LogicElixir

A DSL to write logic programs in Elixir

Installation

Add :logic_elixir to the list of dependencies in mix.exs:

def deps do
  [
     {:logic_elixir, git: "[email protected]:MiguelERuiz/logic_elixir.git", tag: "0.1.0"}
  ]
end

After that, run mix deps.get and mix compile

How to use

Declare the use LogicElixir expression inside your module, as below:

defmodule LogicModule do
  use LogicElixir

  defpred p(5)
end

Supported terms

This version supports a reduced set of Elixir terms and must be used as follows:

  LogicElixir.t() :: integer()
                    | atom()
                    | float()
                    | tuple()
                    | [t()]

Keep in mind that uppercase atoms such as X, Character, etc. are used to represent logic variables.

Declaring predicates

LogicElixir offers defpred macro to declare your logic predicates, and supports both declaring logic facts and rules, as the following examples:

defmodule MiddleEarth do
  use LogicElixir

  # Facts
  defpred hobbit(:frodo)
  defpred hobbit(:sam)
  defpred hobbit(:bilbo)

  defpred wizard(:gandalf)
  defpred wizard(:saruman)

  defpred elf(:legolas)

  # Rules

  defpred fellow(X) do
    # To make a disjunction of goals, use `choice` operator
    choice do
      X = :frodo # Unification of LogicElixir terms
    else
      X = :sam
    else
      X = :legolas
    else
      X = :gandalf
    end
  end

  # Predicates to operate with data structures

  defpred append([], Ys, Ys)

  defpred append([X|Xs], Ys, [X|Zs]) do
    append(Xs, Ys, Zs)
  end

  defpred is_ordered([])

  defpred is_ordered([X | []])

  defpred is_ordered([X | [Y | Ys]]) do
    @(X <= Y)               # Elixir expression evaluation with @ operator
    is_ordered([Y | Ys])
  end
end

A full repository with examples can be found here

Querying predicates

LogicElixir offers findall macro to make queries of your logic predicates. This macro receives three arguments:

• A LogicElixir term
• A LogicElixir goal sequence
• An optional Enumerable term to get the results of the query

findall outputs a Stream with the solution of the query or the result inside the optional Enumerable term. Here there are examples of declaring this macro:

  findall Hobbit, do: hobbit(Hobbit) # without optional Enumerable term
  findall X do
    hobbit(X)
    fellow(X)
  end
  findall X, into: [], do: (hobbit(X) ; fellow(X))
  findall Hobbit, into: [], do: hobbit(Hobbit)

It's useful to encapsulate this macro inside an Elixir function to get the results, as the following examples:

defmodule MiddleEarth do
  use LogicElixir
  # ...
  def hobbits do
    findall Hobbit, do: hobbit(Hobbit)
  end
end

If you open an iex -S mix session, you can get the result:

  iex(1)> MiddleEarth.hobbits
  #Stream<[
  enum: #Function<60.124013645/2 in Stream.transform/3>,
  funs: [#Function<48.124013645/1 in Stream.map/2>]
  ]>
  iex(2)> MiddleEarth.hobbits |> Enum.take(1)
  [:frodo]

Besides, you can declare Elixir functions that receive arguments and use it inside:

defmodule LogicLists do
  use LogicElixir

  defpred append([], Ys, Ys)

  defpred append([X|Xs], Ys, [X|Zs]) do
    append(Xs, Ys, Zs)
  end

  def pairs_of_lists(x) do
    (findall {X, Y}, into: [], do: append(X, Y, x))
  end
end

Again, you can test it in your Elixir shell:

  iex(1)> LogicLists.pairs_of_lists([1,2,3,4,5])
  [
    {[], [1, 2, 3, 4, 5]},
    {[1], [2, 3, 4, 5]},
    {[1, 2], [3, 4, 5]},
    {[1, 2, 3], [4, 5]},
    {[1, 2, 3, 4], [5]},
    {[1, 2, 3, 4, 5], []}
  ]