def test_abstraction():
x = Expression.make('x')
y = Expression.make('y')
z = Expression.make('z')
assert lam(x, x) == I
assert lam(x, y) == APP(K, y)
assert lam(y, APP(APP(x, y), y)) == APP(W, x)
assert lam(z, APP(APP(x, z), APP(y, z))) == APP(APP(S, x), y)
assert lam(z, APP(APP(x, z), y)) == APP(APP(C, x), y)
assert lam(z, APP(x, APP(y, z))) == COMP(x, y)
assert lam(z, COMP(APP(x, z), APP(y, z))) == APP(APP(S, COMP(B, x)), y)
assert lam(z, COMP(APP(x, z), y)) == COMP(APP(CB, y), x)
assert lam(z, COMP(x, APP(y, z))) == COMP(APP(B, x), y)
assert lam(y, COMP(x, y)) == APP(B, x)
assert lam(x, COMP(x, y)) == APP(CB, y)
assert lam(z, JOIN(APP(x, z), APP(y, z))) == JOIN(x, y)
assert lam(z, JOIN(x, APP(y, z))) == COMP(APP(J, x), y)
assert lam(z, JOIN(APP(x, z), y)) == COMP(APP(J, y), x)
assert lam(y, JOIN(x, y)) == APP(J, x)
assert lam(x, JOIN(x, y)) == APP(J, y)
assert lam(z, RAND(APP(x, z), APP(y, z))) == RAND(x, y)
assert lam(z, RAND(x, APP(y, z))) == COMP(APP(R, x), y)
assert lam(z, RAND(APP(x, z), y)) == COMP(APP(R, y), x)
assert lam(y, RAND(x, y)) == APP(R, x)
assert lam(x, RAND(x, y)) == APP(R, y)
def validate(expr):
assert expr.is_rel(), expr
assert expr.name in ['LESS', 'EQUAL']
if expr.name != 'EQUAL':
print 'WARNING: not validating {0}'.format(expr)
return
while True:
try:
lhs, rhs = expr.args
lhs = head_normalize(lhs)
rhs = head_normalize(rhs)
assert len(lhs) == len(rhs),\
'Failed to validate\n {0}\nbecause\n {1} != {2}'.format(
expr, lhs, rhs)
assert lhs[0] == rhs[0],\
'Failed to validate\n {0}\nbecause \n{1} != {2}'.format(
expr, lhs[0], rhs[0])
for args in zip(lhs[1:], rhs[1:]):
validate(Expression.make(expr.name, *args))
break
except RequireVariable:
lhs, rhs = expr.args
fresh = get_fresh(expr.vars)
lhs = APP(lhs, fresh)
rhs = APP(rhs, fresh)
expr = Expression.make(expr.name, lhs, rhs)
except SkipValidation:
print 'WARNING: not validating {0}'.format(expr)
return
def __call__(self, term):
nargs = len(term.args)
if nargs == 0:
return self._fillings if term is HOLE else ()
elif nargs == 1:
name = term.name
key, = term.args
return tuple(Expression.make(name, f) for f in self(key))
elif nargs == 2:
name = term.name
lhs, rhs = term.args
return tuple(itertools.chain(
(Expression.make(name, f, rhs) for f in self(lhs)),
(Expression.make(name, lhs, f) for f in self(rhs)),
))
def define_a(
max_solutions=15,
max_memory=pomagma.analyst.synthesize.MAX_MEMORY,
verbose=1,
address=pomagma.analyst.ADDRESS):
'''
Search for definition of A = Join {<r, s> | r o s [= I}.
Tip: use pyprofile and snakeviz to profile this function:
$ pyprofile -o define_a.pstats -s time src/examples/synthesize.py define_a
$ snakeviz define_a.pstats
'''
assert max_solutions > 0, max_solutions
assert 0 < max_memory and max_memory < 1, max_memory
facts = parse_facts(A_THEORY)
hole = Expression.make('hole')
initial_sketch = parse_expr('HOLE')
language = {
'APP': 1.0,
# 'COMP': 1.6,
'JOIN': 3.0,
'B': 1.0,
'C': 1.3,
'A': 2.0,
'BOT': 2.0,
'TOP': 2.0,
'I': 2.2,
# 'Y': 2.3,
'K': 2.6,
'S': 2.7,
'J': 2.8,
'DIV': 3.0,
}
with pomagma.analyst.connect(address) as db:
results = synthesize_from_facts(
db=db,
facts=facts,
var=hole,
initial_sketch=initial_sketch,
language=language,
max_solutions=max_solutions,
max_memory=max_memory,
verbose=verbose)
print 'Possible Fillings:'
APP = Expression_2('APP')
f = Expression.make('f')
for complexity, term, filling in results:
print simplify_expr(APP(filling, f))
return results
def unguard_vars(expr):
if expr.name == 'VAR':
return expr.args[0]
elif expr.is_var():
return expr
else:
args = map(unguard_vars, expr.args)
return Expression.make(expr.name, *args)
def guard_vars(expr):
"""Whereas pomagma.compiler follows the variable naming convention defined
in pomagma.compiler.signature.is_var(), pomagma.analyst.validate and the
puddle editor require VAR guarded variables."""
if expr.name == 'VAR':
return expr
elif expr.is_var():
return VAR(expr)
else:
args = map(guard_vars, expr.args)
return Expression.make(expr.name, *args)
def weaken_sequent(fact):
if fact.arity == 'UnaryMeta':
return Expression.make(fact.name, weaken_sequent(fact.args[0]))
else:
assert fact.is_rel(), fact
if fact.name == 'EQUAL':
lhs, rhs = fact.args
if lhs == TOP or rhs == BOT:
return LESS(lhs, rhs)
elif rhs == TOP or lhs == BOT:
return LESS(rhs, lhs)
return fact
def test_compile_S():
# Compiling incremental search given: APP APP_x_y APP_y_z
# cost = 2.70067540518
# if S
# for x let APP_S_x
# for y if APP x y let APP_APP_S_x_y
# for z if APP y z let APP_APP_APP_S_x_y_z
# ensure EQUAL APP_APP_APP_S_x_y_z APP_APP_x_z_APP_y_z
S = Expression.make('S')
_test_sequent(
[],
[EQUAL(APP(APP(APP(S, x), y), z), APP(APP(x, z), APP(y, z)))])
def desugar_expr(self):
expr = Expression.make(self.name, *map(desugar_expr, self.args))
if expr.name == 'FUN':
var, body = expr.args
assert var.is_var(), var
expr = body.abstract(var)
elif expr.name == 'FIX':
var, body = expr.args
assert var.is_var(), var
expr = APP(Y, body.abstract(var))
elif expr.name == 'PAIR':
x, y = expr.args
expr = COMP(APP(CI, y), APP(CI, x))
elif expr.name == 'ABIND':
r, s, body = expr.args
assert r.is_var(), r
assert s.is_var(), s
expr = APP(A, body.abstract(s).abstract(r))
elif expr.name == 'FIXES':
typ, inhab = expr.args
expr = EQUAL(APP(typ, inhab), inhab)
return expr
def as_succedent(expr, bound):
while expr.name in ['OPTIONALLY', 'NONEGATE']:
expr = expr.args[0]
antecedents = set()
if expr.arity == 'Equation':
args = []
for arg in expr.args:
if arg.is_var() or arg.var in bound:
args.append(arg.var)
elif arg.args:
args.append(as_atom(arg))
for argarg in arg.args:
antecedents |= as_antecedents(argarg, bound)
else:
assert arg.arity == 'NullaryFunction', arg
args.append(arg.var)
antecedents.add(arg)
succedent = Expression.make(expr.name, *args)
else:
assert expr.args, expr.args
succedent = as_atom(expr)
for arg in expr.args:
antecedents |= as_antecedents(arg, bound)
return antecedents, succedent
def write_event_programs(programs, sequents):
event_tasks = {}
for sequent in sequents:
for event in compiler.get_events(sequent):
name = 'Variable' if event.is_var() else event.name
plans = sorted(compiler.compile_given(sequent, event))
cost = add_costs(c for (c, _, _) in plans)
tasks = event_tasks.setdefault(name, [])
tasks.append((cost, event, sequent, plans))
group_tasks = {}
for name, tasks in event_tasks.iteritems():
groupname = signature.get_arity(name)
group_tasks.setdefault(groupname, {})[name] = sorted(tasks)
group_tasks = sorted(group_tasks.iteritems())
group_id = 0
for groupname, group in group_tasks:
group = sorted(group.iteritems())
arity = signature.get_arity(group[0][0])
for eventname, tasks in group:
total_cost = add_costs(c for (c, _, _, _) in tasks)
programs += [
'',
'# ' + '-' * 76,
'# plans {}.*: total cost = {:0.1f}'.format(
group_id,
total_cost),
'# given {}'.format(eventname),
]
plan_id = 0
for _, event, sequent, plans in tasks:
diagonal = (
len(event.args) == 2 and event.args[0] == event.args[1])
if diagonal:
lhs = event.args[0]
assert lhs.arity == 'Variable'
rhs = Expression.make(lhs.name + '_')
event = Expression.make(event.name, lhs, rhs)
if arity == 'Variable':
given = 'GIVEN_EXISTS {var}'.format(var=event.name)
elif arity == 'UnaryRelation':
given = 'GIVEN_UNARY_RELATION {rel} {key}'.format(
rel=event.name,
key=event.args[0])
elif arity == 'BinaryRelation':
given = 'GIVEN_BINARY_RELATION {rel} {lhs} {rhs}'.format(
rel=event.name,
lhs=event.args[0],
rhs=event.args[1])
elif arity == 'NullaryFunction':
given = 'GIVEN_NULLARY_FUNCTION {fun} {val}'\
.format(
fun=event.name,
val=event.var.name)
elif arity == 'InjectiveFunction':
given = 'GIVEN_INJECTIVE_FUNCTION {fun} {key} {val}'\
.format(
fun=event.name,
key=event.args[0],
val=event.var.name)
elif arity == 'BinaryFunction':
given = 'GIVEN_BINARY_FUNCTION {fun} {lhs} {rhs} {val}'\
.format(
fun=event.name,
lhs=event.args[0],
rhs=event.args[1],
val=event.var.name)
elif arity == 'SymmetricFunction':
given = 'GIVEN_SYMMETRIC_FUNCTION {fun} {lhs} {rhs} {val}'\
.format(
fun=event.name,
lhs=event.args[0],
rhs=event.args[1],
val=event.var.name)
else:
raise ValueError('invalid arity: {}'.format(arity))
header = [given]
if diagonal:
header.append('IF_EQUAL {lhs} {rhs}'.format(
lhs=event.args[0],
rhs=event.args[1]))
for cost, seq, plan in plans:
programs += [
'',
'# plan {}.{}: cost = {:0.1f}'.format(
group_id,
plan_id,
cost),
'# using {}'.format(sequent),
'# infer {}'.format(seq),
]
programs += header
plan.program(programs)
plan_id += 1
group_id += 1
from parsable import parsable
import pomagma.analyst
from pomagma.analyst.synthesize import synthesize_from_facts
from pomagma.compiler.expressions import Expression, Expression_2
from pomagma.compiler.parser import parse_string_to_expr, parse_theory_string
from pomagma.compiler.simplify import simplify_expr
from pomagma.compiler.sugar import desugar_expr
APP = Expression_2('APP')
K = Expression.make('K')
F = Expression.make('F')
def parse_expr(string):
return desugar_expr(parse_string_to_expr(string))
def parse_facts(string):
facts = parse_theory_string(string)['facts']
facts = map(desugar_expr, facts)
for fact in facts:
for var in fact.vars:
assert len(var.name) > 2, 'unbound variable: {}'.format(var)
return facts
A_THEORY = (
'''
EQUAL conj FUN s FUN r FUN f COMP r COMP f s
EQUAL conj FUN s FUN r FUN f COMP COMP r f s
def parse_tokens_to_expr(tokens):
head = tokens.pop()
arity = get_arity(head)
nargs = get_nargs(arity)
args = [parse_tokens_to_expr(tokens) for _ in xrange(nargs)]
return Expression.make(head, *args)
def test_compile_I():
I = Expression.make('I')
_test_sequent(
[],
[EQUAL(APP(I, x), x)])
def test_compile_ap_quote():
AP = Expression.make('AP')
_test_sequent(
[],
[EQUAL(APP(APP(AP, QUOTE(x)), QUOTE(y)), QUOTE(APP(x, y)))])
def test_compile_qt_quote():
QT = Expression.make('QT')
_test_sequent(
[],
[EQUAL(APP(QT, QUOTE(x)), QUOTE(QUOTE(x)))])
def test_compile_eval():
EVAL = Expression.make('EVAL')
_test_sequent(
[],
[EQUAL(APP(EVAL, QUOTE(x)), x)])
def test_compile_comp_x_x_x():
U = Expression.make('U')
_test_sequent(
[EQUAL(COMP(x, x), x)],
[EQUAL(x, APP(U, x))])
def test_compile_bot():
BOT = Expression.make('BOT')
_test_sequent(
[],
[LESS(BOT, x)])
def test_compile_Y():
Y = Expression.make('Y')
_test_sequent(
[],
[EQUAL(APP(Y, f), APP(f, APP(Y, f)))])
def as_atom(expr):
args = [arg.var for arg in expr.args]
return Expression.make(expr.name, *args)
def test_compile_K():
K = Expression.make('K')
_test_sequent(
[],
[EQUAL(APP(APP(K, x), y), x)])
def get_fresh(bound):
for name in 'abcdefghijklmnopqrstuvwxyz':
fresh = Expression.make(name)
if fresh not in bound:
return fresh
raise NotImplementedError('Exceeded fresh variable limit')
from pomagma.compiler.expressions import Expression
from pomagma.compiler.parser import parse_corpus
from pomagma.compiler.util import inputs
from pomagma.util import TODO
HOLE = Expression.make('HOLE')
class Corpus(object):
'''
Corpus is a general-recursive set of definitions with holes.
'''
def __init__(self):
self._defs = {}
def load(self, filename):
with open(filename) as f:
self._defs = parse_corpus(f, filename=filename)
def dump(self, filename):
with open(filename, 'w') as f:
f.write('# Corpus written by {}'.format(__file__))
for var, expr in sorted(self._defs.iteritems()):
assert isinstance(var, basestring), var
assert isinstance(expr, Expression), expr
f.write('\nEQUAL {} {}'.format(var, expr))
def __getitem__(self, var):
assert isinstance(var, Expression), var
assert var.is_var(), var
def abstract(self, var):
assert isinstance(var, Expression)
assert var.is_var()
if self.name == 'VAR':
self = self.args[0]
if self.is_var():
if self == var:
return I
else:
return APP(K, self)
elif self.is_fun():
name = self.name
if var not in self.vars:
return APP(K, self)
elif name == 'APP':
# I,K,C,SW,COMP,eta abstraction
lhs, rhs = self.args
if var in lhs.vars:
lhs_abs = lhs.abstract(var)
if var in rhs.vars:
if rhs == var:
return APP(W, lhs_abs)
else:
return APP(APP(S, lhs_abs), rhs.abstract(var))
else:
return APP(APP(C, lhs_abs), rhs)
else:
assert var in rhs.vars
if rhs == var:
return lhs
else:
return COMP(lhs, rhs.abstract(var))
elif name == 'COMP':
# K,B,CB,C,S,COMP,eta abstraction
lhs, rhs = self.args
if var in lhs.vars:
lhs_abs = lhs.abstract(var)
if var in rhs.vars:
return APP(APP(S, COMP(B, lhs_abs)), rhs.abstract(var))
else:
if lhs == var:
return APP(CB, rhs)
else:
return COMP(APP(CB, rhs), lhs_abs)
else:
assert var in rhs.vars
if rhs == var:
return APP(B, lhs)
else:
return COMP(APP(B, lhs), rhs.abstract(var))
elif name == 'JOIN':
return abstract_symmetric(self, var, J, JOIN)
elif name == 'RAND':
return abstract_symmetric(self, var, R, RAND)
else:
raise AbstractionFailed
elif self.is_rel():
args = [arg.abstract(var) for arg in self.args]
return Expression.make(self.name, *args)
else:
raise ValueError('bad expression: %s' % self.name)
def test_compile_B_comp():
B = Expression.make('B')
_test_sequent(
[],
[EQUAL(APP(APP(B, x), y), COMP(x, y))])
def test_compile_W():
W = Expression.make('W')
_test_sequent(
[],
[EQUAL(APP(APP(W, x), y), APP(APP(x, y), y))])
def test_compile_C():
C = Expression.make('C')
_test_sequent(
[],
[EQUAL(APP(APP(APP(C, x), y), z), APP(APP(x, z), y))])
def insert(self, key, value='HOLE'):
var = Expression.make(key)
expr = Expression.make(value)
self[var] = expr
def test_compile_B_app():
B = Expression.make('B')
_test_sequent(
[],
[EQUAL(APP(APP(APP(B, x), y), z), APP(x, APP(y, z)))])
