formulae

defmodule Formulae do
  @moduledoc ~S"""
  A set of functions to deal with analytical formulae.
  """

  # @eval_in_place Application.get_env(:formulae, :eval_in_place, false)

  @type t :: %{
          __struct__: atom(),
          formula: binary(),
          ast: nil | tuple(),
          module: nil | atom(),
          variables: nil | [atom()],
          eval: nil | (keyword() -> any())
        }
  defstruct formula: nil, ast: nil, module: nil, eval: nil, variables: nil

  @doc """
  Evaluates the formula returning the result back.

  _Examples:_

      iex> Formulae.eval("rem(a, 5) + rem(b, 4) == 0", a: 20, b: 20)
      true
      iex> Formulae.eval("rem(a, 5) == 0", a: 21)
      false
      iex> Formulae.eval("rem(a, 5) + rem(b, 4)", a: 21, b: 22)
      3
  """
  @spec eval(string :: binary(), bindings :: keyword()) :: term()
  def eval(string, bindings \\ []),
    do: with(f <- Formulae.compile(string), do: f.eval.(bindings))

  @doc """
  Checks whether the formula was already compiled into module.

  _Examples:_

      iex> Formulae.compiled?("foo > 42")
      false
      iex> Formulae.compile("foo > 42")
      iex> Formulae.compiled?("foo > 42")
      true
  """
  @spec compiled?(binary() | Formulae.t()) :: boolean()
  def compiled?(input) when is_binary(input),
    do: Formulae |> Module.concat(input) |> Code.ensure_loaded?()

  def compiled?(%Formulae{module: nil}), do: false
  def compiled?(%Formulae{module: _}), do: true

  @doc """
  Compiles the formula into module.

  _Examples:_

      iex> f = Formulae.compile("rem(a, 5) - b == 0")
      iex> f.formula
      "rem(a, 5) - b == 0"
      iex> f.variables
      [:a, :b]
      iex> f.module
      :"Elixir.Formulae.rem(a, 5) - b == 0"
      iex> f.module.eval(a: 12, b: 2)
      true

      iex> f = Formulae.compile("rem(a, 5) - b == 0")
      iex> f.eval.(a: 11, b: 1)
      true
      iex> f.eval.(a: 12, b: 1)
      false
  """
  @spec compile(Formulae.t() | binary()) :: Formulae.t()
  def compile(input) when is_binary(input) do
    Formulae
    |> Module.concat(input)
    |> Code.ensure_loaded()
    |> maybe_create_module(input)
  end

  def compile(%Formulae{formula: input}), do: compile(input)

  @spec maybe_create_module({:module, atom()} | {:error, any()}, input :: binary()) ::
          Formulae.t()
  defp maybe_create_module({:module, module}, input),
    do: %Formulae{
      formula: input,
      module: module,
      ast: module.ast(),
      variables: module.variables(),
      eval: &module.eval/1
    }

  defp maybe_create_module({:error, _}, input) do
    with {:ok, macro} <- Code.string_to_quoted(input),
         {^macro, variables} =
           Macro.prewalk(macro, [], fn
             {var, _, nil} = v, acc -> {v, [var | acc]}
             v, acc -> {v, acc}
           end),
         escaped = Macro.escape(macro),
         variables = Enum.reverse(variables),
         vars = Enum.map(variables, &{&1, Macro.var(&1, nil)}),
         ast =
           (quote generated: true do
              @variables unquote(variables)

              def ast, do: unquote(escaped)
              def variables, do: @variables

              defmacrop do_eval(unquote(vars)), do: {unquote(escaped), unquote(vars)}
              def eval(unquote(vars)), do: unquote(vars) |> do_eval() |> elem(0)

              def eval(%{} = binding),
                do: eval(for k <- @variables, do: {k, Map.get(binding, k)})

              def eval(args),
                do:
                  {:error, {:invalid_arguments, [given: args, expected_keys: unquote(variables)]}}
            end),
         {:module, module, _, _} <-
           Module.create(Module.concat(Formulae, input), ast, __ENV__),
         do: %Formulae{
           formula: input,
           ast: macro,
           module: module,
           variables: variables,
           eval: &module.eval/1
         }
  end

  ##############################################################################

  @doc deprecated: "Use `Formulae.eval/2` instead"

  @doc ~S"""
  Revalidates the formula with bindings given. Returns true if the formula
  strictly evaluates to `true`, `false` otherwise. Compiles the formula
  before evaluation if needed.
  """
  @spec check(string :: binary(), bindings :: keyword()) :: boolean()
  def check(string, bindings \\ []) do
    try do
      Formulae.evaluate(string, bindings)
    rescue
      Formulae.RunnerError -> false
    end
  end

  @doc deprecated: "Use `Formulae.compile/1` and `%Formulae{}.variables` instead"

  @doc ~S"""
  Returns a normalized representation for the formula given.
  """
  def normalize(input) when is_binary(input) do
    with {normalized, {operation, _env, [formula, value]}} <- unit(input),
         bindings <- bindings?(formula) do
      {normalized, {operation, formula, value}, bindings}
    else
      _ -> raise(Formulae.SyntaxError, formula: input, error: {:unknown, inspect(input)})
    end
  end

  @spec ast_and_variables(input :: binary() | Formulae.t(), binding :: keyword()) ::
          {tuple(), keyword()}
  defp ast_and_variables(input, binding) when is_binary(input) do
    input
    |> Formulae.compile()
    |> ast_and_variables(binding)
  end

  defp ast_and_variables(%Formulae{ast: nil, formula: input}, binding),
    do: ast_and_variables(input, binding)

  defp ast_and_variables(%Formulae{ast: ast}, binding) do
    {ast, vars} =
      Macro.prewalk(ast, [], fn
        {var, _, nil} = v, acc when is_atom(var) ->
          if binding[var], do: {binding[var], acc}, else: {v, [var | acc]}

        v, acc ->
          {v, acc}
      end)

    {ast, Enum.reverse(vars)}
  end

  @doc ~S"""
  Curries the formula by substituting the known bindings into it.

  ## Example

      iex> Formulae.curry("(temp - foo * 4) > speed / 3.14", temp: 7, speed: 3.14).formula
      "7 - foo * 4 > 3.14 / 3.14"
  """
  @spec curry(input :: Formulae.t() | binary(), binding :: keyword(), opts :: keyword()) ::
          Formulae.t()
  def curry(input, binding \\ [], opts \\ [])

  def curry(input, binding, _opts) when is_binary(input) do
    {ast, vars} = ast_and_variables(input, binding)
    %Formulae{variables: ^vars} = Formulae.compile(Macro.to_string(ast))
  end

  def curry(%Formulae{formula: formula}, binding, opts) when is_binary(formula),
    do: curry(formula, binding, opts)

  @doc deprecated:
         "Use `Formulae.compile/1` and `%Formulae{}.variables` or `Formula.curry/2` instead"

  @doc ~S"""
  Returns the binding this formula requires.

  ## Examples

      iex> "a > 5" |> Formulae.bindings?
      ~w|a|a

      iex> ":math.sin(a / (3.14 * b)) > c" |> Formulae.bindings?
      ~w|a b c|a

      iex> "a + b * 4 - :math.pow(c, 2) / d > 1.0 * e" |> Formulae.bindings?
      ~w|a b c d e|a
  """
  @spec bindings?(formula :: Formulae.t() | binary(), binding :: keyword()) :: keyword()
  def bindings?(formula, bindings \\ [])

  def bindings?(formula, bindings) when is_binary(formula),
    do: with(f <- Formulae.curry(formula, bindings), do: f.variables)

  def bindings?(formula, bindings) when is_tuple(formula),
    do: bindings?(Macro.to_string(formula), bindings)

  def bindings?(%Formulae{formula: formula}, bindings),
    do: bindings?(formula, bindings)

  ##############################################################################

  # @comparison [:<, :>, :=] # Damn it, José! :≠
  # @booleans   [:&, :|]

  ##############################################################################

  @deprecated "Use `Formulae.eval/2` instead"

  @doc ~S"""
  Produces the normalized representation of formula. If the _rho_ is
  an instance of [`Integer`](http://elixir-lang.org/docs/stable/elixir/Integer.html#content)
  or [`Float`](http://elixir-lang.org/docs/stable/elixir/Float.html#content),
  it’s left intact, otherwise it’s moved to the left side with negation.

  ## Examples

      iex> Formulae.unit("3 > 2")
      {"3 > 2", {:>, [], [3, 2]}}

      iex> Formulae.unit("3 - a > 2")
      {"3 - a > 2", {:>, [], [{:-, [line: 1], [3, {:a, [line: 1], nil}]}, 2]}}

      iex> Formulae.unit("3 > A + 2")
      {"3 > a + 2",
        {:>, [],
          [{:-, [context: Formulae, import: Kernel],
            [3, {:+, [line: 1], [{:a, [line: 1], nil}, 2]}]}, 0]}}

      iex> Formulae.unit("3 >= a + 2")
      {"3 >= a + 2",
        {:>=, [],
          [{:-, [context: Formulae, import: Kernel],
            [3, {:+, [line: 1], [{:a, [line: 1], nil}, 2]}]}, 0]}}

      iex> Formulae.unit("3 a > A + 2")
      ** (Formulae.SyntaxError) Formula [3 a > A + 2] syntax is incorrect (parsing): syntax error before: “a”.

      iex> Formulae.unit("a + 2 = 3")
      {"a + 2 = 3", {:==, [], [{:+, [line: 1], [{:a, [line: 1], nil}, 2]}, 3]}}

      iex> Formulae.unit(~S|A = "3"|)
      {"a = \"3\"", {:==, [], [{:a, [line: 1], nil}, "3"]}}
  """
  def unit(input, env \\ []) when is_binary(input) do
    normalized = String.downcase(input)

    {
      normalized,
      case Code.string_to_quoted(normalized) do
        {:ok, {:>, _, [lh, rh]}} when is_integer(rh) or is_float(rh) ->
          {:>, env, [lh, rh]}

        {:ok, {:>, _, [lh, rh]}} ->
          {:>, env, [quote(do: unquote(lh) - unquote(rh)), 0]}

        {:ok, {:>=, _, [lh, rh]}} when is_integer(rh) or is_float(rh) ->
          {:>=, env, [lh, rh]}

        {:ok, {:>=, _, [lh, rh]}} ->
          {:>=, env, [quote(do: unquote(lh) - unquote(rh)), 0]}

        {:ok, {:<, _, [lh, rh]}} when is_integer(rh) or is_float(rh) ->
          {:<, env, [lh, rh]}

        {:ok, {:<, _, [lh, rh]}} ->
          {:<, env, [quote(do: unquote(lh) - unquote(rh)), 0]}

        {:ok, {:<=, _, [lh, rh]}} when is_integer(rh) or is_float(rh) ->
          {:<=, env, [lh, rh]}

        {:ok, {:<=, _, [lh, rh]}} ->
          {:<=, env, [quote(do: unquote(lh) - unquote(rh)), 0]}

        {:ok, {:=, _, [lh, rh]}} ->
          {:==, env, [lh, rh]}

        {:ok, {:==, _, [lh, rh]}} ->
          {:==, env, [lh, rh]}

        {:ok, {op, _, _}} ->
          raise(Formulae.SyntaxError, formula: input, error: {:operation, double_quote(op)})

        {:error, {1, message, op}} ->
          raise(
            Formulae.SyntaxError,
            formula: input,
            error: {:parsing, message <> double_quote(op)}
          )

        other ->
          raise(Formulae.SyntaxError, formula: input, error: {:unknown, inspect(other)})
      end
    }
  end

  @deprecated "Use `Formulae.eval/2` instead"

  @doc ~S"""
  Evaluates normalized representation of formula.

  ## Examples

      iex> Formulae.evaluate(Formulae.unit("3 > 2"))
      true

      iex> Formulae.evaluate(Formulae.unit("3 < 2"))
      false

      iex> Formulae.evaluate(Formulae.unit("a < 2"), [a: 1])
      true

      iex> Formulae.evaluate(Formulae.unit("a > 2"), [a: 1])
      false

      iex> Formulae.evaluate(Formulae.unit("a < 2"), [])
      ** (Formulae.RunnerError) Formula failed to run (compile): incomplete binding to evaluate a formula, lacking: [:a].

      iex> Formulae.evaluate(Formulae.unit("a + 2 = 3"), [a: 1])
      true

      iex> Formulae.evaluate(Formulae.unit("a + 2 = 3"), [a: 2])
      false

      iex> Formulae.evaluate(Formulae.unit(~S|a = "3"|), [a: "3"])
      true

      iex> Formulae.evaluate(Formulae.unit(~S|a = "3"|), [a: 3])
      false

      iex> Formulae.evaluate(Formulae.unit(~S|a = "3"|), [a: "hello"])
      false

      iex> Formulae.evaluate("a + 2 = 3", [a: 2])
      false

      iex> Formulae.evaluate(~S|a = "3"|, [a: "3"])
      true

      iex> Formulae.evaluate(Formulae.unit("a_b_c_490000 > 2"), [a_b_c_490000: 3])
      true
  """
  def evaluate(input, binding \\ [], opts \\ [])

  def evaluate({_original, ast}, binding, opts),
    do: evaluate(ast, binding, opts)

  def evaluate(input, binding, opts) when is_binary(input),
    do: evaluate(unit(input), binding, opts)

  def evaluate(input, binding, opts) when is_tuple(input) do
    unresolved = bindings?(input, binding)

    if Enum.empty?(unresolved) do
      do_evaluate(input, binding, opts)
    else
      raise(
        Formulae.RunnerError,
        formula: input,
        error:
          {:compile, "incomplete binding to evaluate a formula, lacking: #{inspect(unresolved)}"}
      )
    end
  end

  defp do_evaluate(input, binding, opts) when is_tuple(input) do
    # FIXME Make `nil` acceptable through SQL-like `IS NULL` syntax!
    binding = Enum.reject(binding, fn {_, v} -> is_nil(v) end)

    try do
      case Code.eval_quoted(input, binding, opts) do
        {false, ^binding} -> false
        {true, ^binding} -> true
        other -> raise(Formulae.RunnerError, formula: input, error: {:weird, inspect(other)})
      end
    rescue
      e in CompileError ->
        raise(Formulae.RunnerError, formula: input, error: {:compile, e.description})
    end
  end

  ##############################################################################

  defp double_quote(string) when is_binary(string), do: "“" <> string <> "”"
  defp double_quote(string), do: double_quote(to_string(string))
end