nil";
}
class Cons extends LList {
  final x, xs;
  Cons(this.x, this.xs);
  toString() => "$x:$xs";
}

nil() => new Nil();
cons(x) => (xs) => new Cons(x,xs);

// here starts the real demo

main() {
  // we define an enumerator of booleans
  final trueEnum = singleton(true);
  final falseEnum = singleton(false);
  final boolEnum = (trueEnum + falseEnum).pay();

  // we define an enumerator of lists of booleans
  final nilEnum = singleton(nil());
  consEnum(e) => singleton(cons).apply(boolEnum).apply(e);
  final listEnum = fix((e) => (nilEnum + consEnum(e)).pay());

  // listEnum is made of finite sets of lists of booleans (parts), the
  // first part contains exactly the lists made of 1 constructor
  // (i.e. nil), the second part the lists made of 2 constructors (there
  // aren't any), etc.
  var counter = 0;
  for (final f in listEnum.parts.take(10)) {
    print("all the lists made of $counter constructors: $f");
    counter++;
  }

  // we can access big parts pretty fast
  final trues = listEnum.parts[81][0];
  print("the first list made of 40 elements (81 constructors): $trues");

  // an enumeration can be iterated over as a whole,
  // as a concatenation of its parts
  counter = 0;
  for (final l in listEnum.take(10)) {
    print("list of booleans #$counter: $l");
    counter++;
  }

  // we can access the nth list of the enumeration very fast, even for
  // big ns
  print("member 10^10 of the enumeration: ${listEnum[Math.pow(10,10)]}");
}

Output:

all the lists made of 0 constructors: {}
all the lists made of 1 constructors: {nil}
all the lists made of 2 constructors: {}
all the lists made of 3 constructors: {true:nil, false:nil}
all the lists made of 4 constructors: {}
all the lists made of 5 constructors: {true:true:nil, true:false:nil, false:true:nil, false:false:nil}
all the lists made of 6 constructors: {}
all the lists made of 7 constructors: {true:true:true:nil, true:true:false:nil, true:false:true:nil, true:false:false:nil, false:true:true:nil, false:true:false:nil, false:false:true:nil, false:false:false:nil}
all the lists made of 8 constructors: {}
all the lists made of 9 constructors: {true:true:true:true:nil, true:true:true:false:nil, true:true:false:true:nil, true:true:false:false:nil, true:false:true:true:nil, true:false:true:false:nil, true:false:false:true:nil, true:false:false:false:nil, false:true:true:true:nil, false:true:true:false:nil, false:true:false:true:nil, false:true:false:false:nil, false:false:true:true:nil, false:false:true:false:nil, false:false:false:true:nil, false:false:false:false:nil}
the first list made of 40 elements (81 constructors): true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:true:nil
list of booleans #0: nil
list of booleans #1: true:nil
list of booleans #2: false:nil
list of booleans #3: true:true:nil
list of booleans #4: true:false:nil
list of booleans #5: false:true:nil
list of booleans #6: false:false:nil
list of booleans #7: true:true:true:nil
list of booleans #8: true:true:false:nil
list of booleans #9: true:false:true:nil
member 10^10 of the enumeration: true:true:false:true:false:true:false:true:true:true:true:true:true:false:true:false:false:false:false:false:true:true:false:true:true:true:true:true:true:true:true:true:false:nil

The file example/advanced.dart contains the demo above as well as an enumerator of trees of naturals.