def queries_equivalent(q1: Query,
q2: Query,
state_vars: [EVar],
extern_funcs: {str: TFunc},
assumptions: Exp = ETRUE):
"""Determine whether two queries always return the same result.
This function also checks that the two queries have semantically equivalent
preconditions. Checking the preconditions is necessary to ensure semantic
equivalence of the queries: a query object should be interpreted to mean
"if my preconditions hold then I compute and return my body expression".
If two queries do not have semantically equivalent preconditions, then
there might be cases where one is obligated to return a value and the other
has no defined behavior.
"""
with task("checking query equivalence", q1=q1.name, q2=q2.name):
if q1.ret.type != q2.ret.type:
return False
q1args = dict(q1.args)
q2args = dict(q2.args)
if q1args != q2args:
return False
checker = solver_for_context(context=RootCtx(
state_vars=state_vars,
args=[EVar(a).with_type(t) for (a, t) in q1.args],
funcs=extern_funcs),
assumptions=assumptions)
q1a = EAll(q1.assumptions)
q2a = EAll(q2.assumptions)
return checker.valid(EEq(q1a, q2a)) and checker.valid(
EImplies(q1a, EEq(q1.ret, q2.ret)))
def queries_equivalent(q1 : Query, q2 : Query, state_vars : [EVar], extern_funcs : { str : TFunc }, assumptions : Exp = ETRUE):
"""Determine whether two queries always return the same result.
This function also checks that the two queries have semantically equivalent
preconditions. Checking the preconditions is necessary to ensure semantic
equivalence of the queries: a query object should be interpreted to mean
"if my preconditions hold then I compute and return my body expression".
If two queries do not have semantically equivalent preconditions, then
there might be cases where one is obligated to return a value and the other
has no defined behavior.
"""
with task("checking query equivalence", q1=q1.name, q2=q2.name):
if q1.ret.type != q2.ret.type:
return False
q1args = dict(q1.args)
q2args = dict(q2.args)
if q1args != q2args:
return False
checker = solver_for_context(
context=RootCtx(
state_vars=state_vars,
args=[EVar(a).with_type(t) for (a, t) in q1.args],
funcs=extern_funcs),
assumptions=assumptions)
q1a = EAll(q1.assumptions)
q2a = EAll(q2.assumptions)
return checker.valid(EEq(q1a, q2a)) and checker.valid(EImplies(q1a, EEq(q1.ret, q2.ret)))
def improve(target: Exp,
context: Context,
assumptions: Exp = ETRUE,
stop_callback: Callable[[], bool] = never_stop,
hints: [Exp] = (),
examples: [{
str: object
}] = (),
cost_model: CostModel = None,
ops: [Op] = (),
improve_count: Value = None):
"""Improve the target expression using enumerative synthesis.
This function is a generator that yields increasingly better and better
versions of the input expression `target` in the given `context`. The
`cost_model` defines "better".
It periodically calls `stop_callback` and exits gracefully when
`stop_callback` returns True.
Other parameters:
- assumptions: a precondition. The yielded improvements will only be
correct when the assumptions are true.
- hints: expressions that might be useful. These will be explored
first when looking for improvements.
- examples: inputs that will be used internally to differentiate
semantically distinct expressions. This procedure discovers more
examples as it runs, so there usually isn't a reason to provide any.
- ops: update operations. This function may make different choices
about what expressions are state expressions based on what changes
can happen to that state.
Key differences from "regular" enumerative synthesis:
- Expressions are either "state" expressions or "runtime" expressions,
allowing this algorithm to choose what things to store on the data
structure and what things to compute at query execution time. (The
cost model is ultimately responsible for this choice.)
- If a better version of *any subexpression* for the target is found,
it is immediately substituted in and the overall expression is
returned. This "smooths out" the search space a little, allowing us
find kinda-good solutions very quickly, even if the best possible
solution is out of reach. This is more desireable than running for
an indeterminate amount of time doing nothing.
"""
print("call to improve:")
print("""improve(
target={target!r},
context={context!r},
assumptions={assumptions!r},
stop_callback={stop_callback!r},
hints={hints!r},
examples={examples!r},
cost_model={cost_model!r},
ops={ops!r})""".format(target=target,
context=context,
assumptions=assumptions,
stop_callback=stop_callback,
hints=hints,
examples=examples,
cost_model=cost_model,
ops=ops))
target = inline_lets(target)
target = freshen_binders(target, context)
assumptions = freshen_binders(assumptions, context)
if heuristic_done(target):
print("The target already looks great!")
return
print()
print("improving: {}".format(pprint(target)))
print("subject to: {}".format(pprint(assumptions)))
print()
is_wf = exp_wf(target, context=context, assumptions=assumptions)
assert is_wf, "initial target is not well-formed: {}".format(is_wf)
state_vars = [v for (v, p) in context.vars() if p == STATE_POOL]
if eliminate_vars.value and can_elim_vars(target, assumptions, state_vars):
print("This job does not depend on state_vars.")
# TODO: what can we do about it?
hints = ([freshen_binders(h, context) for h in hints] + [
freshen_binders(wrap_naked_statevars(a, state_vars), context)
for a in break_conj(assumptions)
] + [target])
print("{} hints".format(len(hints)))
for h in hints:
print(" - {}".format(pprint(h)))
vars = list(v for (v, p) in context.vars())
funcs = context.funcs()
solver = solver_for_context(context, assumptions=assumptions)
if not solver.satisfiable(ETRUE):
print("assumptions are unsat; this query will never be called")
yield construct_value(target.type)
return
is_good = possibly_useful(solver, target, context)
assert is_good, "WARNING: this target is already a bad idea\n is_good = {}, target = {}".format(
is_good, target)
examples = list(examples)
if cost_model is None:
cost_model = CostModel(funcs=funcs, assumptions=assumptions)
watched_targets = [target]
blacklist = {}
while True:
# 1. find any potential improvement to any sub-exp of target
for new_target in search_for_improvements(targets=watched_targets,
wf_solver=solver,
context=context,
examples=examples,
cost_model=cost_model,
stop_callback=stop_callback,
hints=hints,
ops=ops,
blacklist=blacklist):
print("Found candidate improvement: {}".format(pprint(new_target)))
# 2. check
with task("verifying candidate"):
counterexample = solver.satisfy(ENot(EEq(target, new_target)))
if counterexample is not None:
if counterexample in examples:
print("assumptions = {!r}".format(assumptions))
print("duplicate example: {!r}".format(counterexample))
print("old target = {!r}".format(target))
print("new target = {!r}".format(new_target))
raise Exception("got a duplicate example")
# a. if incorrect: add example, restart
examples.append(counterexample)
print("new example: {!r}".format(counterexample))
print("wrong; restarting with {} examples".format(
len(examples)))
break
else:
# b. if correct: yield it, watch the new target, goto 1
print("The candidate is valid!")
print(repr(new_target))
print("Determining whether to yield it...")
with task("updating frontier"):
to_evict = []
keep = True
old_better = None
for old_target in watched_targets:
evc = retention_policy(new_target, context, old_target,
context, RUNTIME_POOL,
cost_model)
if old_target not in evc:
to_evict.append(old_target)
if new_target not in evc:
old_better = old_target
keep = False
break
for t in to_evict:
watched_targets.remove(t)
if not keep:
print(
"Whoops! Looks like we already found something better."
)
print(" --> {}".format(pprint(old_better)))
continue
if target in to_evict:
print("Yep, it's an improvement!")
yield new_target
if heuristic_done(new_target):
print("target now matches doneness heuristic")
return
target = new_target
else:
print("Nope, it isn't substantially better!")
watched_targets.append(new_target)
print("Now watching {} targets".format(len(watched_targets)))
break
if improve_count is not None:
with improve_count.get_lock():
improve_count.value += 1
def improve(target: Exp,
context: Context,
assumptions: Exp = T,
stop_callback=never_stop,
hints: [Exp] = (),
examples: [{
str: object
}] = (),
cost_model: CostModel = None,
ops: [Op] = ()):
"""
Improve the target expression using enumerative synthesis.
This function is a generator that yields increasingly better and better
versions of the input expression `target`.
Notes on internals of this algorithm follow.
Key differences from "regular" enumerative synthesis:
- Expressions are either "state" expressions or "runtime" expressions,
allowing this algorithm to choose what things to store on the data
structure and what things to compute at query execution time. (The
cost model is ultimately responsible for this choice.)
- If a better version of *any subexpression* for the target is found,
it is immediately substituted in and the overall expression is
returned. This "smooths out" the search space a little, and lets us
find kinda-good solutions very quickly, even if the best possible
solution is out of reach.
"""
print("call to improve:")
print("""improve(
target={target!r},
context={context!r},
assumptions={assumptions!r},
stop_callback={stop_callback!r},
hints={hints!r},
examples={examples!r},
cost_model={cost_model!r},
ops={ops!r})""".format(target=target,
context=context,
assumptions=assumptions,
stop_callback=stop_callback,
hints=hints,
examples=examples,
cost_model=cost_model,
ops=ops))
target = freshen_binders(target, context)
assumptions = freshen_binders(assumptions, context)
print()
print("improving: {}".format(pprint(target)))
print("subject to: {}".format(pprint(assumptions)))
print()
is_wf = exp_wf(target, context=context, assumptions=assumptions)
if not is_wf:
print(
"WARNING: initial target is not well-formed [{}]; this might go poorly..."
.format(is_wf))
print(pprint(is_wf.offending_subexpression))
print(pprint(is_wf.offending_subexpression.type))
state_vars = [v for (v, p) in context.vars() if p == STATE_POOL]
if eliminate_vars.value and can_elim_vars(target, assumptions, state_vars):
print("This job does not depend on state_vars.")
# TODO: what can we do about it?
hints = ([freshen_binders(h, context) for h in hints] + [
freshen_binders(wrap_naked_statevars(a, state_vars), context)
for a in break_conj(assumptions)
] + [target])
print("{} hints".format(len(hints)))
for h in hints:
print(" - {}".format(pprint(h)))
vars = list(v for (v, p) in context.vars())
funcs = context.funcs()
solver = solver_for_context(context, assumptions=assumptions)
if not solver.satisfiable(T):
print("assumptions are unsat; this query will never be called")
yield construct_value(target.type)
return
examples = list(examples)
if cost_model is None:
cost_model = CostModel(funcs=funcs, assumptions=assumptions)
watched_targets = [target]
learner = Learner(watched_targets,
solver,
context,
examples,
cost_model,
stop_callback,
hints,
ops=ops)
while True:
# 1. find any potential improvement to any sub-exp of target
for new_target in learner.search():
print("Found candidate improvement: {}".format(pprint(new_target)))
# 2. check
with task("verifying candidate"):
counterexample = solver.satisfy(ENot(EEq(target, new_target)))
if counterexample is not None:
if counterexample in examples:
print("assumptions = {!r}".format(assumptions))
print("duplicate example: {!r}".format(counterexample))
print("old target = {!r}".format(target))
print("new target = {!r}".format(new_target))
raise Exception("got a duplicate example")
# a. if incorrect: add example, reset the learner
examples.append(counterexample)
event("new example: {!r}".format(counterexample))
print("wrong; restarting with {} examples".format(
len(examples)))
learner.reset(examples)
break
else:
# b. if correct: yield it, watch the new target, goto 1
print("The candidate is valid!")
print(repr(new_target))
print("Determining whether to yield it...")
with task("updating frontier"):
to_evict = []
keep = True
old_better = None
for old_target in watched_targets:
evc = eviction_policy(new_target, context, old_target,
context, RUNTIME_POOL,
cost_model)
if old_target not in evc:
to_evict.append(old_target)
if new_target not in evc:
old_better = old_target
keep = False
break
for t in to_evict:
watched_targets.remove(t)
if not keep:
print(
"Whoops! Looks like we already found something better."
)
print(" --> {}".format(pprint(old_better)))
continue
if target in to_evict:
print("Yep, it's an improvement!")
yield new_target
if heuristic_done(new_target):
print("target now matches doneness heuristic")
return
target = new_target
else:
print("Nope, it isn't substantially better!")
watched_targets.append(new_target)
print("Now watching {} targets".format(len(watched_targets)))
learner.watch(watched_targets)
break
def improve(
target : Exp,
context : Context,
assumptions : Exp = ETRUE,
stop_callback : Callable[[], bool] = never_stop,
hints : [Exp] = (),
examples : [{str:object}] = (),
cost_model : CostModel = None,
ops : [Op] = (),
improve_count : Value = None):
"""Improve the target expression using enumerative synthesis.
This function is a generator that yields increasingly better and better
versions of the input expression `target` in the given `context`. The
`cost_model` defines "better".
It periodically calls `stop_callback` and exits gracefully when
`stop_callback` returns True.
Other parameters:
- assumptions: a precondition. The yielded improvements will only be
correct when the assumptions are true.
- hints: expressions that might be useful. These will be explored
first when looking for improvements.
- examples: inputs that will be used internally to differentiate
semantically distinct expressions. This procedure discovers more
examples as it runs, so there usually isn't a reason to provide any.
- ops: update operations. This function may make different choices
about what expressions are state expressions based on what changes
can happen to that state.
Key differences from "regular" enumerative synthesis:
- Expressions are either "state" expressions or "runtime" expressions,
allowing this algorithm to choose what things to store on the data
structure and what things to compute at query execution time. (The
cost model is ultimately responsible for this choice.)
- If a better version of *any subexpression* for the target is found,
it is immediately substituted in and the overall expression is
returned. This "smooths out" the search space a little, allowing us
find kinda-good solutions very quickly, even if the best possible
solution is out of reach. This is more desireable than running for
an indeterminate amount of time doing nothing.
"""
print("call to improve:")
print("""improve(
target={target!r},
context={context!r},
assumptions={assumptions!r},
stop_callback={stop_callback!r},
hints={hints!r},
examples={examples!r},
cost_model={cost_model!r},
ops={ops!r})""".format(
target=target,
context=context,
assumptions=assumptions,
stop_callback=stop_callback,
hints=hints,
examples=examples,
cost_model=cost_model,
ops=ops))
target = inline_lets(target)
target = freshen_binders(target, context)
assumptions = freshen_binders(assumptions, context)
if heuristic_done(target):
print("The target already looks great!")
return
print()
print("improving: {}".format(pprint(target)))
print("subject to: {}".format(pprint(assumptions)))
print()
is_wf = exp_wf(target, context=context, assumptions=assumptions)
assert is_wf, "initial target is not well-formed: {}".format(is_wf)
state_vars = [v for (v, p) in context.vars() if p == STATE_POOL]
if eliminate_vars.value and can_elim_vars(target, assumptions, state_vars):
print("This job does not depend on state_vars.")
# TODO: what can we do about it?
hints = ([freshen_binders(h, context) for h in hints]
+ [freshen_binders(wrap_naked_statevars(a, state_vars), context) for a in break_conj(assumptions)]
+ [target])
print("{} hints".format(len(hints)))
for h in hints:
print(" - {}".format(pprint(h)))
vars = list(v for (v, p) in context.vars())
funcs = context.funcs()
solver = solver_for_context(context, assumptions=assumptions)
if not solver.satisfiable(ETRUE):
print("assumptions are unsat; this query will never be called")
yield construct_value(target.type)
return
is_good = possibly_useful(solver, target, context)
assert is_good, "WARNING: this target is already a bad idea\n is_good = {}, target = {}".format(is_good, target)
examples = list(examples)
if cost_model is None:
cost_model = CostModel(funcs=funcs, assumptions=assumptions)
watched_targets = [target]
blacklist = {}
while True:
# 1. find any potential improvement to any sub-exp of target
for new_target in search_for_improvements(
targets=watched_targets,
wf_solver=solver,
context=context,
examples=examples,
cost_model=cost_model,
stop_callback=stop_callback,
hints=hints,
ops=ops,
blacklist=blacklist):
print("Found candidate improvement: {}".format(pprint(new_target)))
# 2. check
with task("verifying candidate"):
counterexample = solver.satisfy(ENot(EEq(target, new_target)))
if counterexample is not None:
if counterexample in examples:
print("assumptions = {!r}".format(assumptions))
print("duplicate example: {!r}".format(counterexample))
print("old target = {!r}".format(target))
print("new target = {!r}".format(new_target))
raise Exception("got a duplicate example")
# a. if incorrect: add example, restart
examples.append(counterexample)
print("new example: {!r}".format(counterexample))
print("wrong; restarting with {} examples".format(len(examples)))
break
else:
# b. if correct: yield it, watch the new target, goto 1
print("The candidate is valid!")
print(repr(new_target))
print("Determining whether to yield it...")
with task("updating frontier"):
to_evict = []
keep = True
old_better = None
for old_target in watched_targets:
evc = retention_policy(new_target, context, old_target, context, RUNTIME_POOL, cost_model)
if old_target not in evc:
to_evict.append(old_target)
if new_target not in evc:
old_better = old_target
keep = False
break
for t in to_evict:
watched_targets.remove(t)
if not keep:
print("Whoops! Looks like we already found something better.")
print(" --> {}".format(pprint(old_better)))
continue
if target in to_evict:
print("Yep, it's an improvement!")
yield new_target
if heuristic_done(new_target):
print("target now matches doneness heuristic")
return
target = new_target
else:
print("Nope, it isn't substantially better!")
watched_targets.append(new_target)
print("Now watching {} targets".format(len(watched_targets)))
break
if improve_count is not None:
with improve_count.get_lock():
improve_count.value += 1