diff --git a/probably/pgcl/parser.py b/probably/pgcl/parser.py
index 7f05a0e..59fdd86 100644
--- a/probably/pgcl/parser.py
+++ b/probably/pgcl/parser.py
@@ -99,6 +99,8 @@
     %import common.WS
 """
 
+_illegal_variable_names = {"true", "false"}
+
 _OPERATOR_TABLE = [[infixl("or", "||")], [infixl("and", "&")],
                    [infixl("leq", "<="),
                     infixl("le", "<"),
@@ -183,6 +185,8 @@ def _child_str(t: Tree, index: int) -> str:
 def _parse_var(t: Tree) -> Var:
     assert t.data == 'var'
     assert t.children[0].type == 'CNAME'  # type: ignore
+    if t.children[0] in _illegal_variable_names:
+        raise SyntaxError(f"Illegal variable name: {t.children[0]}")
     return str(_child_str(t, 0))
 
 
diff --git a/tests/test_distributions.py b/tests/test_parser.py
similarity index 72%
rename from tests/test_distributions.py
rename to tests/test_parser.py
index 2e2e8ce..b954ec0 100644
--- a/tests/test_distributions.py
+++ b/tests/test_parser.py
@@ -1,5 +1,6 @@
 from probably.pgcl.parser import parse_pgcl
 from probably.pgcl.ast import *
+from pytest import raises
 
 def test_all_distributions():
     program = parse_pgcl("""
@@ -23,3 +24,12 @@ def test_all_distributions():
         LogDistExpr(NatLitExpr(1)),
         BernoulliExpr(NatLitExpr(1)),
         BinomialExpr(NatLitExpr(1), NatLitExpr(2))]
+
+def test_illegal_variable_names():
+    illegal_names = {"true", "false"}
+    for name in illegal_names:
+        with raises(SyntaxError) as e:
+            parse_pgcl(f"""
+                nat {name}
+            """)
+        assert "Illegal variable name: " in e.value.msg