def apply_substitute(proof_step, l: [MathObject], user_input: [int], equality):
"""
Try to rewrite the goal or the first selected property using the last
selected property.
"""
goal = proof_step.goal
codes = CodeForLean.empty_code()
heq = l[-1]
left_term = equality.children[0]
right_term = equality.children[1]
success1 = ' ' + _("{} replaced by {}").format(left_term.to_display(),
right_term.to_display()) + ' '
success2 = ' ' + _("{} replaced by {}").format(right_term.to_display(),
left_term.to_display()) + ' '
choices = [(left_term.to_display(),
f'Replace by {right_term.to_display()}'),
(right_term.to_display(),
f'Replace by {left_term.to_display()}')]
if len(l) == 1:
# If the user has chosen a direction, apply substitution
# else if both directions make sense, ask the user for a choice
# else try direct way or else reverse way.
h = l[0].info["name"]
if len(user_input) > 0:
if user_input[0] == 1:
success_msg = success2 + _("in target")
more_code = CodeForLean.from_string(f'rw <- {h}',
success_msg=success_msg)
elif user_input[0] == 0:
success_msg = success1 + _("in target")
more_code = CodeForLean.from_string(f'rw {h}',
success_msg=success_msg)
codes = codes.or_else(more_code)
else:
if goal.target.math_type.contains(left_term) and \
goal.target.math_type.contains(right_term):
raise MissingParametersError(
InputType.Choice,
choices,
title=_("Precision of substitution"),
output=_("Choose which expression you want to replace"))
else:
msg2 = success2 + _("in target")
more_code2 = CodeForLean.from_string(f'rw <- {h}',
success_msg=msg2)
codes = codes.or_else(more_code2)
msg1 = success1 + _("in target")
more_code1 = CodeForLean.from_string(f'rw {h}',
success_msg=msg1)
codes = codes.or_else(more_code1)
if len(l) == 2:
h = l[0].info["name"]
heq_name = l[-1].info["name"]
if len(user_input) > 0:
if user_input[0] == 1:
success_msg = success2 + _("in {}").format(h)
more_code = CodeForLean.from_string(f'rw <- {heq_name} at {h}',
success_msg=success_msg)
codes = codes.or_else(more_code)
elif user_input[0] == 0:
success_msg = success1 + _("in {}").format(h)
more_code = CodeForLean.from_string(f'rw {heq_name} at {h}',
success_msg=success_msg)
codes = codes.or_else(more_code)
else:
if l[0].math_type.contains(left_term) and \
l[0].math_type.contains(right_term):
raise MissingParametersError(
InputType.Choice,
choices,
title=_("Precision of substitution"),
output=_("Choose which expression you want to replace"))
# h, heq_name = heq_name, h
# codes = codes.or_else(f'rw <- {heq_name} at {h}')
# codes = codes.or_else(f'rw {heq_name} at {h}')
msg2 = success2 + _("in {}").format(h)
more_code2 = CodeForLean.from_string(f'rw <- {heq_name} at {h}',
success_msg=msg2)
codes = codes.or_else(more_code2)
msg1 = success1 + _("in {}").format(h)
more_code1 = CodeForLean.from_string(f'rw {heq_name} at {h}',
success_msg=msg1)
codes = codes.or_else(more_code1)
if heq.is_for_all():
# if property is, e.g. "∀n, u n = c"
# there is a risk of meta vars if Lean does not know to which n
# applying the equality
codes = codes.and_then('no_meta_vars')
return codes
def action_new_object(proof_step,
selected_objects: [MathObject],
user_input: [str] = None,
target_selected: bool = True) -> CodeForLean:
"""
Introduce new object / sub-goal / function
"""
goal = proof_step.goal
codes = []
# Choose between object/sub-goal/function
if not user_input:
raise MissingParametersError(InputType.Choice,
[(_("Object"), _("Introduce a new object")),
(_("Goal"), _("Introduce a new "
"intermediate sub-goal")),
(_("Function"), _("Introduce a new "
"function"))],
title=_("New object"),
output=_("Choose what to introduce:"))
# Choice = new object
if user_input[0] == 0:
if len(user_input) == 1: # Ask for name
raise MissingParametersError(InputType.Text,
title="+",
output=_("Name your object:"))
if len(user_input) == 2: # Ask for new object
raise MissingParametersError(InputType.Text,
title="+",
output=_("Introduce a new object")
+ "(" + _("e.g.")
+ "0, {1}, f(2), ...)")
else: # Send code
name = user_input[1]
new_hypo_name = get_new_hyp(proof_step)
new_object = user_input[2]
codes = CodeForLean.from_string(f"let {name} := {new_object}")
codes = codes.and_then(f"have {new_hypo_name} : {name} = "
f"{new_object}")
codes = codes.and_then("refl")
codes.add_success_msg(_("New object {} added to the context").
format(name))
if goal.target.is_for_all():
# User might want to prove a universal property "∀x..."
# and mistake "new object" for introduction of the relevant x.
codes.add_error_msg(_("You might try the ∀ button..."))
# Choice = new sub-goal
elif user_input[0] == 1:
if len(user_input) == 1:
raise MissingParametersError(InputType.Text,
title="+",
output=_("Introduce new subgoal:"))
else:
new_hypo_name = get_new_hyp(proof_step)
codes = CodeForLean.from_string(f"have {new_hypo_name}:"
f" ({user_input[1]})")
codes.add_success_msg(_("New target will be added to the context "
"after being proved"))
codes.add_subgoal(user_input[1])
# Choice = new function
elif user_input[0] == 2:
return introduce_fun(proof_step, selected_objects)
return codes