def f(t):
if isinstance(t, Nom):
return
if isinstance(t, Var):
ref = t.ref
if isinstance(ref, Link):
return f(ref.ty)
if isinstance(ref, (Unbound, Bound)):
return
if isinstance(ref, Gen):
free_var_set.add(ty)
return
raise TypeError(type(ref))
if isinstance(t, App):
f(t.f)
f(t.arg)
return
if isinstance(t, Arrow):
f(t.arg)
f(t.ret)
return
if isinstance(t, Forall):
f(t.ty)
return
raise TypeError(type(ty))
def f(t):
if isinstance(t, Var):
ref = t.ref
if isinstance(ref, Link):
return f(ref.ty)
if isinstance(ref, (Gen, Bound)):
return
if isinstance(ref, Unbound):
if ref.id is tvar_id:
error("recursive types")
elif ref.level > tvar_level:
t.ref = Unbound(ref.id, tvar_level)
return
raise TypeError(type(ref))
if isinstance(t, App):
f(t.f)
f(t.arg)
return
if isinstance(t, Arrow):
f(t.arg)
f(t.ret)
return
if isinstance(t, Forall):
f(t.ty)
return
if isinstance(t, Nom):
return
raise TypeError(type(t))
def f(t: Ty):
if isinstance(t, Var):
ref = t.ref
if isinstance(ref, Link):
f(ref.ty)
return
if isinstance(ref, Gen):
error("impossible")
if isinstance(ref, Bound):
return
if isinstance(ref, Unbound):
if ref.level > level:
other_id = ref.id
t.ref = Bound(other_id)
if other_id not in var_id_lst:
var_id_lst.append(other_id)
return
raise TypeError(type(t))
if isinstance(t, App):
f(t.f)
f(t.arg)
return
if isinstance(t, Arrow):
f(t.arg)
f(t.ret)
return
if isinstance(t, Forall):
f(t.ty)
return
if isinstance(t, Nom):
return
raise TypeError(type(t))
def infer(env: Env, level: int, term: Expr):
if isinstance(term, EVar):
try:
return env.type_of_name(term.v)
except KeyError:
error("variable {} undefined".format(term.v))
if isinstance(term, EFun):
fn_env = env.new_scope()
var_lst = []
pn, ann = term.param
if ann:
var_lst_sec, arg_ty = inst_ty_ann(level + 1, *ann)
var_lst.extend(var_lst_sec)
else:
arg_ty = Var(Unbound(object(), level + 1))
var_lst.append(arg_ty)
fn_env.enter(pn, arg_ty)
inferred_ret_ty = infer(fn_env, level + 1, term.body)
if is_annotated(term.body):
ret_ty = inferred_ret_ty
else:
ret_ty = inst(level + 1, inferred_ret_ty)
if not all(map(is_mono, var_lst)):
error("polymorphc parameter inferred: {}".format(''.join(map(ppt, var_lst))))
ret_ty = generalise(level, Arrow(arg_ty, ret_ty))
return ret_ty
if isinstance(term, ELet):
var_name = term.id
bound = term.bound
body = term.body
var_ty = infer(env, level + 1, bound)
new_env = env.new_scope()
new_env.enter(var_name, var_ty)
return infer(new_env, level, body)
if isinstance(term, EApp):
fn_expr = term.f
arg = term.arg
fn_ty = inst(level + 1, infer(env, level + 1, fn_expr))
param_ty, ret_ty = match_fun_ty(fn_ty)
infer_arg(env, level + 1, param_ty, arg)
ret_ty = generalise(level, inst(level + 1, ret_ty))
return ret_ty
if isinstance(term, EAnn):
_, ty = inst_ty_ann(level, *term.ann)
expr_ty = infer(env, level, term.expr)
subsume(level, ty, expr_ty)
return ty
if isinstance(term, EOmit):
ty = Var(Unbound(object(), level))
return ty
if isinstance(term, EInt):
return Nom("int")
raise TypeError(type(term))
def ppt_io(t: Ty, io: StringIO, miss: MissingDict):
if isinstance(t, Forall):
s1 = ' '.join(map(lambda x: miss[x], t.bounds))
io.write('forall ')
io.write(s1)
io.write('. ')
ppt_io(t.ty, io, miss)
return
if isinstance(t, Nom):
io.write(t.name)
return
if isinstance(t, Var):
ref = t.ref
if isinstance(ref, Bound):
return io.write(miss[ref.id])
if isinstance(ref, Unbound):
io.write('^')
return io.write(miss[ref.id])
if isinstance(ref, Link):
return ppt_io(ref.ty, io, miss)
if isinstance(ref, Gen):
io.write('gen<')
return io.write(miss[ref.id])
raise TypeError(type(ref))
if isinstance(t, App):
io.write('(')
ppt_io(t.f, io, miss)
io.write(' ')
ppt_io(t.arg, io, miss)
io.write(')')
return
if isinstance(t, Arrow):
io.write('(')
ppt_io(t.arg, io, miss)
io.write(' -> ')
ppt_io(t.ret, io, miss)
io.write(')')
return
raise TypeError(type(t))
def f(id_ty_map: Dict[object, Ty], t):
if isinstance(t, Nom):
return t
if isinstance(t, Var):
ref = t.ref
if isinstance(ref, Link):
return f(id_ty_map, ref.ty)
if isinstance(ref, Bound):
return id_ty_map.get(ref.id) or t
return t
if isinstance(t, App):
return App(f(id_ty_map, t.f), f(id_ty_map, t.arg))
if isinstance(t, Arrow):
return Arrow(f(id_ty_map, t.arg), f(id_ty_map, t.ret))
if isinstance(t, Forall):
bounds = t.bounds
return Forall(bounds, f({k: v for k, v in id_ty_map.items() if k not in bounds}, t.ty))
raise TypeError(type(t))