✨ forward chaining v0.

.gitignore

@@ -1 +1,2 @@
-__pycache__
+__pycache__
+*.prof

Makefile

@@ -0,0 +1,5 @@
+.PHONY: prof
+
+prof:
+	python -m cProfile -o sine_patre.prof sine_patre.py
+	snakeviz sine_patre.prof

fol/__init__.py

@@ -1,5 +1,6 @@
 from fol import lexer
 from fol import parser
+from fol import kb
 from fol import pretty
 from fol import cnf
 from fol.unify import unify

fol/cnf.py

@@ -1,12 +1,28 @@
 import fol
 
 
+class Counter:
+    def __init__(self):
+        self.values = {}
+        self.counter = 0
+
+    def get(self, name):
+        if name in self.values.keys():
+            return self.values[name]
+        self.values[name] = self.counter
+        self.counter += 1
+        return self.counter - 1
+
+    def begin(self):
+        self.values = {}
+
+
 def elim_imp(f):
     res = fol.node.Node(f.name, f.value)
 
     if f.name == 'IMP':
         a = fol.node.Node('NOT')
-        a.add_child(f.children[0])
+        a.add_child(elim_imp(f.children[0]))
         res = fol.node.Node('OR')
         res.add_child(elim_imp(a))
         res.add_child(elim_imp(f.children[1]))
@@ -23,9 +39,9 @@ def neg(f):
 
     if f.name == 'NOT' and f.children[0].name in ['OR', 'AND']:
         p = fol.node.Node('NOT')
-        p.add_child(f.children[0].children[0])
+        p.add_child(neg(f.children[0].children[0]))
         q = fol.node.Node('NOT')
-        q.add_child(f.children[0].children[1])
+        q.add_child(neg(f.children[0].children[1]))
 
         if f.children[0].name == 'OR':
             res = fol.node.Node('AND')
@@ -38,24 +54,23 @@ def neg(f):
             res.add_child(neg(q))
             return res
 
+    res = fol.node.Node(f.name, f.value)
+
+    for c in f.children:
+        res.add_child(neg(c))
+
     return res
 
 
-def normalize(f, values={}):
+def normalize(f, counter):
     res = fol.node.Node(f.name, f.value)
 
     if f.name == 'VAR':
-        if f.value in values.keys():
+        res.value = f'x{counter.get(f.value)}'
-            res.value = values[f.value]
-        else:
-            new_name = f'x{len(values)}'
-            values[res.value] = new_name
-            res.value = new_name
-
         return res
 
     for child in f.children:
-        res.add_child(normalize(child))
+        res.add_child(normalize(child, counter))
 
     return res
 
@@ -207,7 +222,12 @@ def distrib(f):
     return f
 
 
-def cnf(f):
+def cnf(f, counter=None):
-    return distrib(
+    if counter is None:
-        skolem(prenex(normalize(neg(elim_imp(f)))))
+        counter = Counter()
+
+    g = distrib(
+        skolem(prenex(normalize(neg(elim_imp(f)), counter)))
     ).remove_quant('FORALL')
+
+    return g

fol/kb.py

@@ -0,0 +1,168 @@
+import fol
+
+
+class Kb:
+    def __init__(self):
+        self.base = []
+        self.counter = fol.cnf.Counter()
+
+    def make_f(self, h):
+        self.counter.begin()
+        f = h
+        if type(f) is str:
+            f = fol.p(f)
+        self.counter.begin()
+        f = fol.cnf.cnf(f, self.counter)
+
+        if f.name == 'OR':
+            f = f.list_of('OR')
+        else:
+            f = [f]
+
+        return f
+
+    def make_req(self, h):
+        f = h
+        if type(f) is str:
+            f = fol.p(f)
+
+        if f.name == 'OR':
+            f = f.list_of('OR')
+        else:
+            f = [f]
+
+        return f
+
+    def check_request(self, request):
+        for r in request:
+            if r.name not in ['NOT', 'PRED']:
+                raise Exception(f'invalid statement {repr(r)}')
+
+    def conds(self, statement):
+        result = []
+        for f in statement:
+            if f.name == 'NOT':
+                result.append(f.children[0])
+        return result
+
+    def conclusion(self, statement):
+        for f in statement:
+            if f.name != 'NOT':
+                return f
+        return None
+
+    @property
+    def rules(self):
+        res = []
+        for r in self.base:
+            if len(r) > 1:
+                res.append(r)
+        return res
+
+    @property
+    def facts(self):
+        res = []
+        for r in self.base:
+            if len(r) == 1:
+                res.append(r[0])
+        return res
+
+    def exists(self, f):
+        h = self.make_f(f)
+        for g in self.base:
+            if self.clause_equals(h, g):
+                return True
+        return False
+
+    def clause_equals(self, left, right):
+        if len(left) != len(right):
+            return False
+
+        for element in left:
+            if not self.clause_in(element, right):
+                return False
+
+        for element in right:
+            if not self.clause_in(element, left):
+                return False
+
+        return True
+
+    def clause_in(self, clause, lst):
+        for other in lst:
+            same = fol.unify(clause, other) is not None
+            if same:
+                return True
+        return False
+
+    def tell(self, request):
+        req = self.make_f(request)
+        self.check_request(req)
+        self.base.append(req)
+
+    def ask(self, request):
+        for i in range(20):
+            n = len(self.base)
+            self.update()
+            if n == len(self.base):
+                break
+
+        req = self.make_req(request)
+        results = []
+
+        for f in self.base:
+            s = fol.unify(f, req)
+            if s is not None:
+                results.append(s)
+
+        return results
+
+    def update(self):
+        for rule in self.rules:
+            conclusion = self.conclusion(rule)
+            solution = []
+            solutions = []
+            self.solve(rule, self.conds(rule), self.facts, solution, solutions)
+            for sol in solutions:
+                concl = conclusion.subst(sol)
+                if not self.exists(concl):
+                    self.base.append([concl])
+                    return
+
+    def merge_substs(self, substs):
+        res = {}
+        for s in substs:
+            for k in s.keys():
+                if k in res.keys() and not res[k].equals(s[k]):
+                    return None
+                res[k] = s[k]
+        return res
+
+    def solve(self, rule, conds, facts, solution, solutions):
+        if len(conds) == 0:
+            substs = []
+
+            for sol in solution:
+                s = fol.unify(sol[0], sol[1])
+                if s is not None:
+                    substs.append(s)
+
+            s = self.merge_substs(substs)
+
+            if s is not None:
+                solutions.append(s)
+            return
+
+        for cond in conds:
+            for fact in facts:
+                solution.append((cond, fact))
+
+                self.solve(
+                    rule,
+                    [c for c in conds if c != cond],
+                    [f for f in facts if f != fact],
+                    solution,
+                    solutions
+                )
+
+                solution.pop()

fol/node.py

@@ -1,3 +1,6 @@
+import fol
+
+
 class Node:
     def __init__(self, name, value=None):
         self.name = name
@@ -8,7 +11,7 @@ class Node:
         self.children.append(child)
 
     def __repr__(self):
-        return str(self)
+        return fol.pretty.get(self)
 
     def __str__(self):
         res = self.name
@@ -68,3 +71,32 @@ class Node:
                 return False
 
         return True
+
+    def list_of(self, name):
+        result = []
+
+        if self.name == name:
+            for c in self.children:
+                if c.name != name:
+                    result.append(c)
+                result.extend(c.list_of(name))
+
+        return result
+
+    def flatten(self):
+        result = self.list_of(self.name)
+        print(result)
+        root = fol.node.Node(self.name, self.value)
+        root.children = result
+        return root
+
+    def find_by_name(self, name):
+        if self.name == name:
+            return [self]
+
+        res = []
+
+        for c in self.children:
+            res.extend(c.find_by_name(name))
+
+        return res

fol/pretty.py

@@ -1,6 +1,3 @@
-import fol
-
-
 def get(f):
     if f.name == 'EXISTS':
         return f'\\exist {get(f.children[0])}({get(f.children[1])})'

fol/tests/test_cnf.py

@@ -32,7 +32,8 @@ def test_cnf_neg(f, res):
      'Pre(f(x0)) -> Post(g(g(x1), x0))'),
 ])
 def test_cnf_normalize(f, res):
-    assert fol.cnf.normalize(fol.p(f)).equals(fol.p(res))
+    counter = fol.cnf.Counter()
+    assert fol.cnf.normalize(fol.p(f), counter).equals(fol.p(res))
 
 
 @pytest.mark.parametrize(['f', 'res'], [
@@ -116,7 +117,12 @@ def test_distrib(oracle, f):
 
 @pytest.mark.parametrize(['f', 'oracle'], [
     ('Friend(x, y) -> Friend(y, x)',
-     '~Friend(x0, x1) | Friend(x1, x0)')
+     '~Friend(x0, x1) | Friend(x1, x0)'),
+
+    ('(Friend(x, y) & Friend(y, z)) -> Friend(x, z)',
+     '(~Friend(x0, x1) | ~Friend(x1, x2)) | Friend(x0, x2)')
 ])
 def test_cnf(oracle, f):
+    print(fol.pretty.get(fol.p(f)))
+    print(fol.pretty.get(fol.cnf.cnf(fol.p(f))))
     assert fol.cnf.cnf(fol.p(f)).equals(fol.p(oracle))

fol/tests/test_kb.py

@@ -0,0 +1,11 @@
+import fol
+
+
+def test_kb_simple():
+    kb = fol.kb.Kb()
+    kb.tell('Friend(ALICE, BOB)')
+
+    res = kb.ask('Friend(ALICE, x)')
+
+    assert len(res) == 1
+    assert res[0]['x'].value == 'BOB'

fol/tests/test_unify.py

@@ -6,16 +6,37 @@ def test_unify_simple():
         fol.p('Hello(x)'),
         fol.p('Hello(ALICE)')
     )
+
     assert subst is not None
     assert len(subst) == 1
     assert str(subst['x']) == 'CONST[ALICE]'
 
 
+def test_unify_equals():
+    subst = fol.unify(
+        fol.p('Hello(ALICE)'),
+        fol.p('Hello(ALICE)')
+    )
+
+    assert subst is not None
+    assert len(subst) == 0
+
+
+def test_unify_different_predicate_name():
+    subst = fol.unify(
+        fol.p('Hello(x)'),
+        fol.p('World(ALICE)')
+    )
+
+    assert subst is None
+
+
 def test_unify_fun():
     subst = fol.unify(
         fol.p('Hello(x, f(x))'),
         fol.p('Hello(ALICE, f(ALICE))')
     )
+
     assert subst is not None
     assert len(subst) == 1
     assert str(subst['x']) == 'CONST[ALICE]'

fol/unify.py

@@ -1,29 +1,84 @@
+import fol
+
+
 def unify(lhs, rhs):
-    res = {}
+    s = {}
-    try:
+    return _unify(lhs, rhs, s)
-        unify_res(lhs, rhs, res)
+
-    except Exception:
+
+def _unify(lhs, rhs, s):
+    if s is None:
         return None
-    return res
+    elif is_equal(lhs, rhs):
+        return s
+    elif is_var(lhs):
+        return unify_var(lhs, rhs, s)
+    elif is_var(rhs):
+        return unify_var(rhs, lhs, s)
+    elif is_compound(lhs) and is_compound(rhs) and (
+            lhs.name == rhs.name and lhs.value == rhs.value
+            ):
 
-
+        return _unify(
-def unify_res(lhs, rhs, result):
+            lhs.children,
-    if lhs.name == 'VAR':
+            rhs.children,
-        unify_var(lhs, rhs, result)
+            s
-    elif rhs.name == 'VAR':
+        )
-        unify_var(rhs, lhs, result)
+    elif is_list(lhs) and is_list(rhs):
-    else:
+        if len(lhs) != len(rhs):
-        left = lhs.children
+            return None
-        right = rhs.children
+        elif len(lhs) == 0:
-        if len(left) == len(right):
+            return s
-            for i in range(len(left)):
+        elif len(lhs) == 1:
-                unify_res(left[i], right[i], result)
+            return _unify(lhs[0], rhs[0], s)
-
-
-def unify_var(var, rhs, result):
-    if rhs.name in ['VAR', 'CONST', 'FUN'] and rhs.value != var.value:
-        if var.value in result.keys() \
-           and not result[var.value].equals(rhs):
-            raise Exception('')
         else:
-            result[var.value] = rhs
+            return _unify(lhs[1:], rhs[1:], _unify(lhs[0], rhs[0], s))
+    else:
+        return None
+
+
+def unify_var(var, x, s):
+    if var.value in s.keys():
+        return _unify(s[var.value], x, s)
+    elif x in s.keys():
+        return _unify(var, s[x], s)
+    elif occur_check(var, x):
+        return None
+    else:
+        s[var.value] = x
+        return s
+
+
+def occur_check(var, x):
+    if var.name == x.name and var.value == x.value:
+        return True
+
+    for child in x.children:
+        if occur_check(var, child):
+            return True
+
+    return False
+
+
+def is_compound(f):
+    if type(f) is fol.node.Node:
+        return len(f.children) > 0
+    return False
+
+
+def is_equal(lhs, rhs):
+    if type(lhs) is str and type(rhs) is str:
+        return lhs == rhs
+
+    if type(lhs) is fol.node.Node and type(rhs) is fol.node.Node:
+        return lhs.equals(rhs)
+
+    return False
+
+
+def is_var(f):
+    return type(f) is fol.node.Node and f.name == 'VAR'
+
+
+def is_list(value):
+    return type(value) is list

sine_patre.py

@@ -1,2 +1,13 @@
+import fol
+
 if __name__ == '__main__':
-    print('Hello, World!')
+    kb = fol.kb.Kb()
+    try:
+        kb.tell('Friend(ALICE, BOB)')
+        kb.tell('Friend(BOB, CLAIRE)')
+        kb.tell('Friend(x, y) -> Friend(y, x)')
+        kb.tell('(Friend(x, y) & Friend(y, z)) -> Friend(x, z)')
+
+        print(kb.ask('Friend(ALICE, x)'))
+    except KeyboardInterrupt:
+        pass