def test_derivation_with_general_window(): block = fully_cross_block([color, text, congruent_bookend], [color, text], []) # congruent bookend - yes d = Derivation(16, [[0, 2], [1, 3]], congruent_bookend) backend_request = BackendRequest(19) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(17, Or([And([1, 3]), And([2, 4])])), Iff(19, Or([And([13, 15]), And([14, 16])])) ]), 19) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf] # congruent bookend - no d = Derivation(17, [[0, 3], [1, 2]], congruent_bookend) backend_request = BackendRequest(19) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(18, Or([And([1, 4]), And([2, 3])])), Iff(20, Or([And([13, 16]), And([14, 15])])) ]), 19) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def test_tseitin_rep_iff(): from sweetpea.logic import __tseitin_rep, _Cache clauses = [] cache = _Cache(3) # Make sure return is correct and value was cached. assert __tseitin_rep(Iff(1, 2), clauses, cache) == 3 assert cache.get(str(Iff(1, 2))) == 3 # Make sure equivalence clauses were added. assert Or([ 1, 2, 3 ]) in clauses assert Or([Not(1), Not(2), 3 ]) in clauses assert Or([ 1, Not(2), Not(3)]) in clauses assert Or([Not(1), 2, Not(3)]) in clauses # Don't duplicate clauses when the cache was already populated. clauses = [] cache = _Cache(3) # Prewarm the cache. assert cache.get(str(Iff(1, 2))) == 3 assert __tseitin_rep(Iff(1, 2), clauses, cache) == 3 # Make sure no clauses were added. assert clauses == []
def test_to_cnf_switching(): formula = Or([ And([3, 4]), And([Not(2), Or([1, 5])]) ]) expected_cnf = And([ Or([3, Not(6)]), Or([4, Not(6)]), Or([1, 5, 6]), Or([Not(2), 6]) ]) assert to_cnf_switching(formula, 6) == (expected_cnf, 7) formula = And([ Iff(1, And([2, 3])), Iff(4, And([5, 6])) ]) expected_cnf = And([ Or([1, Not(2), Not(3)]), Or([Not(1), 2]), Or([Not(1), 3]), Or([4, Not(5), Not(6)]), Or([Not(4), 5]), Or([Not(4), 6]) ]) assert to_cnf_switching(formula, 7) == (expected_cnf, 7)
def test_eliminate_iff(): from sweetpea.logic import __eliminate_iff # P <-> Q ==> (P v ~Q) ^ (~P v Q) assert __eliminate_iff(Iff(1, 2)) == And([Or([1, Not(2)]), Or([Not(1), 2])]) assert __eliminate_iff(Iff(1, And([2, 3]))) == And([ Or([1, Not(And([2, 3]))]), Or([Not(1), And([2, 3])]) ])
def test_derivation(): # Congruent derivation d = Derivation(4, [[0, 2], [1, 3]], con_factor) backend_request = BackendRequest(24) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(5, Or([And([1, 3]), And([2, 4])])), Iff(11, Or([And([7, 9]), And([8, 10])])), Iff(17, Or([And([13, 15]), And([14, 16])])), Iff(23, Or([And([19, 21]), And([20, 22])])) ]), 24) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf] # Incongruent derivation d = Derivation(5, [[0, 3], [1, 2]], con_factor) backend_request = BackendRequest(24) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(6, Or([And([1, 4]), And([2, 3])])), Iff(12, Or([And([7, 10]), And([8, 9])])), Iff(18, Or([And([13, 16]), And([14, 15])])), Iff(24, Or([And([19, 22]), And([20, 21])])) ]), 24) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def test_to_cnf_naive(): assert to_cnf_naive(1, 2) == (And([1]), 2) assert to_cnf_naive(And([1]), 2) == (And([1]), 2) assert to_cnf_naive(And([1, 2]), 3) == (And([1, 2]), 3) assert to_cnf_naive(Or([1, 2]), 3) == (And([Or([1, 2])]), 3) assert to_cnf_naive(Or([1, And([2, 3])]), 4) == (And([Or([1, 2]), Or([1, 3])]), 4) formula = And([Iff(1, And([2, 3])), Iff(4, And([5, 6]))]) expected_cnf = And([ Or([1, Not(2), Not(3)]), Or([Not(1), 2]), Or([Not(1), 3]), Or([4, Not(5), Not(6)]), Or([Not(4), 5]), Or([Not(4), 6]) ]) assert to_cnf_switching(formula, 7) == (expected_cnf, 7)
def apply(block: MultipleCrossBlock, backend_request: BackendRequest) -> None: # Treat each crossing seperately, and repeat the same process as fullycross for c in block.crossing: fresh = backend_request.fresh # Step 1: Get a list of the trials that are involved in the crossing. crossing_size = max(block.min_trials, block.crossing_size()) crossing_trials = list(filter(lambda t: all(map(lambda f: f.applies_to_trial(t), c)), range(1, block.trials_per_sample() + 1))) crossing_trials = crossing_trials[:crossing_size] # Step 2: For each trial, cross all levels of all factors in the crossing. crossing_factors = list(map(lambda t: (list(product(*[block.factor_variables_for_trial(f, t) for f in c]))), crossing_trials)) # Step 3: For each trial, cross all levels of all design-only factors in the crossing. design_factors = cast(List[List[List[int]]], []) design_factors = list(map(lambda _: [], crossing_trials)) for f in list(filter(lambda f: f not in c and not f.has_complex_window, block.design)): for i, t in enumerate(crossing_trials): design_factors[i].append(block.factor_variables_for_trial(f, t)) design_combinations = cast(List[List[Tuple[int, ...]]], []) design_combinations = list(map(lambda l: list(product(*l)), design_factors)) # Step 4: For each trial, combine each of the crossing factors with all of the design-only factors. crossings = cast(List[List[List[Tuple[int, ...]]]], []) for i, t in enumerate(crossing_trials): crossings.append(list(map(lambda c: [c] + design_combinations[i], crossing_factors[i]))) # Step 5: Remove crossings that are not possible. # From here on ignore all values other than the first in every list. crossings = block.filter_excluded_derived_levels(crossings) # Step 6: Allocate additional variables to represent each crossing. num_state_vars = list(map(lambda c: len(c), crossings)) state_vars = list(range(fresh, fresh + sum(num_state_vars))) fresh += sum(num_state_vars) # Step 7: Associate each state variable with its crossing. flattened_crossings = list(chain.from_iterable(crossings)) iffs = list(map(lambda n: Iff(state_vars[n], And([*flattened_crossings[n][0]])), range(len(state_vars)))) # Step 8: Constrain each crossing to occur in only one trial. states = list(chunk(state_vars, block.crossing_size())) transposed = cast(List[List[int]], list(map(list, zip(*states)))) # We Use n < 2 rather than n = 1 here because they may exclude some levels from the crossing. # This ensures that there won't be duplicates, while still allowing some to be missing. # backend_request.ll_requests += list(map(lambda l: LowLevelRequest("LT", 2, l), transposed)) backend_request.ll_requests += list(map(lambda l: LowLevelRequest("GT", 0, l), transposed)) (cnf, new_fresh) = block.cnf_fn(And(iffs), fresh) backend_request.cnfs.append(cnf) backend_request.fresh = new_fresh
def test_derivation_with_transition(): block = fully_cross_block([color, text, color_repeats_factor], [color, text], []) # Color repeats derivation d = Derivation(16, [[0, 4], [1, 5]], color_repeats_factor) backend_request = BackendRequest(23) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(17, Or([And([1, 5]), And([2, 6])])), Iff(19, Or([And([5, 9]), And([6, 10])])), Iff(21, Or([And([9, 13]), And([10, 14])])) ]), 23) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf] # Color does not repeat derivation d = Derivation(17, [[0, 5], [1, 4]], color_repeats_factor) backend_request = BackendRequest(23) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(18, Or([And([1, 6]), And([2, 5])])), Iff(20, Or([And([5, 10]), And([6, 9])])), Iff(22, Or([And([9, 14]), And([10, 13])])) ]), 23) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_multiple_transitions(): block = fully_cross_block( [color, text, color_repeats_factor, text_repeats_factor], [color, text], []) # Text repeats derivation d = Derivation(22, [[2, 6], [3, 7]], text_repeats_factor) backend_request = BackendRequest(29) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(23, Or([And([3, 7]), And([4, 8])])), Iff(25, Or([And([7, 11]), And([8, 12])])), Iff(27, Or([And([11, 15]), And([12, 16])])) ]), 29) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf] # Text does not repeat derivation d = Derivation(23, [[2, 7], [3, 6]], text_repeats_factor) backend_request = BackendRequest(29) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(24, Or([And([3, 8]), And([4, 7])])), Iff(26, Or([And([7, 12]), And([8, 11])])), Iff(28, Or([And([11, 16]), And([12, 15])])) ]), 29) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def __apply_derivation(self, block: Block, backend_request: BackendRequest) -> None: trial_size = block.variables_per_trial() cross_size = block.trials_per_sample() iffs = [] for n in range(cross_size): or_clause = Or(list(And(list(map(lambda x: x + (n * trial_size) + 1, l))) for l in self.dependent_idxs)) iffs.append(Iff(self.derived_idx + (n * trial_size) + 1, or_clause)) (cnf, new_fresh) = block.cnf_fn(And(iffs), backend_request.fresh) backend_request.cnfs.append(cnf) backend_request.fresh = new_fresh
def test_derivation_with_three_level_transition(): f = Factor("f", ["a", "b", "c"]) f_transition = Factor("transition", [ DerivedLevel("aa", Transition(lambda c: c[0] == "a" and c[1] == "a", [f])), DerivedLevel("ab", Transition(lambda c: c[0] == "a" and c[1] == "b", [f])), DerivedLevel("ac", Transition(lambda c: c[0] == "a" and c[1] == "c", [f])), DerivedLevel("ba", Transition(lambda c: c[0] == "b" and c[1] == "a", [f])), DerivedLevel("bb", Transition(lambda c: c[0] == "b" and c[1] == "b", [f])), DerivedLevel("bc", Transition(lambda c: c[0] == "b" and c[1] == "c", [f])), DerivedLevel("ca", Transition(lambda c: c[0] == "c" and c[1] == "a", [f])), DerivedLevel("cb", Transition(lambda c: c[0] == "c" and c[1] == "b", [f])), DerivedLevel("cc", Transition(lambda c: c[0] == "c" and c[1] == "c", [f])), ]) block = fully_cross_block([f, f_transition], [f], []) # a-a derivation d = Derivation(9, [[0, 3]], f_transition) backend_request = BackendRequest(28) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([Iff(10, Or([And([1, 4])])), Iff(19, Or([And([4, 7])]))]), 28) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def test_derivation_with_unusual_order(): d = Derivation(0, [[4, 2], [5, 3]], congruency) backend_request = BackendRequest(64) d.apply(block, backend_request) (expected_cnf, expected_fresh) = to_cnf_tseitin( And([ Iff(1, Or([And([5, 3]), And([6, 4])])), Iff(9, Or([And([13, 11]), And([14, 12])])), Iff(17, Or([And([21, 19]), And([22, 20])])), Iff(25, Or([And([29, 27]), And([30, 28])])), Iff(33, Or([And([37, 35]), And([38, 36])])), Iff(41, Or([And([45, 43]), And([46, 44])])), Iff(49, Or([And([53, 51]), And([54, 52])])), Iff(57, Or([And([61, 59]), And([62, 60])])), ]), 64) assert backend_request.fresh == expected_fresh assert backend_request.cnfs == [expected_cnf]
def __apply_derivation_with_complex_window(self, block: Block, backend_request: BackendRequest) -> None: trial_size = block.variables_per_trial() trial_count = block.trials_per_sample() iffs = [] f = self.factor window = f.levels[0].window t = 0 for n in range(trial_count): if not f.applies_to_trial(n + 1): continue num_levels = len(f.levels) get_trial_size = lambda x: trial_size if x < block.grid_variables() else len(block.decode_variable(x+1)[0].levels) or_clause = Or(list(And(list(map(lambda x: x + (t * window.stride * get_trial_size(x) + 1), l))) for l in self.dependent_idxs)) iffs.append(Iff(self.derived_idx + (t * num_levels) + 1, or_clause)) t += 1 (cnf, new_fresh) = block.cnf_fn(And(iffs), backend_request.fresh) backend_request.cnfs.append(cnf) backend_request.fresh = new_fresh
def test_fully_cross_with_uncrossed_simple_factors(): other = Factor('other', ['l1', 'l2']) block = fully_cross_block([color, text, other], [color, text], []) backend_request = BackendRequest(25) FullyCross.apply(block, backend_request) (expected_cnf, _) = to_cnf_tseitin( And([ Iff(25, And([1, 3])), Iff(26, And([1, 4])), Iff(27, And([2, 3])), Iff(28, And([2, 4])), Iff(29, And([7, 9])), Iff(30, And([7, 10])), Iff(31, And([8, 9])), Iff(32, And([8, 10])), Iff(33, And([13, 15])), Iff(34, And([13, 16])), Iff(35, And([14, 15])), Iff(36, And([14, 16])), Iff(37, And([19, 21])), Iff(38, And([19, 22])), Iff(39, And([20, 21])), Iff(40, And([20, 22])) ]), 41) assert backend_request.fresh == 74 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [25, 29, 33, 37]), LowLevelRequest("GT", 0, [26, 30, 34, 38]), LowLevelRequest("GT", 0, [27, 31, 35, 39]), LowLevelRequest("GT", 0, [28, 32, 36, 40]) ]
def test_fully_cross_with_three_factors(): (expected_cnf, _) = to_cnf_tseitin( And([ Iff(65, And([3, 5, 7])), Iff(66, And([3, 5, 8])), Iff(67, And([3, 6, 7])), Iff(68, And([3, 6, 8])), Iff(69, And([4, 5, 7])), Iff(70, And([4, 5, 8])), Iff(71, And([4, 6, 7])), Iff(72, And([4, 6, 8])), Iff(73, And([11, 13, 15])), Iff(74, And([11, 13, 16])), Iff(75, And([11, 14, 15])), Iff(76, And([11, 14, 16])), Iff(77, And([12, 13, 15])), Iff(78, And([12, 13, 16])), Iff(79, And([12, 14, 15])), Iff(80, And([12, 14, 16])), Iff(81, And([19, 21, 23])), Iff(82, And([19, 21, 24])), Iff(83, And([19, 22, 23])), Iff(84, And([19, 22, 24])), Iff(85, And([20, 21, 23])), Iff(86, And([20, 21, 24])), Iff(87, And([20, 22, 23])), Iff(88, And([20, 22, 24])), Iff(89, And([27, 29, 31])), Iff(90, And([27, 29, 32])), Iff(91, And([27, 30, 31])), Iff(92, And([27, 30, 32])), Iff(93, And([28, 29, 31])), Iff(94, And([28, 29, 32])), Iff(95, And([28, 30, 31])), Iff(96, And([28, 30, 32])), Iff(97, And([35, 37, 39])), Iff(98, And([35, 37, 40])), Iff(99, And([35, 38, 39])), Iff(100, And([35, 38, 40])), Iff(101, And([36, 37, 39])), Iff(102, And([36, 37, 40])), Iff(103, And([36, 38, 39])), Iff(104, And([36, 38, 40])), Iff(105, And([43, 45, 47])), Iff(106, And([43, 45, 48])), Iff(107, And([43, 46, 47])), Iff(108, And([43, 46, 48])), Iff(109, And([44, 45, 47])), Iff(110, And([44, 45, 48])), Iff(111, And([44, 46, 47])), Iff(112, And([44, 46, 48])), Iff(113, And([51, 53, 55])), Iff(114, And([51, 53, 56])), Iff(115, And([51, 54, 55])), Iff(116, And([51, 54, 56])), Iff(117, And([52, 53, 55])), Iff(118, And([52, 53, 56])), Iff(119, And([52, 54, 55])), Iff(120, And([52, 54, 56])), Iff(121, And([59, 61, 63])), Iff(122, And([59, 61, 64])), Iff(123, And([59, 62, 63])), Iff(124, And([59, 62, 64])), Iff(125, And([60, 61, 63])), Iff(126, And([60, 61, 64])), Iff(127, And([60, 62, 63])), Iff(128, And([60, 62, 64])), ]), 129) backend_request = BackendRequest(65) FullyCross.apply(block, backend_request) assert backend_request.fresh == 258 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [65, 73, 81, 89, 97, 105, 113, 121]), LowLevelRequest("GT", 0, [66, 74, 82, 90, 98, 106, 114, 122]), LowLevelRequest("GT", 0, [67, 75, 83, 91, 99, 107, 115, 123]), LowLevelRequest("GT", 0, [68, 76, 84, 92, 100, 108, 116, 124]), LowLevelRequest("GT", 0, [69, 77, 85, 93, 101, 109, 117, 125]), LowLevelRequest("GT", 0, [70, 78, 86, 94, 102, 110, 118, 126]), LowLevelRequest("GT", 0, [71, 79, 87, 95, 103, 111, 119, 127]), LowLevelRequest("GT", 0, [72, 80, 88, 96, 104, 112, 120, 128]) ]
def test_fully_cross_simple(): block = fully_cross_block([color, text], [color, text], []) (expected_cnf, _) = to_cnf_tseitin( And([ Iff(17, And([1, 3])), Iff(18, And([1, 4])), Iff(19, And([2, 3])), Iff(20, And([2, 4])), Iff(21, And([5, 7])), Iff(22, And([5, 8])), Iff(23, And([6, 7])), Iff(24, And([6, 8])), Iff(25, And([9, 11])), Iff(26, And([9, 12])), Iff(27, And([10, 11])), Iff(28, And([10, 12])), Iff(29, And([13, 15])), Iff(30, And([13, 16])), Iff(31, And([14, 15])), Iff(32, And([14, 16])) ]), 33) backend_request = BackendRequest(17) FullyCross.apply(block, backend_request) assert backend_request.fresh == 66 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [17, 21, 25, 29]), LowLevelRequest("GT", 0, [18, 22, 26, 30]), LowLevelRequest("GT", 0, [19, 23, 27, 31]), LowLevelRequest("GT", 0, [20, 24, 28, 32]) ]
def test_fully_cross_with_transition_in_crossing(): direction = Factor("direction", ["up", "down"]) block = fully_cross_block([direction, color, color_repeats_factor], [direction, color_repeats_factor], []) backend_request = BackendRequest(29) FullyCross.apply(block, backend_request) (expected_cnf, _) = to_cnf_tseitin( And([ Iff(29, And([5, 21])), Iff(30, And([5, 22])), Iff(31, And([6, 21])), Iff(32, And([6, 22])), Iff(33, And([9, 23])), Iff(34, And([9, 24])), Iff(35, And([10, 23])), Iff(36, And([10, 24])), Iff(37, And([13, 25])), Iff(38, And([13, 26])), Iff(39, And([14, 25])), Iff(40, And([14, 26])), Iff(41, And([17, 27])), Iff(42, And([17, 28])), Iff(43, And([18, 27])), Iff(44, And([18, 28])), ]), 45) assert backend_request.fresh == 78 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [29, 33, 37, 41]), LowLevelRequest("GT", 0, [30, 34, 38, 42]), LowLevelRequest("GT", 0, [31, 35, 39, 43]), LowLevelRequest("GT", 0, [32, 36, 40, 44]) ]
def test_fully_cross_with_transition_in_design(design): block = fully_cross_block(design, [color, text], []) backend_request = BackendRequest(23) FullyCross.apply(block, backend_request) (expected_cnf, _) = to_cnf_tseitin( And([ Iff(23, And([1, 3])), Iff(24, And([1, 4])), Iff(25, And([2, 3])), Iff(26, And([2, 4])), Iff(27, And([5, 7])), Iff(28, And([5, 8])), Iff(29, And([6, 7])), Iff(30, And([6, 8])), Iff(31, And([9, 11])), Iff(32, And([9, 12])), Iff(33, And([10, 11])), Iff(34, And([10, 12])), Iff(35, And([13, 15])), Iff(36, And([13, 16])), Iff(37, And([14, 15])), Iff(38, And([14, 16])) ]), 39) assert backend_request.fresh == 72 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [23, 27, 31, 35]), LowLevelRequest("GT", 0, [24, 28, 32, 36]), LowLevelRequest("GT", 0, [25, 29, 33, 37]), LowLevelRequest("GT", 0, [26, 30, 34, 38]) ]
def test_fully_cross_with_constraint(): (expected_cnf, _) = to_cnf_tseitin( And([ Iff(25, And([1, 3])), Iff(26, And([1, 4])), Iff(27, And([2, 3])), Iff(28, And([2, 4])), Iff(29, And([7, 9])), Iff(30, And([7, 10])), Iff(31, And([8, 9])), Iff(32, And([8, 10])), Iff(33, And([13, 15])), Iff(34, And([13, 16])), Iff(35, And([14, 15])), Iff(36, And([14, 16])), Iff(37, And([19, 21])), Iff(38, And([19, 22])), Iff(39, And([20, 21])), Iff(40, And([20, 22])) ]), 41) backend_request = BackendRequest(25) FullyCross.apply(block, backend_request) assert backend_request.fresh == 74 assert backend_request.cnfs == [expected_cnf] assert backend_request.ll_requests == [ LowLevelRequest("GT", 0, [25, 29, 33, 37]), LowLevelRequest("GT", 0, [26, 30, 34, 38]), LowLevelRequest("GT", 0, [27, 31, 35, 39]), LowLevelRequest("GT", 0, [28, 32, 36, 40]) ]