############# Section 5
# Program, VC, and Instantiation
def pgm(x, ret):
return IteBool(x == nil, ret == nil, ret == next(x))
def vc(x, ret):
return Implies(dlist(x),
Implies(pgm(x, ret), list(ret)))
deref = [x]
const = [nil]
verification_condition = vc(x,ret)
# End of input
###########################################################################################################################
# Lemma synthesis stub
##########################################################################################################################
config_params = {'mode': 'random', 'num_true_models':0}
config_params['pfp_dict'] = pfp_dict
config_params['use_cex_models'] = True
name = 'dlist-list'
grammar_string = importlib_resources.read_text('experiments', 'grammar_{}.sy'.format(name))
synth_dict = {}
solveProblem(fcts_z3, axioms_python, axioms_z3, unfold_recdefs_z3, unfold_recdefs_python, deref, const, verification_condition, name, grammar_string, config_params, synth_dict)
AddRecDefinition(bst, x, If(x == nil, True,
And(0 < key(x),
And(key(x) < 100,
And(bst(lft(x)),
And(bst(rght(x)),
And(maxr(lft(x)) <= key(x),
key(x) <= minr(rght(x)))))))))
AddRecDefinition(hbst, x, If(x == nil, fgsetsort.lattice_bottom,
SetAdd(SetUnion(hbst(lft(x)), hbst(rght(x))), x)))
AddAxiom((), lft(nil) == nil)
AddAxiom((), rght(nil) == nil)
# Problem parameters
goal = Implies(bst(x), Implies(And(x != nil,
And(IsMember(y, hbst(x)),
And(k == minr(x),
And(k == minr(y), y != nil)))),
k == minr(lft(y))))
# parameters representing the grammar for synth-fun and
# terms on which finite model is extracted
# TODO: extract this automatically from grammar_string
v = Var('v', fgsort)
lemma_grammar_args = [v, y, k, nil]
lemma_grammar_terms = {v, lft(v), rght(v), nil, y}
name = 'bst-minimal'
grammar_string = importlib_resources.read_text('experiments', 'grammar_{}.sy'.format(name))
solveProblem(lemma_grammar_args, lemma_grammar_terms, goal, name, grammar_string)
# Uncomment this line for fixed_depth=1 mode
# config_params['goal_instantiation_mode'] = proveroptions.fixed_depth # Default depth is 1
# Uncomment these two lines for manual instantiation mode
# config_params['goal_instantiation_mode'] = proveroptions.manual_instantiation
# config_params['goal_instantiation_terms'] = {x, nxt(x)}
goal_heaplet_1a = Implies(hlseg(x, y, v), Implies(lseg(y, z), hlseg(x, z, v)))
goal_heaplet_1b = Implies(
lseg(x, y), Implies(y != nil, Implies(lseg(y, z), hlseg(x, z, y))))
goal_heaplet_2 = Implies(hlseg(x, z, v),
Implies(lseg(y, z), Or(v == y, hlseg(x, y, v))))
# lemma synthesis
v1, v2, v3, v4 = Vars('v1 v2 v3 v4', fgsort)
lemma_grammar_args = [v1, v2, nil]
lemma_grammar_terms = {
v1, nil,
nxt(nil), v2,
nxt(v2),
nxt(v1),
nxt(nxt(v1)),
nxt(nxt(nxt(v1)))
}
name = 'lseg-nil-list'
grammar_string = importlib_resources.read_text('experiments',
'grammar_{}.sy'.format(name))
solveProblem(lemma_grammar_args, lemma_grammar_terms, goal_heaplet_1a, name,
grammar_string)