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Filename :
Cat.py
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class Graph: def __init__(self, objects, arrows): self.objects = objects # Sequence of objects self.arrows = arrows # Map[name] ->pair(object, object) def source(self, x): return self.arrows[x][0] def target(self, x): return self.arrows[x][1] def get_dual(self): objects = self.objects arrows = dict([(arrow, (tgt, src)) for (arrow, (src, tgt)) in list(self.arrows.items())]) return self.__class__(objects, arrows) class Cat: # Category presented by a graph (with objects and generators) and relations. def __init__(self, graph, relations): # category is defined by the parameters: # graph.objects: sequenceof(O) # graph.arrows: dict mapping(A, pairof(O in objects)) # relations: sequence(pairof(sequence(A), sequence(A))) self.graph = graph self.relations = relations def get_dual(self): graph = self.graph.get_dual() relations = dual_relations(self.relations) return self.__class__(graph, relations) class Functor: def __init__(self, fo, fa, src=None, tgt=None): self.fo = adapt_function(fo) self.fa = adapt_function(fa) self.src = src self.tgt = tgt class Function: def __init__(self, map, src, tgt): f = getattr(map, '__getitem__', None) if callable(f): pass else: f = map if not callable(f): raise TypeError( 'Function: map is neither callable or indexable') self.f = f self.src = src self.tgt = tgt def __getitem__(self, *args): return self.f(*args) def __call__(self, *args, **kwargs): return self.f(*args, **kwargs) def __str__(self): return '%s(%s, %s, %s)' % (self.__class__, self.src, self.tgt, self.f) def asdict(self): return dict([(x, self[x]) for x in self.src]) def items(self): return [(x, self[x]) for x in self.src] def keys(self): return list(self.src) def values(self): return [v for (k, v) in list(self.items())] class Identity(Function): def __init__(self, src): Function.__init__(lambda x: x, src, src) def check_graph(G): # Check that G is a valid graph object # with arrows that have all source and target in G.objects Gob = G.objects for a in G.arrows: if not G.source(a) in Gob: raise ValueError( 'Arrow %r has source %r not in graph objects' % (a, G.source(a))) if not G.target(a) in Gob: raise ValueError( 'Arrow %r has target %r not in graph objects' % (a, G.target(a))) def check_rules(R, G): # Check that the rules in R contain valid composing arrows in graph G coms = [] for (left, right) in R: coms.append(left) coms.append(right) for com in coms: a0 = None for a in com: if a not in G.arrows: raise ValueError( 'Arrow %r, used in a rule, is not a valid arrow' % (a,)) if a0 is not None: if G.source(a) != G.target(a0): raise ValueError('''\ Source of arrow %r (%r) does not match target of arrow %r (%r)''' % ( a, G.source(a), a0, G.target(a0))) a0 = a def check_cat(C): check_graph(C.graph) check_rules(C.relations, C.graph) def oarcat(objects, arrows, relations): return Cat(Graph(objects, arrows), relations) def adapt_function(f): if not isinstance(f, Function): if isinstance(f, dict): src = list(f.keys()) tgt = list(f.values()) else: src = None tgt = None f = Function(f, src, tgt) return f def dual_relations(relations): dual = [] for (a, b) in relations: a = list(a) b = list(b) a.reverse() b.reverse() dual.append((tuple(a), tuple(b))) return dual