PEP 532: Rework De Morgan's Laws section

pep-0532.txt

@@ -778,37 +778,40 @@ combination of ``not`` operations.
 
 For ``and`` and ``or`` in Python, these invariants can be described as follows::
 
-    assert (A and B) == (not (not A or not B))
-    assert (A or B) == (not (not A and not B))
+    assert bool(A and B) == bool(not (not A or not B))
+    assert bool(A or B) == bool(not (not A and not B))
 
 That is, if you take one of the operators, invert both operands, switch to the
 other operator, and then invert the overall result, you'll get the same
-answer as you did from the original operator. (This may seem redundant,
-but in many situations it actually lets you eliminate double negatives and find
-tautologically true or false subexpressions, thus reducing the overall
-expression size).
+answer (in a boolean sense) as you did from the original operator. (This may
+seem redundant, but in many situations it actually lets you eliminate double
+negatives and find tautologically true or false subexpressions, thus reducing
+the overall expression size).
 
 For circuit breakers, defining a suitable invariant is complicated by the
-fact that they're designed to eliminate themselves from the expression result
-when they're short-circuited, which is an inherently asymmetric behaviour.
-Accordingly, that inherent asymmetry needs to be corrected for when mapping
-De Morgan's Laws to the expected behaviour of symmetric circuit breakers.
+fact that they're often going to be designed to eliminate themselves from the
+expression result when they're short-circuited, which is an inherently
+asymmetric behaviour. Accordingly, that inherent asymmetry needs to be
+accounted for when mapping De Morgan's Laws to the expected behaviour of
+symmetric circuit breakers.
+
+One way this complication can be addressed is to wrap the operand that would
+otherwise short-circuit in ``operator.true``, ensuring that when ``bool`` is
+applied to the overall result, it uses the same definition of truth that was
+used to decide which branch to evaluate, rather than applying ``bool`` directly
+to the circuit breaker's input value.
 
 Specifically, for the new short-circuiting operators, the following properties
 would be reasonably expected to hold for any well-behaved symmetric circuit
-breaker that implements all of ``__bool__``, ``__not__``, ``__then__``, and
-``__else__``:
+breaker that implements both ``__bool__`` and ``__not__``::
 
-    cb_A = to_cb(A)
-    cb_B = to_cb(B)
-    assert (B if cb_A) is short_circuit(not (not cb_A else not cb_B))
-    assert (cb_A else B) is short_circuit(not (not cb_B if not cb_A))
+    assert bool(B if true(A)) == bool(not (true(not A) else not B))
+    assert bool(true(A) else B) == bool(not (not B if true(not A)))
 
-Where ``to_cb`` returns a symmetric circuit breaker that produces the supplied
-value when short-circuited, and ``short_circuit`` is defined as::
-
-    def short_circuit(expr):
-        return expr if expr else expr
+Note the order of operations on the right hand side (applying ``true``
+*after* inverting the input circuit breaker) - this ensures that an
+assertion is actually being made about ``type(A).__not__``, rather than
+merely being about the behaviour of ``type(true(A)).__not__``.
 
 At the very least, ``types.CircuitBreaker`` instances would respect this
 logic, allowing existing boolean expression optimisations (like double