Fix for unify algorithm in logic.py (aimacode#1101)

alessandrocuda · antmarakis · commit e5204f69feaa · 2019-08-19T14:17:55.000+01:00
* Fix issue aimacode#1053 Unify algorithm fixed by performing a perform a cascade substitution when a new mapping is added This issue was already known and fixed in the aima-java repo. * added two more test in test_logic.py updated documentation for cascade_substitution function in logic.py * Fixed brackets missing in test_logic.py for the new test * Fixed typo error, missing space and double quotes for docstrings * comments changed to cascade_substitution function in logic.py
diff --git a/logic.py b/logic.py
@@ -193,8 +193,7 @@ def parse_definite_clause(s):
 
 
 # Useful constant Exprs used in examples and code:
-A, B, C, D, E, F, G, P, Q, x, y, z = map(Expr, 'ABCDEFGPQxyz')
-
+A, B, C, D, E, F, G, P, Q, a, x, y, z, u = map(Expr, 'ABCDEFGPQaxyzu')
 
 # ______________________________________________________________________________
 
@@ -1370,7 +1369,9 @@ def unify_var(var, x, s):
     elif occur_check(var, x, s):
         return None
     else:
-        return extend(s, var, x)
+        new_s = extend(s, var, x)
+        cascade_substitution(new_s)
+        return new_s
 
 
 def occur_check(var, x, s):
@@ -1415,6 +1416,33 @@ def subst(s, x):
     else:
         return Expr(x.op, *[subst(s, arg) for arg in x.args])
 
+def cascade_substitution(s):
+    """This method allows to return a correct unifier in normal form
+    and perform a cascade substitution to s.
+    For every mapping in s perform a cascade substitution on s.get(x)
+    and if it is replaced with a function ensure that all the function 
+    terms are correct updates by passing over them again.
+
+    This issue fix: https://github.com/aimacode/aima-python/issues/1053
+    unify(expr('P(A, x, F(G(y)))'), expr('P(z, F(z), F(u))')) 
+    must return {z: A, x: F(A), u: G(y)} and not {z: A, x: F(z), u: G(y)}
+    
+    >>> s = {x: y, y: G(z)}
+    >>> cascade_substitution(s)
+    >>> print(s)
+    {x: G(z), y: G(z)}
+    
+    Parameters
+    ----------
+    s : Dictionary
+        This contain a substution
+    """
+
+    for x in s:
+        s[x] = subst(s, s.get(x))
+        if isinstance(s.get(x), Expr) and not is_variable(s.get(x)):
+        # Ensure Function Terms are correct updates by passing over them again.
+            s[x] = subst(s, s.get(x))
 
 def standardize_variables(sentence, dic=None):
     """Replace all the variables in sentence with new variables."""
diff --git a/tests/test_logic.py b/tests/test_logic.py
@@ -163,7 +163,13 @@ def test_unify():
     assert unify(x & 4 & y, 6 & y & 4, {}) == {x: 6, y: 4}
     assert unify(expr('A(x)'), expr('A(B)')) == {x: B}
     assert unify(expr('American(x) & Weapon(B)'), expr('American(A) & Weapon(y)')) == {x: A, y: B}
+    assert unify(expr('P(F(x,z), G(u, z))'), expr('P(F(y,a), y)')) == {x: G(u, a), z: a, y: G(u, a)}
 
+    # test for https://github.com/aimacode/aima-python/issues/1053
+    # unify(expr('P(A, x, F(G(y)))'), expr('P(z, F(z), F(u))')) 
+    # must return {z: A, x: F(A), u: G(y)} and not {z: A, x: F(z), u: G(y)}
+    assert unify(expr('P(A, x, F(G(y)))'), expr('P(z, F(z), F(u))')) == {z: A, x: F(A), u: G(y)}
+    assert unify(expr('P(x, A, F(G(y)))'), expr('P(F(z), z, F(u))')) == {x: F(A), z: A, u: G(y)}
 
 def test_pl_fc_entails():
     assert pl_fc_entails(horn_clauses_KB, expr('Q'))
