def d3():
return (parse_typ(('a', '->', 'b')),
parse_ctx(
OrderedDict([
("s", (("a", "->", ("b", "->", "c")), '->',
(("a", "->", "b"), "->", ("a", "->", "c")))),
("k", ("a", "->", ("b", "->", "a"))),
])), 5)
def d2():
return (parse_typ('B'),
parse_ctx(
OrderedDict([
("f", ("A", "->", 'B')),
("x", "A"),
("y", "B"),
])), 5)
def domain_primes():
PRIME_LIMIT = 2000000
PRIMES = set(primes(PRIME_LIMIT))
global_symbols = {
'plus': lambda x: (lambda y: x + y),
'minus': lambda x: (lambda y: x - y),
'times': lambda x: (lambda y: x * y),
'rdiv': lambda p: (lambda q: p / q if q else 1),
}
R = 'R'
numbers = [(str(i + 1), R) for i in range(10)]
primes_lt_100 = primes(100)
goal = parse_typ(R)
stuff = [('plus', (R, '->', (R, '->', R))),
('minus', (R, '->', (R, '->', R))),
('times', (R, '->', (R, '->', R))),
('rdiv', (R, '->', (R, '->', R))), ('x', R),
('c', R)] # + numbers + [(str(p), R) for p in primes_lt_100]
gamma = parse_ctx(OrderedDict(stuff))
cache = FitnessCache()
def fitness(individual_app_tree):
global size_d
size = individual_app_tree.count_nodes()[app_tree.Leaf]
size_d[size] = size_d.get(size, 0) + 1
s = "lambda x,c : %s" % individual_app_tree.eval_str()
cres = cache.d.get(s, None)
if cres is not None:
return cres
fun = eval(s, global_symbols)
assert callable(fun)
try:
got = 0
i = 0
old = set()
while True:
candidate = fun(i, 0)
assert candidate < PRIME_LIMIT
if candidate not in PRIMES:
break
if candidate not in old:
got += 1
old.add(candidate)
i += 1
score = got
except (OverflowError, ValueError):
score = 0.0
cache.update(s, score)
return score
return goal, gamma, fitness, (lambda: len(cache)), cache
def make_family_1():
t_img = parse_typ('I') # simple Image type
t_op2 = fun_typ((t_img, t_img), t_img) # Simple binary operation
t_op4 = fun_typ((t_img, t_img, t_img, t_img),
t_img) # Simple tetra operation
goal = t_img
gamma = parse_ctx(
OrderedDict([(H, t_op2), (V, t_op2), (Q, t_op4), (W, t_img),
(B, t_img)]))
return goal, gamma
def domain_parity(SIZE):
values = product(*((True, False) for _ in range(SIZE)))
ALL = [(bits, reduce(xor, bits)) for bits in values]
global_symbols = {
# 's_xor': lambda x: (lambda y: x ^ y),
's_and': lambda x: (lambda y: x and y),
's_or': lambda x: (lambda y: x or y),
's_nand': lambda x: (lambda y: not (x and y)),
's_nor': lambda x: (lambda y: not (x or y)),
}
R = 'R'
goal = parse_typ(R)
vars = ['b%d' % i for i in range(SIZE)]
var_str = ','.join(vars)
stuff = [
# ('s_xor', (R, '->', (R, '->', R))),
('s_and', (R, '->', (R, '->', R))),
('s_or', (R, '->', (R, '->', R))),
('s_nor', (R, '->', (R, '->', R))),
('s_nand', (R, '->', (R, '->', R))),
] + [(v, R) for v in vars]
gamma = parse_ctx(OrderedDict(stuff))
cache = FitnessCache()
def format_one(eval_str):
return "lambda %s : %s" % (var_str, eval_str)
def fitness(individual_app_tree):
global size_d
size = individual_app_tree.count_nodes()[app_tree.Leaf]
size_d[size] = size_d.get(size, 0) + 1
s = format_one(individual_app_tree.eval_str())
cres = cache.d.get(s, None)
if cres is not None:
return cres
fun = eval(s, global_symbols)
assert callable(fun)
score = 0
for values, result in ALL:
if fun(*values) == result:
score += 1
cache.update(s, score)
return score
return goal, gamma, fitness, (lambda: len(cache)), cache
def make_simple_motion_domain(lib_defs):
R = parse_typ('R')
gamma = parse_ctx(
OrderedDict([(x0_sym, R), (v0_sym, R), (t_sym, R), (a_sym, R),
(half_sym, R), (plus_sym, fun_typ((R, R), R)),
(times_sym, fun_typ((R, R), R)),
(pair_sym, pair_cons_typ)]))
goal = parse_typ((P, R, R))
title = 'Simple Motion Lib'
optimal_size = 19
return title, goal, gamma, optimal_size
def d():
R = 'R'
return (parse_typ(R),
parse_ctx(
OrderedDict([
('plus', (R, '->', (R, '->', R))),
('minus', (R, '->', (R, '->', R))),
('times', (R, '->', (R, '->', R))),
('rdiv', (R, '->', (R, '->', R))),
('sin', (R, '->', R)),
('cos', (R, '->', R)),
('exp', (R, '->', R)),
('rlog', (R, '->', R)),
('x', R),
])), 20)
def d_lame_even_parity():
return (parse_typ('Bool'),
parse_ctx(OrderedDict([
("copy", ('a', '->', ('P', 'a', 'a'))),
("seri", (('a', '->', 'b'), '->', (('b', '->', 'c'), '->', ('a', '->', 'c')))),
("para", (('a', '->', 'b'), '->', (('c', '->', 'd'), '->', (('P', 'a', 'c'), '->', ('P', 'b', 'd'))))),
("s_and", (('P', 'Bool', 'Bool'), '->', 'Bool')),
("s_or", (('P', 'Bool', 'Bool'), '->', 'Bool')),
("s_nand", (('P', 'Bool', 'Bool'), '->', 'Bool')),
("s_nor", (('P', 'Bool', 'Bool'), '->', 'Bool')),
('foldr', ((('P', 'Bool', 'Bool'), '->', 'Bool'), '->', ('Bool', '->', (('List', 'Bool'), '->', 'Bool')))),
('True', 'Bool'),
('False', 'Bool'),
('xs', ('List', 'Bool')),
])),
9)
def d_general_even_parity_sk():
return (
parse_typ('Bool'),
parse_ctx(
OrderedDict([
('xs', ('List', 'Bool')),
("s", (("a", "->", ("b", "->", "c")), '->',
(("a", "->", "b"), "->", ("a", "->", "c")))),
("k", ("a", "->", ("b", "->", "a"))),
("and", ('Bool', '->', ('Bool', '->', 'Bool'))),
("or", ('Bool', '->', ('Bool', '->', 'Bool'))),
("nand", ('Bool', '->', ('Bool', '->', 'Bool'))),
("nor", ('Bool', '->', ('Bool', '->', 'Bool'))),
('foldr', (('a', '->', ('b', '->', 'b')), '->',
('b', '->', (('List', 'a'), '->', 'b')))),
('true', 'Bool'), ('false', 'Bool')
# ("head", (('List', 'Bool'), '->', ('Maybe', 'Bool'))),
# ("tail", (('List', 'Bool'), '->', ('Maybe', ('List', 'Bool')))),
])),
5)
def d1():
return (parse_typ(
(('P', 'A', ('P', 'A', 'A')), '->', ('P', 'A', ('P', 'A', 'A')))),
parse_ctx(
OrderedDict([
("s", (("a", "->", ("b", "->", "c")), '->',
(("a", "->", "b"), "->", ("a", "->", "c")))),
("k", ("a", "->", ("b", "->", "a"))),
("seri", (("Dag", 'a', 'b'), '->',
(("Dag", 'b', 'c'), '->', ("Dag", 'a', 'c')))),
("para", (("Dag", 'a', 'b'), '->',
(("Dag", 'c', 'd'), '->',
("Dag", ('P', 'a', 'c'), ('P', 'b', 'd'))))),
("mkDag", (("a", "->", "b"), '->', ("Dag", "a", "b"))),
("deDag", (
("Dag", "a", "b"),
'->',
("a", "->", "b"),
)),
("mkP", ("a", "->", ("b", "->", ('P', "a", 'b')))),
("fst", (('P', "a", 'b'), '->', 'a')),
("snd", (('P', "a", 'b'), '->', 'b')),
])), 4)
def make_smart_motion_domain(lib_defs):
u_typ_fun_sym = parse_typ('U')
def u(*args):
return parse_typ((u_typ_fun_sym, ) + args)
pos_typ = u('1', '0')
speed_typ = u('1', '-1')
time_typ = u('0', '1')
acceleration_typ = u('1', '-2')
dimensionless_typ = u('0', '0')
m, s, m1, m2, s1, s2 = map(parse_typ, ('m', 's', 'm1', 'm2', 's1', 's2'))
u_ms = u(m, s)
u_m1s1 = u(m1, s1)
u_m2s2 = u(m2, s2)
plus_m, plus_s = map(parse_typ, ('Pm', 'Ps'))
m_vals = range(0, 2)
s_vals = range(-2, 2)
def make_plus_eqs(plus_pred, name_prefix, vals):
eqs = []
i = 1
for a in vals:
for b in vals:
c = a + b
if c in vals:
eq_typ = parse_typ((plus_pred, str(a), str(b), str(c)))
eq_sym = name_prefix + str(i)
eqs.append((eq_sym, eq_typ))
lib_defs[eq_sym] = None # equations need no implementation
i += 1
return eqs
m_eq_typs = make_plus_eqs(plus_m, 'pm', m_vals)
s_eq_typs = make_plus_eqs(plus_s, 'ps', s_vals)
inputs = [(x0_sym, pos_typ), (v0_sym, speed_typ), (t_sym, time_typ),
(a_sym, acceleration_typ)]
constants = [(half_sym, dimensionless_typ)]
typ_plus = fun_typ((u_ms, u_ms), u_ms)
typ_times = fun_typ(
((plus_m, m1, m2, m), (plus_s, s1, s2, s), u_m1s1, u_m2s2), u_ms)
operators = [(plus_sym, typ_plus), (times_smart_sym, typ_times)]
pair_stuff = [(pair_sym, pair_cons_typ)]
gamma_list = inputs + constants + operators + m_eq_typs + s_eq_typs + pair_stuff
gamma = parse_ctx(OrderedDict(gamma_list))
goal = parse_typ((P, pos_typ, speed_typ))
title = 'Smart Motion Lib'
optimal_size = 29
# TODO !
return title, goal, gamma, optimal_size