Code cleanup

model.py

@@ -16,9 +16,9 @@ from typing import Dict, List, Optional, Set, Tuple
 __all__ = ['ModelValue', 'ModelFunction', 'Model', 'Interpretation']
 
 class ModelValue:
-    def __init__(self, name):
+    def __init__(self, name: str, hashed_value: Optional[int] = None):
         self.name = name
-        self.hashed_value = hash(self.name)
+        self.hashed_value = hashed_value if hashed_value is not None else hash(self.name)
         self.__setattr__ = immutable
     def __str__(self):
         return self.name
@@ -27,7 +27,7 @@ class ModelValue:
     def __eq__(self, other):
         return isinstance(other, ModelValue) and self.name == other.name
     def __deepcopy__(self, _):
-        return ModelValue(self.name)
+        return ModelValue(self.name, self.hashed_value)
 
 class ModelFunction:
     def __init__(self, arity: int, mapping, operation_name = ""):
@@ -109,58 +109,76 @@ Interpretation = Dict[Operation, ModelFunction]
 class OrderTable:
     def __init__(self):
         # a : {x | x <= a }
-        self.ordering: Dict[ModelValue, Set[ModelValue]] = defaultdict(set)
+        self.le_map: Dict[ModelValue, Set[ModelValue]] = defaultdict(set)
+        # a : {x | x >= a}
+        self.ge_map: Dict[ModelValue, Set[ModelValue]] = defaultdict(set)
 
     def add(self, x, y):
         """
         Add x <= y
         """
-        self.ordering[y].add(x)
+        self.le_map[y].add(x)
+        self.ge_map[x].add(y)
 
     def is_lt(self, x, y):
-        return y in self.ordering[x]
+        return x in self.le_map[y]
 
     def meet(self, x, y) -> Optional[ModelValue]:
-        X = self.ordering[x]
+        X = self.le_map[x]
-        Y = self.ordering[y]
+        Y = self.le_map[y]
 
         candidates = X.intersection(Y)
 
-        for m in candidates:
+        # Grab all elements greater than each of the candidates
-            gt_all_candidates = True
+        candidate_ge_maps = (self.ge_map[candidate] for candidate in candidates)
-            for w in candidates:
+        common_ge_values = reduce(set.intersection, candidate_ge_maps)
-                if not self.is_lt(w, m):
-                    gt_all_candidates = False
-                    break
 
-            if gt_all_candidates:
+        # Intersect with candidates to get the values that satisfy
-                return m
+        # the meet properties
+        result_set = candidates.intersection(common_ge_values)
 
-        # Otherwise the meet does not exist
+        # NOTE: The meet may not exist, in which case return None
-        print("Meet does not exist", (x, y), candidates)
+        result = next(iter(result_set), None)
-        return None
+        return result
 
     def join(self, x, y) -> Optional[ModelValue]:
-        # Grab the collection of elements greater than x and y
+        X = self.ge_map[x]
-        candidates = set()
+        Y = self.ge_map[y]
-        for w in self.ordering:
-            if self.is_lt(x, w) and self.is_lt(y, w):
-                candidates.add(w)
 
-        for j in candidates:
+        candidates = X.intersection(Y)
-            lt_all_candidates = True
-            for w in candidates:
-                if not self.is_lt(j, w):
-                    lt_all_candidates = False
-                    break
 
-            if lt_all_candidates:
+        # Grab all elements smaller than each of the candidates
-                return j
+        candidate_le_maps = (self.le_map[candidate] for candidate in candidates)
+        common_le_values = reduce(set.intersection, candidate_le_maps)
 
-        # Otherwise the join does not exist
+        # Intersect with candidatse to get the values that satisfy
-        print("Join does not exist", (x, y), candidates)
+        # the join properties
+        result_set = candidates.intersection(common_le_values)
+
+        # NOTE: The join may not exist, in which case return None
+        result = next(iter(result_set), None)
+        return result
+
+    def top(self) -> Optional[ModelValue]:
+        ge_maps = (self.ge_map[candidate] for candidate in self.ge_map)
+        result_set = reduce(set.intersection, ge_maps)
+
+        # Either not unique or does not exist
+        if len(result_set) != 1:
             return None
 
+        return next(iter(result_set))
+
+    def bottom(self) -> Optional[ModelValue]:
+        le_maps = (self.le_map[candidate] for candidate in self.le_map)
+        result_set = reduce(set.intersection, le_maps)
+
+        # Either not unique or does not exist
+        if len(result_set) != 1:
+            return None
+
+        return next(iter(result_set))
+
 
 class Model:
     def __init__(
@@ -276,36 +294,47 @@ def satisfiable(logic: Logic, model: Model, interpretation: Dict[Operation, Mode
     return True
 
 
-
 def model_closure(initial_set: Set[ModelValue], mfunctions: Set[ModelFunction], forbidden_element: Optional[ModelValue]) -> Set[ModelValue]:
     """
     Given an initial set of model values and a set of model functions,
     compute the complete set of model values that are closed
     under the operations.
 
-    If top or bottom is encountered, then we end the saturation procedure early.
+    If the forbidden element is encountered, then we end the saturation procedure early.
     """
     closure_set: Set[ModelValue] = initial_set
     last_new: Set[ModelValue] = initial_set
     changed: bool = True
     forbidden_found = False
 
+    arities = set()
+    for mfun in mfunctions:
+        arities.add(mfun.arity)
+
     while changed:
         changed = False
         new_elements: Set[ModelValue] = set()
         old_closure: Set[ModelValue] = closure_set - last_new
 
         # arity -> args
-        cached_args = defaultdict(list)
+        args_by_arity = defaultdict(list)
 
-        # Pass elements into each model function
+        # Motivation: We want to only compute arguments that we have not
+        # seen before
+        for arity in arities:
+            for num_new in range(1, arity + 1):
+                new_args = combinations_with_replacement(last_new, r=num_new)
+                old_args = combinations_with_replacement(old_closure, r=arity - num_new)
+                # Determine every possible ordering of the concatenated new and
+                # old model values.
+                for new_arg, old_arg in product(new_args, old_args):
+                    for combined_args in permutations(new_arg + old_arg):
+                        args_by_arity[arity].append(combined_args)
+
+
+        # Pass each argument into each model function
         for mfun in mfunctions:
-
+            for args in args_by_arity[mfun.arity]:
-            # If a previous function shared the same arity,
-            # we'll use the same set of computed arguments
-            # to pass into the model functions.
-            if mfun.arity in cached_args:
-                for args in cached_args[mfun.arity]:
                 # Compute the new elements
                 # given the cached arguments.
                 element = mfun(*args)
@@ -321,42 +350,6 @@ def model_closure(initial_set: Set[ModelValue], mfunctions: Set[ModelFunction],
             if forbidden_found:
                 break
 
-                # We don't need to compute the arguments
-                # thanks to the cache, so move onto the
-                # next function.
-                continue
-
-            # At this point, we don't have cached arguments, so we need
-            # to compute this set.
-
-            # Each argument must have at least one new element to not repeat
-            # work. We'll range over the number of new model values within our
-            # argument.
-            for num_new in range(1, mfun.arity + 1):
-                new_args = combinations_with_replacement(last_new, r=num_new)
-                old_args = combinations_with_replacement(old_closure, r=mfun.arity - num_new)
-                # Determine every possible ordering of the concatenated
-                # new and old model values.
-                for new_arg, old_arg in product(new_args, old_args):
-                    for args in permutations(new_arg + old_arg):
-                        cached_args[mfun.arity].append(args)
-                        element = mfun(*args)
-                        if element not in closure_set:
-                            new_elements.add(element)
-
-                        # Optimization: Break out of computation
-                        # early when forbidden element is found
-                        if forbidden_element is not None and element == forbidden_element:
-                            forbidden_found = True
-                            break
-
-                    if forbidden_found:
-                        break
-
-                if forbidden_found:
-                    break
-
-
         closure_set.update(new_elements)
         changed = len(new_elements) > 0
         last_new = new_elements

parse_magic.py

@@ -72,6 +72,45 @@ class ModelBuilder:
         # Map symbol to model function
         self.custom_model_functions: Dict[str,  ModelFunction] = {}
 
+    def build(self, model_name: str) -> Tuple[Model, Dict[Operation, ModelFunction]]:
+        """Create Model"""
+        assert self.size > 0
+        assert self.size + 1 == len(self.carrier_list)
+        assert len(self.designated_values) <= len(self.carrier_list)
+        assert self.mimplication is not None
+
+        # Implication is required to be present
+        logical_operations = { self.mimplication }
+        interpretation = {
+            Implication: self.mimplication
+        }
+
+        # Other model functions and logical
+        # operations are optional
+        if self.mnegation is not None:
+            logical_operations.add(self.mnegation)
+            interpretation[Negation] = self.mnegation
+        if self.mconjunction is not None:
+            logical_operations.add(self.mconjunction)
+            interpretation[Conjunction] = self.mconjunction
+        if self.mdisjunction is not None:
+            logical_operations.add(self.mdisjunction)
+            interpretation[Disjunction] = self.mdisjunction
+        if self.mnecessitation is not None:
+            logical_operations.add(self.mnecessitation)
+            interpretation[Necessitation] = self.mnecessitation
+
+        # Custom model function definitions
+        for custom_mf in self.custom_model_functions.values():
+            if custom_mf is not None:
+                logical_operations.add(custom_mf)
+                op = Operation(custom_mf.operation_name, custom_mf.arity)
+                interpretation[op] = custom_mf
+
+        model = Model(set(self.carrier_list), logical_operations, self.designated_values, ordering=self.ordering, name=model_name)
+        return (model, interpretation)
+
+
 class Stage:
     def __init__(self, name: str):
         self.name = name
@@ -194,7 +233,7 @@ def parse_matrices(infile: SourceFile) -> Iterator[Tuple[Model, Dict[Operation,
             case "end":
                 break
             case "process_model":
-                yield process_model(stages.name(), current_model_parts)
+                yield current_model_parts.build(stages.name())
                 stage = stage.next
             case "size":
                 processed = process_sizes(infile, current_model_parts, first_run)
@@ -300,7 +339,7 @@ def process_orders(infile: SourceFile, current_model_parts: ModelBuilder) -> boo
 
 def process_designateds(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 4"""
-    designated_values = parse_single_designated(infile, current_model_parts.size)
+    designated_values = parse_single_designated(infile, current_model_parts.size, current_model_parts.carrier_list)
     if designated_values is None:
         return False
 
@@ -309,7 +348,7 @@ def process_designateds(infile: SourceFile, current_model_parts: ModelBuilder) -
 
 def process_implications(infile: SourceFile, current_model_parts: ModelBuilder) -> bool:
     """Stage 5"""
-    mimplication = parse_single_dyadic_connective(infile, "→", current_model_parts.size)
+    mimplication = parse_single_dyadic_connective(infile, "→", current_model_parts.size, current_model_parts.carrier_list)
     if mimplication is None:
         return False
 
@@ -330,7 +369,7 @@ def process_custom_connective(infile: SourceFile, symbol: str, adicity: int, cur
     elif adicity == 1:
         mfunction = parse_single_monadic_connective(infile, symbol, current_model_parts.size, current_model_parts.carrier_list)
     elif adicity == 2:
-        mfunction = parse_single_dyadic_connective(infile, symbol, current_model_parts.size)
+        mfunction = parse_single_dyadic_connective(infile, symbol, current_model_parts.size, current_model_parts.carrier_list)
     else:
         raise NotImplementedError("Unable to process connectives of adicity greater than 2")
 
@@ -340,39 +379,6 @@ def process_custom_connective(infile: SourceFile, symbol: str, adicity: int, cur
     current_model_parts.custom_model_functions[symbol] = mfunction
     return True
 
-def process_model(model_name: str, mp: ModelBuilder) -> Tuple[Model, Dict[Operation, ModelFunction]]:
-    """Create Model"""
-    assert mp.size > 0
-    assert mp.size + 1 == len(mp.carrier_list)
-    assert len(mp.designated_values) <= len(mp.carrier_list)
-    assert mp.mimplication is not None
-
-    logical_operations = { mp.mimplication }
-    interpretation = {
-        Implication: mp.mimplication
-    }
-    if mp.mnegation is not None:
-        logical_operations.add(mp.mnegation)
-        interpretation[Negation] = mp.mnegation
-    if mp.mconjunction is not None:
-        logical_operations.add(mp.mconjunction)
-        interpretation[Conjunction] = mp.mconjunction
-    if mp.mdisjunction is not None:
-        logical_operations.add(mp.mdisjunction)
-        interpretation[Disjunction] = mp.mdisjunction
-    if mp.mnecessitation is not None:
-        logical_operations.add(mp.mnecessitation)
-        interpretation[Necessitation] = mp.mnecessitation
-
-    for custom_mf in mp.custom_model_functions.values():
-        if custom_mf is not None:
-            logical_operations.add(custom_mf)
-            op = Operation(custom_mf.operation_name, custom_mf.arity)
-            interpretation[op] = custom_mf
-
-    model = Model(set(mp.carrier_list), logical_operations, mp.designated_values, ordering=mp.ordering, name=model_name)
-    return (model, interpretation)
-
 
 def parse_header(infile: SourceFile) -> UglyHeader:
     """
@@ -406,7 +412,6 @@ def parse_size(infile: SourceFile, first_run: bool) -> Optional[int]:
     """
     Parse the line representing the matrix size.
     """
-
     size = int(infile.next_line())
 
     # HACK: When necessitation and custom connectives are enabled
@@ -417,7 +422,9 @@ def parse_size(infile: SourceFile, first_run: bool) -> Optional[int]:
 
     if size == -1:
         return None
+
     assert size > 0, f"Unexpected size at line {infile.line_in_file}"
+
     return size
 
 def mvalue_from_index(i: int) -> ModelValue:
@@ -433,55 +440,9 @@ def parse_mvalue(x: str) -> ModelValue:
     """
     return mvalue_from_index(int(x))
 
-def determine_cresult(size: int, ordering: Dict[ModelValue, ModelValue], a: ModelValue, b: ModelValue) -> ModelValue:
-    """
-    Determine what a ∧ b should be given the ordering table.
-    """
-    for i in range(size + 1):
-        c = mvalue_from_index(i)
 
-        if not ordering[(c, a)]:
+def parse_single_order(infile: SourceFile, size: int, carrier_list: List[ModelValue]) -> Optional[
-            continue
+    Tuple[OrderTable, Optional[ModelFunction], Optional[ModelFunction]]]:
-        if not ordering[(c, b)]:
-            continue
-
-        invalid = False
-        for j in range(size + 1):
-            d = mvalue_from_index(j)
-            if c == d:
-                continue
-            if ordering[(c, d)]:
-                if ordering[(d, a)] and ordering [(d, b)]:
-                    invalid = True
-
-        if not invalid:
-            return c
-
-def determine_dresult(size: int, ordering: Dict[ModelValue, ModelValue], a: ModelValue, b: ModelValue) -> ModelValue:
-    """
-    Determine what a ∨ b should be given the ordering table.
-    """
-    for i in range(size + 1):
-        c = mvalue_from_index(i)
-        if not ordering[(a, c)]:
-            continue
-        if not ordering[(b, c)]:
-            continue
-
-        invalid = False
-
-        for j in range(size + 1):
-            d = mvalue_from_index(j)
-            if d == c:
-                continue
-            if ordering[(d, c)]:
-                if ordering[(a, d)] and ordering[(b, d)]:
-                    invalid = True
-
-        if not invalid:
-            return c
-
-def parse_single_order(infile: SourceFile, size: int, carrier_list: List[ModelValue]) -> Optional[Tuple[OrderTable, ModelFunction, ModelFunction]]:
     """
     Parse the line representing the ordering table
     """
@@ -509,21 +470,12 @@ def parse_single_order(infile: SourceFile, size: int, carrier_list: List[ModelVa
     for x, y in product(carrier_list, carrier_list):
         cresult = ordering.meet(x, y)
         if cresult is None:
-            print("[Warning] Conjunction and Disjunction are not well-defined")
+            return ordering, None, None
-            print(f"{x} ∧ {y} = ??")
-            return None, None
-        else:
-            print(f"{x} ∧ {y} = {cresult}")
         cmapping[(x, y)] = cresult
 
         dresult = ordering.join(x, y)
-        # dresult = determine_dresult(size, omapping, x, y)
         if dresult is None:
-            print("[Warning] Conjunction and Disjunction are not well-defined")
+            return ordering, None, None
-            print(f"{x} ∨ {y} = ??")
-            return None, None
-        else:
-            print(f"{x} ∨ {y} = {dresult}")
         dmapping[(x, y)] = dresult
 
     mconjunction = ModelFunction(2, cmapping, "∧")
@@ -531,7 +483,7 @@ def parse_single_order(infile: SourceFile, size: int, carrier_list: List[ModelVa
 
     return ordering, mconjunction, mdisjunction
 
-def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[ModelValue]]:
+def parse_single_designated(infile: SourceFile, size: int, carrier_list: List[ModelValue]) -> Optional[Set[ModelValue]]:
     """
     Parse the line representing which model values are designated.
     """
@@ -544,9 +496,8 @@ def parse_single_designated(infile: SourceFile, size: int) -> Optional[Set[Model
 
     designated_values = set()
 
-    for i, j in zip(range(size + 1), row):
+    for x, j in zip(carrier_list, row):
         if j == '1':
-            x = mvalue_from_index(i)
             designated_values.add(x)
 
     return designated_values
@@ -579,7 +530,7 @@ def parse_single_monadic_connective(infile: SourceFile, symbol: str, size: int,
 
     return ModelFunction(1, mapping, symbol)
 
-def parse_single_dyadic_connective(infile: SourceFile, symbol: str, size: int) -> Optional[ModelFunction]:
+def parse_single_dyadic_connective(infile: SourceFile, symbol: str, size: int, carrier_list: List[ModelValue]) -> Optional[ModelFunction]:
     first_token = next(infile)
     if first_token == "-1":
         return None
@@ -588,20 +539,14 @@ def parse_single_dyadic_connective(infile: SourceFile, symbol: str, size: int) -
     try:
         table = [first_token] + [next(infile) for _ in range((size + 1)**2 - 1)]
     except StopIteration:
-        pass
+        raise Exception(f"{symbol} table does not match expected size at line {infile.line_in_file}")
-
-    assert len(table) == (size + 1)**2, f"{symbol} table does not match expected size at line {infile.line_in_file}"
 
     mapping = {}
     table_i = 0
-    for i in range(size + 1):
-        x = mvalue_from_index(i)
-        for j in range(size + 1):
-            y = mvalue_from_index(j)
 
+    for x, y in product(carrier_list, carrier_list):
         r = parse_mvalue(table[table_i])
         table_i += 1
-
         mapping[(x, y)] = r
 
     return ModelFunction(2, mapping, symbol)

vsp.py

@@ -2,6 +2,7 @@
 Check to see if the model has the variable
 sharing property.
 """
+from collections import defaultdict
 from itertools import chain, combinations, product
 from typing import List, Optional, Set, Tuple
 from common import set_to_str
@@ -9,73 +10,34 @@ from model import (
     Model, model_closure, ModelFunction, ModelValue, OrderTable
 )
 
-def preseed(
+class Cache:
-        initial_set: Set[ModelValue],
+    def __init__(self):
-        cache:List[Tuple[Set[ModelValue], Set[ModelValue]]]):
+        # input size -> cached (inputs, outputs)
+        self.c = defaultdict(list)
+
+    def add(self, i: Set[ModelValue], o: Set[ModelValue]):
+        self.c[len(i)].append((i, o))
+
+    def get_closest(self, initial_set: Set[ModelValue]) -> Optional[Tuple[Set[ModelValue], bool]]:
         """
-    Given a cache of previous model_closure calls,
+        Iterate through our cache starting with the cached
-    use this to compute an initial model closure
+        inputs closest in size to the initial_set and
-    set based on the initial set.
+        find the one that's a subset of initial_set.
 
-    Basic Idea:
+        Returns cached_output, and whether the initial_set is the same
-    Let {1, 2, 3} -> X be in the cache.
+        as the cached_input.
-    If {1,2,3} is a subset of initial set,
-    then X is the subset of the output of model_closure.
-
-    This is used to speed up subsequent calls to model_closure
         """
-    candidate_preseed: Tuple[Set[ModelValue], int] = (None, None)
+        initial_set_size = len(initial_set)
+        sizes = range(initial_set_size, 0, -1)
 
-    for i, o in cache:
+        for size in sizes:
-        if i < initial_set:
+            if size not in self.c:
-            cost = len(initial_set - i)
+                continue
-            # If i is a subset with less missing elements than
-            # the previous candidate, then it's the new candidate.
-            if candidate_preseed[1] is None or cost < candidate_preseed[1]:
-                candidate_preseed = o, cost
 
-    same_set = candidate_preseed[1] == 0
+            for cached_input, cached_output in self.c[size]:
-    return candidate_preseed[0], same_set
+                if cached_input <= initial_set:
+                    return cached_output, size == initial_set_size
 
-
-def find_top(algebra: Set[ModelValue], mconjunction: Optional[ModelFunction], mdisjunction: Optional[ModelFunction]) -> Optional[ModelValue]:
-    """
-    Find the top of the order lattice.
-    T || a = T, T && a = a for all a in the carrier set
-    """
-    if mconjunction is None or mdisjunction is None:
-        return None
-
-    for x in algebra:
-        is_top = True
-        for y in algebra:
-            if mdisjunction(x, y) != x or mconjunction(x, y) != y:
-                is_top = False
-                break
-        if is_top:
-            return x
-
-    print("[Warning] Failed to find the top of the lattice")
-    return None
-
-def find_bottom(algebra: Set[ModelValue], mconjunction: Optional[ModelFunction], mdisjunction: Optional[ModelFunction]) -> Optional[ModelValue]:
-    """
-    Find the bottom of the order lattice
-    F || a = a, F && a = F for all a in the carrier set
-    """
-    if mconjunction is None or mdisjunction is None:
-        return None
-
-    for x in algebra:
-        is_bottom = True
-        for y in algebra:
-            if mdisjunction(x, y) != y or mconjunction(x, y) != x:
-                is_bottom = False
-                break
-        if is_bottom:
-            return x
-
-    print("[Warning] Failed to find the bottom of the lattice")
         return None
 
 def order_dependent(subalgebra1: Set[ModelValue], subalegbra2: Set[ModelValue], ordering: OrderTable):
@@ -106,17 +68,49 @@ Subalgebra 1: {set_to_str(self.subalgebra1)}
 Subalgebra 2: {set_to_str(self.subalgebra2)}
 """
 
+def quick_vsp_unsat_incomplete(xs, ys, model, top, bottom, negation_defined) -> bool:
+    """
+    Return True if VSP cannot be satisfied
+    through some incomplete checks.
+    """
+    # If the left subalgebra contains bottom
+    # or the right subalgebra contains top
+    # skip this pair
+    if top is not None and top in ys:
+        return True
+    if bottom is not None and bottom in xs:
+        return True
+
+    # If a subalgebra doesn't have at least one
+    # designated value, move onto the next pair.
+    # Depends on no intersection between xs and ys
+    if xs.isdisjoint(model.designated_values):
+        return True
+
+    if ys.isdisjoint(model.designated_values):
+        return True
+
+    # If the two subalgebras intersect, move
+    # onto the next pair.
+    if not xs.isdisjoint(ys):
+        return True
+
+    # If the subalgebras are order-dependent, skip this pair
+    if order_dependent(xs, ys, model.ordering):
+        return True
+    if negation_defined and order_dependent(ys, xs, model.ordering):
+        return True
+
+    # We can't immediately rule out that these
+    # subalgebras don't exhibit VSP
+    return False
+
 def has_vsp(model: Model, impfunction: ModelFunction,
-            mconjunction: Optional[ModelFunction] = None,
+            negation_defined: bool) -> VSP_Result:
-            mdisjunction: Optional[ModelFunction] = None,
-            mnegation: Optional[ModelFunction] = None) -> VSP_Result:
     """
     Checks whether a model has the variable
     sharing property.
     """
-    top = find_top(model.carrier_set, mconjunction, mdisjunction)
-    bottom = find_bottom(model.carrier_set, mconjunction, mdisjunction)
-
     # NOTE: No models with only one designated
     # value satisfies VSP
     if len(model.designated_values) == 1:
@@ -124,68 +118,44 @@ def has_vsp(model: Model, impfunction: ModelFunction,
 
     assert model.ordering is not None, "Expected ordering table in model"
 
+    top = model.ordering.top()
+    bottom = model.ordering.bottom()
+
     # Compute I the set of tuples (x, y) where
     # x -> y does not take a designiated value
-    I: Set[Tuple[ModelValue, ModelValue]] = set()
+    I: List[Tuple[ModelValue, ModelValue]] = []
 
     for (x, y) in product(model.carrier_set, model.carrier_set):
         if impfunction(x, y) not in model.designated_values:
-            I.add((x, y))
+            I.append((x, y))
 
     # Construct the powerset of I without the empty set
-    s = list(I)
+    I_power = chain.from_iterable(combinations(I, r) for r in range(1, len(I) + 1))
-    I_power = chain.from_iterable(combinations(s, r) for r in range(1, len(s) + 1))
     # ((x1, y1)), ((x1, y1), (x2, y2)), ...
 
-    # Closure cache
+    closure_cache = Cache()
-    closure_cache: List[Tuple[Set[ModelValue], Set[ModelValue]]] = []
 
     # Find the subalgebras which falsify implication
     for xys in I_power:
 
         xs = { xy[0] for xy in xys }
+        ys = { xy[1] for xy in xys }
+
+        if quick_vsp_unsat_incomplete(xs, ys, model, top, bottom, negation_defined):
+            continue
+
         orig_xs = xs
-        cached_xs = preseed(xs, closure_cache)
+        cached_xs = closure_cache.get_closest(xs)
-        if cached_xs[0] is not None:
+        if cached_xs is not None:
             xs |= cached_xs[0]
 
-        ys = {xy[1] for xy in xys}
         orig_ys = ys
-        cached_ys = preseed(ys, closure_cache)
+        cached_ys = closure_cache.get_closest(ys)
-        if cached_ys[0] is not None:
+        if cached_ys is not None:
             ys |= cached_ys[0]
 
-
+        xs_ys_updated = cached_xs is not None or cached_ys is not None
-        # NOTE: Optimziation before model_closure
+        if xs_ys_updated and quick_vsp_unsat_incomplete(xs, ys, model, top, bottom, negation_defined):
-        # If the two subalgebras intersect, move
-        # onto the next pair.
-        if len(xs & ys) > 0:
-            continue
-
-        # NOTE: Optimization
-        # If a subalgebra doesn't have at least one
-        # designated value, move onto the next pair.
-        # Depends on no intersection between xs and ys
-        if len(xs & model.designated_values) == 0:
-            continue
-
-        if len(ys & model.designated_values) == 0:
-            continue
-
-        # NOTE: Optimization
-        # If the left subalgebra contains bottom
-        # or the right subalgebra contains top
-        # skip this pair
-        if top is not None and top in ys:
-            continue
-        if bottom is not None and bottom in xs:
-            continue
-
-        # NOTE: Optimization
-        # If the subalgebras are order-dependent, skip this pair
-        if order_dependent(xs, ys, model.ordering):
-            continue
-        if mnegation is not None and order_dependent(ys, xs, model.ordering):
             continue
 
         # Compute the closure of all operations
@@ -193,8 +163,8 @@ def has_vsp(model: Model, impfunction: ModelFunction,
         carrier_set_left: Set[ModelValue] = model_closure(xs, model.logical_operations, bottom)
 
         # Save to cache
-        if cached_xs[0] is not None and not cached_ys[1]:
+        if cached_xs is None or (cached_xs is not None and not cached_xs[1]):
-            closure_cache.append((orig_xs, carrier_set_left))
+            closure_cache.add(orig_xs, carrier_set_left)
 
         if bottom is not None and bottom in carrier_set_left:
             continue
@@ -204,15 +174,15 @@ def has_vsp(model: Model, impfunction: ModelFunction,
         carrier_set_right: Set[ModelValue] = model_closure(ys, model.logical_operations, top)
 
         # Save to cache
-        if cached_ys[0] is not None and not cached_ys[1]:
+        if cached_ys is None or (cached_ys is not None and not cached_ys[1]):
-            closure_cache.append((orig_ys, carrier_set_right))
+            closure_cache.add(orig_ys, carrier_set_right)
 
         if top is not None and top in carrier_set_right:
             continue
 
         # If the carrier set intersects, then move on to the next
         # subalgebra
-        if len(carrier_set_left & carrier_set_right) > 0:
+        if not carrier_set_left.isdisjoint(carrier_set_right):
             continue
 
         # See if for all pairs in the subalgebras, that

vspursuer.py

@@ -1,17 +1,20 @@
 #!/usr/bin/env python3
 
-# NOTE: Perhaps we should use process_cpu_count but that's not available to all Python versions
+from datetime import datetime
-from os import cpu_count
 from typing import Dict, Iterator, Optional, Tuple
 from queue import Empty as QueueEmpty
 import argparse
 import multiprocessing as mp
 
-from logic import Conjunction, Disjunction, Negation, Implication, Operation
+from logic import Negation, Implication, Operation
 from model import Model, ModelFunction
 from parse_magic import SourceFile, parse_matrices
 from vsp import has_vsp, VSP_Result
 
+def print_with_timestamp(message):
+    current_time = datetime.now().strftime("%Y-%m-%d %H:%M:%S")
+    print(f"[{current_time}] {message}")
+
 def restructure_solutions(solutions: Iterator[Tuple[Model, Dict[Operation, ModelFunction]]], skip_to: Optional[str]) -> \
     Iterator[Tuple[Model, ModelFunction, Optional[ModelFunction], Optional[ModelFunction], Optional[ModelFunction]]]:
     """
@@ -32,17 +35,15 @@ def restructure_solutions(solutions: Iterator[Tuple[Model, Dict[Operation, Model
 
         # NOTE: Implication must be defined, the rest may not
         impfunction = interpretation[Implication]
-        mconjunction = interpretation.get(Conjunction)
+        negation_defined = Negation in interpretation
-        mdisjunction = interpretation.get(Disjunction)
+        yield (model, impfunction, negation_defined)
-        mnegation = interpretation.get(Negation)
-        yield (model, impfunction, mconjunction, mdisjunction, mnegation)
 
-def has_vsp_plus_model(model, impfunction, mconjunction, mdisjunction, mnegation) -> Tuple[Optional[Model], VSP_Result]:
+def has_vsp_plus_model(model, impfunction, negation_defined) -> Tuple[Optional[Model], VSP_Result]:
     """
     Wrapper which also stores the models along with its vsp result
     """
-    vsp_result = has_vsp(model, impfunction, mconjunction, mdisjunction, mnegation)
+    vsp_result = has_vsp(model, impfunction, negation_defined)
-    # NOTE: Memory optimization - Don't return model if it doens't have VSP
+    # NOTE: Memory optimization - Don't return model if it doesn't have VSP
     model = model if vsp_result.has_vsp else None
     return (model, vsp_result)
 
@@ -60,8 +61,8 @@ def worker_vsp(task_queue: mp.Queue, result_queue: mp.Queue):
             # If sentinal value, break
             if task is None:
                 break
-            (model, impfunction, mconjunction, mdisjunction, mnegation) = task
+            (model, impfunction, negation_defined) = task
-            result = has_vsp_plus_model(model, impfunction, mconjunction, mdisjunction, mnegation)
+            result = has_vsp_plus_model(model, impfunction, negation_defined)
             result_queue.put(result)
     finally:
         # Either an exception occured or the worker finished
@@ -91,37 +92,22 @@ def worker_parser(data_file_path: str, num_sentinal_values: int, task_queue: mp.
         for _ in range(num_sentinal_values):
             task_queue.put(None)
 
+def multi_process_runner(num_cpu: int, data_file_path: str, skip_to: Optional[str]):
+    """
+    Run VSPursuer in a multi-process configuration.
+    """
+    assert num_cpu > 1
 
-
-
-if __name__ == "__main__":
-    parser = argparse.ArgumentParser(description="VSP Checker")
-    parser.add_argument("--verbose", action='store_true', help="Print out all parsed matrices")
-    parser.add_argument("-i", type=str, help="Path to MaGIC ugly data file")
-    parser.add_argument("-c", type=int, help="Number of CPUs to use. Default: MAX - 2.")
-    parser.add_argument("--skip-to", type=str, help="Skip until a model name is found and process from then onwards.")
-    args = vars(parser.parse_args())
-
-    data_file_path = args.get("i")
-    if data_file_path is None:
-        data_file_path = input("Path to MaGIC Ugly Data File: ")
-
-
-    num_cpu = args.get("c")
-    if num_cpu is None:
-        num_cpu = max(cpu_count() - 2, 1)
-
-    # Set up parallel verification
     num_tested = 0
     num_has_vsp = 0
-    num_workers = max(num_cpu - 1, 1)
+    num_workers = num_cpu - 1
 
     # Create queues
     task_queue = mp.Queue(maxsize=1000)
     result_queue = mp.Queue()
 
     # Create dedicated process to parse the MaGIC file
-    process_parser = mp.Process(target=worker_parser, args=(data_file_path, num_workers, task_queue, args.get("skip_to")))
+    process_parser = mp.Process(target=worker_parser, args=(data_file_path, num_workers, task_queue, skip_to))
     process_parser.start()
 
     # Create dedicated processes which check VSP
@@ -135,7 +121,6 @@ if __name__ == "__main__":
     # Check results and add new tasks until finished
     result_sentinal_count = 0
     while True:
-
         # Read a result
         try:
             result = result_queue.get(True, 60)
@@ -171,7 +156,7 @@ if __name__ == "__main__":
 
         # Process result
         model, vsp_result = result
-        print(vsp_result)
+        print_with_timestamp(vsp_result)
         num_tested += 1
 
         if vsp_result.has_vsp:
@@ -180,7 +165,47 @@ if __name__ == "__main__":
         if vsp_result.has_vsp:
             num_has_vsp += 1
 
+    print_with_timestamp(f"Tested {num_tested} models, {num_has_vsp} of which satisfy VSP")
 
-    print(f"Tested {num_tested} models, {num_has_vsp} of which satisfy VSP")
+def single_process_runner(data_file_path: str, skip_to: Optional[str]):
+    num_tested = 0
+    num_has_vsp = 0
+
+    data_file = open(data_file_path, "r")
+    solutions = parse_matrices(SourceFile(data_file))
+    solutions = restructure_solutions(solutions, skip_to)
+
+    for model, impfunction, negation_defined in solutions:
+        model, vsp_result = has_vsp_plus_model(model, impfunction, negation_defined)
+        print_with_timestamp(vsp_result)
+        num_tested += 1
+
+        if vsp_result.has_vsp:
+            print(model)
+
+        if vsp_result.has_vsp:
+            num_has_vsp += 1
+
+    print_with_timestamp(f"Tested {num_tested} models, {num_has_vsp} of which satisfy VSP")
 
 
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description="VSP Checker")
+    parser.add_argument("--verbose", action='store_true', help="Print out all parsed matrices")
+    parser.add_argument("-i", type=str, help="Path to MaGIC ugly data file")
+    parser.add_argument("-c", type=int, help="Number of CPUs to use. Default: 1")
+    parser.add_argument("--skip-to", type=str, help="Skip until a model name is found and process from then onwards.")
+    args = vars(parser.parse_args())
+
+    data_file_path = args.get("i")
+    if data_file_path is None:
+        data_file_path = input("Path to MaGIC Ugly Data File: ")
+
+    num_cpu = args.get("c")
+    if num_cpu is None:
+        num_cpu = 1
+
+    if num_cpu == 1:
+        single_process_runner(data_file_path, args.get("skip_to"))
+    else:
+        multi_process_runner(num_cpu, data_file_path, args.get("skip_to"))