def parse(self, data):
self.name = data['name']
try:
self.type = parser.parse_type(data['type'])
self.cname = theory.thy.get_overload_const_name(
self.name, self.type)
for rule in data['rules']:
with context.fresh_context(defs={self.name: self.type}):
prop = parser.parse_term(rule['prop'])
# Test conclusion of the prop
_, concl = prop.strip_implies()
f, _ = concl.strip_comb()
if f != Const(self.name, self.type):
raise ItemException(
"Inductive %s: wrong head of conclusion" % self.name)
self.rules.append({'name': rule['name'], 'prop': prop})
except Exception as error:
self.type = data['type']
self.rules = data['rules']
self.error = error
self.trace = traceback2.format_exc()
def parse(self, data):
self.name = data['name']
try:
self.type = parser.parse_type(data['type'])
self.cname = theory.thy.get_overload_const_name(
self.name, self.type)
for rule in data['rules']:
with context.fresh_context(defs={self.name: self.type}):
prop = parser.parse_term(rule['prop'])
# prop should be an equality
if not prop.is_equals():
raise ItemException("Fun %s: rule is not an equality" %
self.name)
f, args = prop.lhs.strip_comb()
if f != Const(self.name, self.type):
raise ItemException("Fun %s: wrong head of lhs" %
self.name)
lhs_vars = set(v.name for v in prop.lhs.get_vars())
rhs_vars = set(v.name for v in prop.rhs.get_vars())
if not rhs_vars.issubset(lhs_vars):
raise ItemException(
"Fun %s: extra variables in rhs: %s" %
(self.name, ", ".join(v for v in rhs_vars - lhs_vars)))
self.rules.append({'prop': prop})
except Exception as error:
self.type = data['type']
self.rules = data['rules']
self.error = error
self.trace = traceback2.format_exc()
def parse(self, data):
self.name = data['name']
try:
with context.fresh_context(vars=data['vars']):
self.vars = context.ctxt.vars
self.prop = parser.parse_term(data['prop'])
# theorem does not already exist
if theory.thy.has_theorem(self.name):
raise ItemException("Theorem %s: theorem already exists")
# prop should not contain extra variables
self_vars = set(self.vars.keys())
prop_vars = set(v.name for v in self.prop.get_vars())
if not prop_vars.issubset(self_vars):
raise ItemException(
"Theorem %s: extra variables in prop: %s" %
(self.name, ", ".join(v for v in prop_vars - self_vars)))
except Exception as error:
self.vars = data['vars']
self.prop = data['prop']
self.error = error
self.trace = traceback2.format_exc()
if 'attributes' in data:
self.attributes = data['attributes']
def load_system(filename):
dn = os.path.dirname(os.path.realpath(__file__))
with open(os.path.join(dn, 'examples/' + filename + '.json'),
encoding='utf-8') as a:
data = json.load(a)
basic.load_theory('gcl')
name = data['name']
vars = []
for nm, str_T in data['vars'].items():
T = parser.parse_type(str_T)
vars.append(Var(nm, T))
for i, nm in enumerate(data['states']):
theory.thy.add_term_sig(nm, NatType)
theory.thy.add_theorem(nm + "_def",
Thm([], Eq(Const(nm, NatType), Nat(i))))
states = [Const(nm, NatType) for nm in data['states']]
rules = []
for rule in data['rules']:
if isinstance(rule['var'], str):
rule_var = Var(rule['var'], NatType)
cur_vars = {v.name: v.T for v in vars + [rule_var]}
else:
assert isinstance(rule['var'], list)
rule_var = [Var(nm, NatType) for nm in rule['var']]
cur_vars = {v.name: v.T for v in vars + rule_var}
with context.fresh_context(vars=cur_vars):
guard = parser.parse_term(rule['guard'])
assign = dict()
for k, v in rule['assign'].items():
assign[parser.parse_term(k)] = parser.parse_term(v)
rules.append((rule_var, guard, assign))
invs = []
for inv in data['invs']:
inv_vars = [Var(nm, NatType) for nm in inv['vars']]
with context.fresh_context(vars={v.name: v.T
for v in vars + inv_vars}):
prop = parser.parse_term(inv['prop'])
invs.append((inv_vars, prop))
return ParaSystem(name, vars, states, rules, invs)
def apply(self, state, id, data, prevs):
with context.fresh_context(vars=state.get_vars(id)):
A = parser.parse_term(data['case'])
for v in A.get_vars():
if v.name not in context.ctxt.vars:
raise AssertionError('Apply case: extra variable %s' %
v.name)
state.apply_tactic(id, tactic.cases(), args=A)
def apply(self, state, id, data, prevs):
# Find variable
with context.fresh_context(vars=state.get_vars(id)):
assert data[
'var'] in context.ctxt.vars, "induction: cannot find variable."
var = Var(data['var'], context.ctxt.vars[data['var']])
state.apply_tactic(id,
tactic.var_induct(),
args=(data['theorem'], var))
def apply(self, state, id, data, prevs):
with context.fresh_context(vars=state.get_vars(id)):
t = parser.parse_term(data['s'])
for v in t.get_vars():
if v.name not in context.ctxt.vars:
raise AssertionError(
'Instantiate exists: extra variable %s' % v.name)
state.apply_tactic(id, tactic.inst_exists_goal(), args=t, prevs=[])
def apply(self, state, id, data, prevs):
with context.fresh_context(vars=state.get_vars(id)):
t = parser.parse_term(data['s'])
for v in t.get_vars():
if v.name not in context.ctxt.vars:
raise AssertionError(
'Forall elimination: extra variable %s' % v.name)
state.add_line_before(id, 1)
state.set_line(id, 'forall_elim_gen', args=t, prevs=prevs)
def apply(self, state, id, data, prevs):
inst = Inst()
with context.fresh_context(vars=state.get_vars(id)):
for key, val in data.items():
if key.startswith("param_"):
inst[key[6:]] = parser.parse_term(val)
if inst:
state.apply_tactic(id, tactic.apply_prev(), args=inst, prevs=prevs)
else:
state.apply_tactic(id, tactic.apply_prev(), prevs=prevs)
def apply(self, state, id, data, prevs):
cur_item = state.get_proof_item(id)
hyps = cur_item.th.hyps
with context.fresh_context(vars=state.get_vars(id)):
C = parser.parse_term(data['goal'])
for v in C.get_vars():
if v.name not in context.ctxt.vars:
raise AssertionError('Insert goal: extra variable %s' %
v.name)
state.add_line_before(id, 1)
state.set_line(id, 'sorry', th=Thm(hyps, C))
def apply(self, state, id, data, prevs):
assert len(prevs) == 1, "exists_elim"
# Parse the list of variable names
with context.fresh_context(vars=state.get_vars(id)):
names = [name.strip() for name in data['names'].split(',')]
for name in names:
if name in context.ctxt.vars:
raise AssertionError(
"Instantiate exists: duplicate name %s" % name)
exists_item = state.get_proof_item(prevs[0])
exists_prop = exists_item.th.prop
assert exists_prop.is_exists(), "exists_elim"
vars, body = logic.strip_exists(exists_prop, names)
# Add one line for each variable, and one line for body of exists
state.add_line_before(id, len(vars) + 1)
for i, var in enumerate(vars):
state.set_line(id.incr_id(i),
'variable',
args=(var.name, var.T),
prevs=[])
state.set_line(id.incr_id(len(vars)), 'assume', args=body, prevs=[])
# Find the intros at the end, append exists fact and new variables
# and assumptions to prevs.
new_intros = [prevs[0]] + [id.incr_id(i) for i in range(len(vars) + 1)]
i = len(vars) + 1
while True:
try:
item = state.get_proof_item(id.incr_id(i))
except ProofStateException:
raise AssertionError(
"exists_elim: cannot find intros at the end")
else:
if item.rule == 'intros':
if item.args is None:
item.args = [exists_prop]
else:
item.args = [exists_prop] + item.args
item.prevs = item.prevs[:-1] + new_intros + [
item.prevs[-1]
]
break
else:
state.set_line(id.incr_id(i), item.rule, args=item.args, prevs=item.prevs, \
th=Thm(list(item.th.hyps) + [body], item.th.prop))
i += 1
def apply(self, state, id, data, prevs):
inst = Inst()
with context.fresh_context(vars=state.get_vars(id)):
for key, val in data.items():
if key.startswith("param_"):
if val != '':
inst[key[6:]] = parser.parse_term(val)
th = theory.get_theorem(data['theorem'])
# Check whether to ask for parameters
As, C = th.prop.strip_implies()
match_svars = term.get_svars(As[:len(prevs)])
all_svars = th.prop.get_svars()
param_svars = [
v for v in all_svars
if v not in match_svars and 'param_' + v.name not in data
]
if param_svars:
raise theory.ParameterQueryException(
list("param_" + v.name for v in param_svars))
# First test apply_theorem
prev_ths = [state.get_proof_item(prev).th for prev in prevs]
macro = logic.apply_theorem_macro(with_inst=True)
res_th = macro.eval((data['theorem'], inst), prev_ths)
state.add_line_before(id, 1)
if inst:
state.set_line(id,
'apply_theorem_for',
args=(data['theorem'], inst),
prevs=prevs)
else:
state.set_line(id,
'apply_theorem',
args=data['theorem'],
prevs=prevs)
id2 = id.incr_id(1)
new_id = state.find_goal(state.get_proof_item(id2).th, id2)
if new_id is not None:
state.replace_id(id2, new_id)
def parse(self, data):
self.name = data['name']
try:
self.type = parser.parse_type(data['type'])
self.cname = theory.thy.get_overload_const_name(
self.name, self.type)
with context.fresh_context(defs={self.name: self.type}):
self.prop = parser.parse_term(data['prop'])
# prop should be an equality
if not self.prop.is_equals():
raise ItemException("Definition %s: prop is not an equality" %
self.name)
f, args = self.prop.lhs.strip_comb()
if f != Const(self.name, self.type):
raise ItemException("Definition %s: wrong head of lhs" %
self.name)
lhs_vars = set(v.name for v in args)
rhs_vars = set(v.name for v in self.prop.rhs.get_vars())
if len(lhs_vars) != len(args):
raise ItemException(
"Definition %s: variables on lhs must be distinct" %
self.name)
if not rhs_vars.issubset(lhs_vars):
raise ItemException(
"Definition %s: extra variables in rhs: %s" %
(self.name, ", ".join(v for v in rhs_vars - lhs_vars)))
except Exception as error:
self.type = data['type']
self.prop = data['prop']
self.error = error
self.trace = traceback2.format_exc()
if 'attributes' in data:
self.attributes = data['attributes']
def display_step(self, state, data):
id = data['goal_id']
with context.fresh_context(vars=state.get_vars(id)):
goal = parser.parse_term(data['goal'])
return pprint.N("have ") + printer.print_term(goal)