text: import ast
  from types import FunctionType
  from typing import Dict, List, NamedTuple, Union
  
  import astor
  import jax
  import networkx as nx
  
  import mcx
  from mcx.core.graph import GraphicalModel
  from mcx.core.nodes import Argument, RandVar
  
  
  class Artifact(NamedTuple):
      compiled_fn: FunctionType
      args: List[str]
      fn_name: str
      fn_source: str
  
  
  def compile_to_logpdf(graph: GraphicalModel, namespace: Dict) -> Artifact:
      """Compile a graphical model into a log-probability density function.
  
      Example
      -------
  
      Let us consider a simple linear regression example:
  
          >>> @mcx.model
          ... def linear_regression(x, lmbda=1.):
          ...     scale <~ Exponential(lmbda)
          ...     coeff <~ Normal(0, 1)
          ...     y = np.dot(x, coeff)
          ...     predictions <~ Normal(y, scale)
          ...     return predictions
  
      MCX parses this definition into a graphical model. This function compiles
      the graph in a python function that returns the values of the
      log-probability density function:
  
          >>> def linear_regression_logpdf(x, scale, coeffs, predictions, lmbda=1.):
          ...     logpdf = 0
          ...     logpdf += Exponential(lmbda).logpdf(scale)
          ...     logpdf += Normal(0, 1).logpdf(coeff)
          ...     y = np.dot(x, coeff)
          ...     logpdf += Normal(y, coeff).logpdf(predictions)
          ...     return logpdf
  
      The logpdf is then partially applied on the dataset {(x, prediction)} for
      inference.
  
      Of course it would impact the core
  
  
      Parameters
      ----------
      model:
          A probabilistic graphical model.
      namespace:
          The names contained in the model definition's global scope.
  
      Returns
      -------
      logpdf:
          A function that returns the log probability of a model at one point the
          parameter space.
      var_names:
          The name of the random variables arguments of the logpdf function, in
          the order in which they appear.
      logpdf_source:
          A string containing the source code of the logpdf. Useful for inspection
          by the user.
      """
      fn_name = graph.name + "_logpdf"
  
      #
      # ARGUMENTS
      #
  
      kwarg_nodes = [
          node[1]["content"]
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is not None
      ]
  
      # The (keyword) arguments of the model definition and random variables
      # are passed as arguments to the logpdf.
      model_kwargs = [kwarg.to_logpdf_iadd() for kwarg in kwarg_nodes]
      model_arguments = [
          node[1]["content"].to_logpdf_iadd()
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is None
      ]
      random_variables = [
          ast.arg(arg=node[1]["content"].name, annotation=None)
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], RandVar)
      ]
  
      logpdf_arguments = random_variables + model_arguments + model_kwargs
  
      # We propagate the kwargs' default values
      defaults = [kwarg.default_value for kwarg in kwarg_nodes]
  
      #
      # FUNCTION BODY
      # To write the function body, we traverse the graph in topological order
      # while incrementing the value of the logpdf.
      #
  
      body: List[Union[ast.Assign, ast.Constant, ast.Num, ast.Return]] = []
      body.append(
          ast.Assign(
              targets=[ast.Name(id="logpdf", ctx=ast.Store())],
              value=ast.Constant(value=0),
          )
      )
      ordered_nodes = [
          graph.nodes[node]["content"]
          for node in nx.topological_sort(graph)
          if not isinstance(graph.nodes[node]["content"], Argument)
      ]
      for node in ordered_nodes:
          body.append(node.to_logpdf_iadd())
  
      returned = ast.Return(value=ast.Name(id="logpdf", ctx=ast.Load()))
      body.append(returned)
  
      logpdf_ast = ast.Module(
          body=[
              ast.FunctionDef(
                  name=fn_name,
                  args=ast.arguments(
                      args=logpdf_arguments,
                      vararg=None,
                      kwarg=None,
                      posonlyargs=[],
                      kwonlyargs=[],
                      defaults=defaults,
                      kw_defaults=[],
                  ),
                  body=body,
                  decorator_list=[],
              )
          ],
          type_ignores=[],
      )
      logpdf_ast = ast.fix_missing_locations(logpdf_ast)
      logpdf = compile(logpdf_ast, filename="<ast>", mode="exec")
      exec(logpdf, namespace)
      fn = namespace[fn_name]
  
      argument_names = [arg.arg for arg in logpdf_arguments]
  
      return Artifact(fn, argument_names, fn_name, astor.code_gen.to_source(logpdf_ast))
  
  
  def compile_to_loglikelihoods(graph: GraphicalModel, namespace: Dict) -> Artifact:
      """
  
      Example
      -------
  
      Let us consider a simple linear regression example:
  
          >>> @mcx.model
          ... def linear_regression(x, lmbda=1.):
          ...     scale <~ Exponential(lmbda)
          ...     coeff <~ Normal(0, 1)
          ...     y = np.dot(x, coeff)
          ...     predictions <~ Normal(y, scale)
          ...     return predictions
  
      We can get the log-likelihood contribution of each parameter by doing:
  
          >>> def linear_regression_logpdf(x, scale, coeffs, predictions, lmbda=1.):
          ...     logpdf_scale = Exponential(lmbda).logpdf(scale)
          ...     logpdf_coeff = Normal(0, 1).logpdf(coeff)
          ...     y = np.dot(x, coeff)
          ...     logpdf_predictions = Normal(y, coeff).logpdf(predictions)
          ...     return np.array([logpdf_scale, logpdf_coeff, logpdf_predictions])
      """
  
      fn_name = graph.name + "_loglikelihoods"
  
      #
      # ARGUMENTS
      #
  
      kwarg_nodes = [
          node[1]["content"]
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is not None
      ]
  
      # The (keyword) arguments of the model definition and random variables
      # are passed as arguments to the logpdf.
      model_kwargs = [kwarg.to_logpdf() for kwarg in kwarg_nodes]
      model_arguments = [
          node[1]["content"].to_logpdf()
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is None
      ]
      random_variables = [
          ast.arg(arg=node[1]["content"].name, annotation=None)
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], RandVar)
      ]
  
      logpdf_arguments = random_variables + model_arguments + model_kwargs
  
      # We propagate the kwargs' default values
      defaults = [kwarg.default_value for kwarg in kwarg_nodes]
  
      #
      # FUNCTION BODY
      # To write the function body, we traverse the graph in topological order
      # while incrementing the value of the logpdf.
      #
  
      body: List[Union[ast.Assign, ast.Constant, ast.Num, ast.Return]] = []
      ordered_nodes = [
          graph.nodes[node]["content"]
          for node in nx.topological_sort(graph)
          if not isinstance(graph.nodes[node]["content"], Argument)
      ]
      # ordered_transformations = [
      # graph.nodes[node]["content"].name
      # for node in nx.topological_sort(graph)
      # if isinstance(graph.nodes[node]["content"], Transformation)
      # ]
      for node in ordered_nodes:
          body.append(node.to_logpdf())
  
      # Returned values
      #
      # In this situation we want to function to return both the individual
      # values of the log-likelihood as well as the values of the deterministic
      # variables.
  
      returned = ast.Return(
          value=ast.Dict(
              keys=[
                  ast.Constant(value=f"{name.arg}", kind=None)
                  for name in random_variables
              ],
              values=[
                  ast.Name(id=f"logpdf_{name.arg}", ctx=ast.Load())
                  for name in random_variables
              ],
          ),
          type_ignores=[],
      )
      body.append(returned)
  
      logpdf_ast = ast.Module(
          body=[
              ast.FunctionDef(
                  name=fn_name,
                  args=ast.arguments(
                      args=logpdf_arguments,
                      vararg=None,
                      kwarg=None,
                      posonlyargs=[],
                      kwonlyargs=[],
                      defaults=defaults,
                      kw_defaults=[],
                  ),
                  body=body,
                  decorator_list=[],
              )
          ],
          type_ignores=[],
      )
      logpdf_ast = ast.fix_missing_locations(logpdf_ast)
      logpdf = compile(logpdf_ast, filename="<ast>", mode="exec")
      exec(logpdf, namespace)
      fn = namespace[fn_name]
  
      argument_names = [arg.arg for arg in logpdf_arguments]
  
      return Artifact(fn, argument_names, fn_name, astor.code_gen.to_source(logpdf_ast))
  
  
  def compile_to_sampler(graph, namespace) -> Artifact:
      """Compile the model in a function that generates prior samples from the
      model's random variables.
  
      (TODO): Check that the parameters used to initialize distributions respect
      the constraints. This cannot be done dynamically once the model is JIT
      compiled.
  
      Args:
          model: A probabilistic program definition.
          namespace: The model definition's global scope.
      Returns:
          sample_fn: A JIT compiled function that returns prior predictive
              samples from the model. The function's signature is of the form:
              `model_sampler(rng_key, *args, sample_shape=())`
      """
      fn_name = graph.name + "_sampler"
  
      kwargs = [
          node[1]["content"]
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is not None
      ]
  
      args = (
          [ast.arg(arg="rng_key", annotation=None)]
          + [
              node[1]["content"].to_sampler()
              for node in graph.nodes(data=True)
              if isinstance(node[1]["content"], Argument)
              and node[1]["content"].default_value is None
          ]
          + [k.to_sampler() for k in kwargs]
      )
  
      defaults = [k.default_value for k in kwargs]
  
      body = []
      ordered_nodes = [
          graph.nodes[node]["content"]
          for node in nx.topological_sort(graph)
          if not isinstance(graph.nodes[node]["content"], Argument)
      ]
      for node in ordered_nodes:
          body.append(node.to_sampler(graph))
  
      returned_vars = [
          ast.Name(id=node.name, ctx=ast.Load())
          for node in ordered_nodes
          if not isinstance(node, mcx.core.graph.Var)
      ]
  
      returned = ast.Return(
          value=ast.Tuple(
              elts=returned_vars,
              ctx=ast.Load(),
          )
      )
      body.append(returned)
  
      sampler_ast = ast.Module(
          body=[
              ast.FunctionDef(
                  name=fn_name,
                  args=ast.arguments(
                      args=args,
                      vararg=None,
                      kwarg=None,
                      posonlyargs=[],
                      kwonlyargs=[],
                      defaults=defaults,
                      kw_defaults=[],
                  ),
                  body=body,
                  decorator_list=[],
              )
          ],
          type_ignores=[],
      )
      sampler_ast = ast.fix_missing_locations(sampler_ast)
  
      sampler = compile(sampler_ast, filename="<ast>", mode="exec")
      exec(sampler, namespace)
      fn = namespace[fn_name]
      fn = jax.jit(fn, static_argnums=(0, 1))
  
      returned_names = [arg.id for arg in returned_vars]
  
      return Artifact(fn, returned_names, fn_name, astor.code_gen.to_source(sampler_ast))
  
  
  def compile_to_forward_sampler(graph, namespace, jit=False) -> Artifact:
      """Compile the model in a function that generates prior samples from the
      model's generated variables.
  
      (TODO): Check that the parameters used to initialize distributions respect
      the constraints. This cannot be done dynamically once the model is JIT
      compiled.
  
      Args:
          model: A probabilistic program definition.
          namespace: The model definition's global scope.
      Returns:
          sample_fn: A JIT compiled function that returns prior predictive
              samples from the model. The function's signature is of the form:
              `model_sampler(rng_key, *args, sample_shape=())`
      """
      fn_name = graph.name + "_forward_sampler"
  
      kwargs = [
          node[1]["content"]
          for node in graph.nodes(data=True)
          if isinstance(node[1]["content"], Argument)
          and node[1]["content"].default_value is not None
      ]
  
      args = (
          [ast.arg(arg="rng_key", annotation=None)]
          + [ast.arg(arg="sample_shape", annotation=None)]
          + [
              node[1]["content"].to_sampler()
              for node in graph.nodes(data=True)
              if isinstance(node[1]["content"], Argument)
              and node[1]["content"].default_value is None
          ]
          + [k.to_sampler() for k in kwargs]
      )
  
      defaults = [k.default_value for k in kwargs]
  
      body = []
      ordered_nodes = [
          graph.nodes[node]["content"]
          for node in nx.topological_sort(graph)
          if not isinstance(graph.nodes[node]["content"], Argument)
      ]
      for node in ordered_nodes:
          body.append(node.to_sampler(graph))
  
      returned_vars = [
          ast.Name(id=node.name, ctx=ast.Load())
          for node in ordered_nodes
          if not isinstance(node, mcx.core.graph.Var) and node.is_returned
      ]
      if len(returned_vars) == 1:
          returned = ast.Return(returned_vars[0])
      else:
          returned = ast.Return(
              value=ast.Tuple(
                  elts=returned_vars,
                  ctx=ast.Load(),
              )
          )
      body.append(returned)
      sampler_ast = ast.Module(
          body=[
              ast.FunctionDef(
                  name=fn_name,
                  args=ast.arguments(
                      args=args,
                      vararg=None,
                      kwarg=None,
                      posonlyargs=[],
                      kwonlyargs=[],
                      defaults=defaults,
                      kw_defaults=[],
                  ),
                  body=body,
                  decorator_list=[],
              )
          ],
          type_ignores=[],
      )
      sampler_ast = ast.fix_missing_locations(sampler_ast)
  
      sampler = compile(sampler_ast, filename="<ast>", mode="exec")
      exec(sampler, namespace)
  
      returned_names = [arg.id for arg in returned_vars]
  
      return Artifact(
          namespace[fn_name],
          returned_names,
          fn_name,
          astor.code_gen.to_source(sampler_ast),
      )
  