A Ruby gem for non-linear pattern-matching with backtracking
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README.md

The Gem for Egison Pattern Matching

This Gem provides a way to access non-linear pattern-matching against unfree data types from Ruby. We can directly express pattern-matching against lists, multisets, and sets using this gem.

Installation

$ gem install egison

or

$ git clone https://github.com/egison/egison-ruby.git
$ cd egison-ruby
$ make

or

$ gem install bundler (if you need)
$ echo "gem 'egison', :git => 'https://github.com/egison/egison-ruby.git'" > Gemfile
$ bundle install

Basic Usage

The library provides Egison#match_all and Egison#match.

require 'egison'

include Egison

match_all(object) do
  with(pattern) do
    ...
  end
end

match(object) do
  with(pattern) do
    ...
  end
  with(pattern) do
    ...
  end
  ...
end

If a pattern matches, a block passed to with is called and returns its result.

In our pattern-matching system, there are cases that pattern-matching has multiple results. match_all calls the block passed to with for each pattern-matching result and returns all results as an array. match_all takes one single match-clause.

On the other hand, match takes multiple match-clauses. It pattern-matches from the first match-clause. If a pattern matches, it calls the block passed to the matched match-clause and returns a result for the first pattern-matching result.

Patterns

Element Patterns and Subcollection Patterns

An element pattern matches the element of the target array.

A subcollection pattern matches the subcollection of the target array. A subcollection pattern has * ahead.

A literal that contain _ ahead is a pattern-variable. We can refer the result of pattern-matching through them.

match_all([1, 2, 3]) do
  with(List.(*_hs, _x, *_ts)) do
    [hs, x, ts]
  end
end  #=> [[[],1,[2,3]],[[1],2,[3]],[[1,2],3,[]]

Three Matchers: List, Multiset, Set

We can write pattern-matching against lists, multisets, and sets. When we regard an array as a multiset, the order of elements is ignored. When we regard an array as a set, the duplicates and order of elements are ignored.

_ is a wildcard. It matches with any object. Note that __ and ___ are also interpreted as a wildcard. This is because _ and __ are system variables and sometimes have its own meaning.

match_all([1, 2, 3]) do
  with(List.(_a, _b, *_)) do
    [a, b]
  end
end  #=> [[1, 2]]

match_all([1, 2, 3]) do
  with(Multiset.(_a, _b, *_)) do
    [a, b]
  end
end  #=> [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]

match_all([1, 2, 3]) do
  with(Set.(_a, _b, *_)) do
    [a, b]
  end
end  #=> [[1, 1],[1, 2],[1, 3],[2, 1],[2, 2],[2, 3],[3, 1],[3, 2],[3, 3]]

Note that _[] is provided as syntactic sugar for List.().

match_all([1, 2, 3]) do
  with(_[_a, _b, *_]) do
    [a, b]
  end
end  #=> [[1, 2]]

Non-Linear Patterns

Non-linear pattern is the most important feature of our pattern-matching system. Our pattern-matching system allows users multiple occurrences of same variables in a pattern. A Pattern whose form is __("...") is a value pattern. In the place of ..., we can write any ruby expression we like. It matches the target when the target is equal with the value that ... evaluated to.

match_all([5, 3, 4, 1, 2]) do
  with(Multiset.(_a, __("a + 1"), __("a + 2"), *_)) do
    a
  end
end  #=> [1,2,3]

When, the expression in the place of ... is a single variable, we can omit (" and ") as follow.

match_all([1, 2, 3, 2, 5]) do
  with(Multiset.(_a, __a, *_)) do
    a
  end
end  #=> [2,2]

Pattern Matching against Stream (Infinite List)

We can do pattern-matching against streams with the match_stream expression.

def nats
  (1..Float::INFINITY)
end

match_stream(nats){ with(Multiset.(_m, _n, *_)) { [m, n] } }.take(10)
#=>[[1, 2], [1, 3], [2, 1], [1, 4], [2, 3], [3, 1], [1, 5], [2, 4], [3, 2], [4, 1]]

match_stream(nats){ with(Set.(_m, _n, *_)) { [m, n] } }.take(10)
#=>[[1, 1], [1, 2], [2, 1], [1, 3], [2, 2], [3, 1], [1, 4], [2, 3], [3, 2], [4, 1]]

Demonstrations

Combinations

We can enumerates all combinations of the elements of a collection with pattern-matching.

require 'egison'

include Egison

p(match_all([1,2,3,4,5]) do with(List.(*_, _x, *_, _y, *_)) { [x, y] } end)
#=> [[1, 2], [1, 3], [1, 4], [1, 5], [2, 3], [2, 4], [2, 5], [3, 4], [3, 5], [4, 5]]

p(match_all([1,2,3,4,5]) do with(List.(*_, _x, *_, _y, *_, _z, *_)) { [x, y, z] } end)
#=> [[1, 2, 3], [1, 2, 4], [1, 2, 5], [1, 3, 4], [1, 3, 5], [1, 4, 5], [2, 3, 4], [2, 3, 5], [2, 4, 5], [3, 4, 5]]

Poker Hands

We can write patterns for all poker-hands in one single pattern. It is as follow. Isn't it exciting?

require 'egison'

include Egison

def poker_hands cs
  match(cs) do
    with(Multiset.(_[_s, _n], _[__s, __("n+1")], _[__s, __("n+2")], _[__s, __("n+3")], _[__s, __("n+4")])) do
      "Straight flush"
    end
    with(Multiset.(_[_, _n], _[_, __n], _[_, __n], _[_, __n], _)) do
      "Four of kind"
    end
    with(Multiset.(_[_, _m], _[_, __m], _[_, __m], _[_, _n], _[_, __n])) do
      "Full house"
    end
    with(Multiset.(_[_s, _], _[__s, _], _[__s, _], _[__s, _], _[__s, _])) do
      "Flush"
    end
    with(Multiset.(_[_, _n], _[_, __("n+1")], _[_, __("n+2")], _[_, __("n+3")], _[_, __("n+4")])) do
      "Straight"
    end
    with(Multiset.(_[_, _n], _[_, __n], _[_, __n], _, _)) do
      "Three of kind"
    end
    with(Multiset.(_[_, _m], _[_, __m], _[_, _n], _[_, __n], _)) do
      "Two pairs"
    end
    with(Multiset.(_[_, _n], _[_, __n], _, _, _)) do
      "One pair"
    end
    with(Multiset.(_, _, _, _, _)) do
      "Nothing"
    end
  end
end

p(poker_hands([["diamond", 1], ["diamond", 3], ["diamond", 5], ["diamond", 4], ["diamond", 2]])) #=> "Straight flush"
p(poker_hands([["diamond", 1], ["club", 2], ["club", 1], ["heart", 1], ["diamond", 2]])) #=> "Full house"
p(poker_hands([["diamond", 4], ["club", 2], ["club", 5], ["heart", 1], ["diamond", 3]])) #=> "Straight"
p(poker_hands([["diamond", 4], ["club", 10], ["club", 5], ["heart", 1], ["diamond", 3]])) #=> "Nothing"

Twin Primes and Prime Triplets

The following code enumerates all twin primes with pattern-matching! I believe it is also a really exciting demonstration.

require 'egison'
require 'prime'

include Egison

twin_primes = match_stream(Prime) {
  with(List.(*_, _p, __("p + 2"), *_)) {
    [p, p + 2]
  }
}

p twin_primes.take(10)
#=>[[3, 5], [5, 7], [11, 13], [17, 19], [29, 31], [41, 43], [59, 61], [71, 73], [101, 103], [107, 109]]

We can also enumerate prime triplets using and-patterns and or-patterns effectively.

prime_triplets = match_stream(Prime) {
  with(List.(*_, _p, And(Or(__("p + 2"), __("p + 4")), _m), __("p + 6"), *_)) {
    [p, m, p + 6]
  }
}

p prime_triplets.take(10)
#=>[[5, 7, 11], [7, 11, 13], [11, 13, 17], [13, 17, 19], [17, 19, 23], [37, 41, 43], [41, 43, 47], [67, 71, 73], [97, 101, 103], [101, 103, 107]]

Algebraic Data Types

Of course, we can also patten match against algebraic data types as ordinary functional programming languages. Here is a simple example.

class User < Struct.new(:name, :gender, :married, :doctor, :professor)
  def greet
    match(self) do
      with(User.(_name,       _,    _,    _, true)) { "Hello, Prof. #{name}!" }
      with(User.(_name,       _,    _, true,    _)) { "Hello, Dr. #{name}!" }
      with(User.(_name, :female, true,    _,    _)) { "Hello, Mrs. #{name}!" }
      with(User.(_name, :female,    _,    _,    _)) { "Hello, Ms. #{name}!" }
      with(User.(_name,   :male,    _,    _,    _)) { "Hello, Mr. #{name}!" }
      with(User.(_name,       _,    _,    _,    _)) { "Hello, #{name}!" }
    end
  end
end

u1 = User.new("Egi", :male, true, false, false)
p(u1.greet)#=>"Hello, Mr. Egi!"

u2 = User.new("Nanaka", :girl, false, false, false)
p(u2.greet)#=>"Hello, Nanaka!"

u3 = User.new("Hirai", :male, true, true, false)
p(u3.greet)#=>"Hello, Dr. Hirai!"

u4 = User.new("Hagiya", :male, true, true, true)
p(u4.greet)#=>"Hello, Prof. Hagiya!"

You can find more demonstrations in the sample directory.

About Egison

If you get to love the above pattern-matching, please try the Egison programming language, too. Egison is the pattern-matching oriented, purely functional programming language. Actually, the original pattern-matching system of Egison is more powerful. For example, we can do following things in the original Egison.

  • We can define new pattern-constructors.
  • We can modularize useful patterns.

There is a new programming world!

Contact

If you get interested in this Gem, please contact Satoshi Egi or tweet to @Egison_Lang.

We will talk about this gem in RubyKaigi 2014!

LICENSE

The license of this library code is BSD. I learned how to implement pattern-matching in Ruby and how to write a gem from the code of the pattern-match gem by Kazuki Tsujimoto. I designed syntax of pattern-matching to go with that gem. This library contains the copy from that gem. The full license text is here.

Sponsors

This project is sponsored by Rakuten, Inc. and Rakuten Institute of Technology.