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+The semantics of each operator with regard to its input and output *result
+kinds* vary. However there is a large set of operators that share common
+semantics. These Operators are called *Pure Operator*s and identified as such
+in documentation and reference.
+
+*Pure Op*s only change when any of their inputs change and are often
+equivalent to a pure mathematical function. The inputs of a *Pure Op* can be
+mixed between all kinds of results, subject to the following rules:
+
+- If any of the inputs is a !-stream, the output is also an !-stream and will
+  only fire when the input stream does. All other inputs will be sampled at
+  that moment. At most one !-stream is allowed as an input.
+- Otherwise, if there are one more ~-streams in the inputs, the output will
+  also be a ~-stream and will be updated whenever any of the inputs changes.
+- Otherwise the output is a constant.
+
+The input and output *types* are defined by the concrete Op.
+
+As an example, let's consider [math/+][]:
+
+    (import* math time)
+
+    (trace (+ 1 2 3))
+    #((+ num= num= num=) -> num=
+      trace (+ 1 2 3): <num= 6>)
+
+    (trace (+ 1 2 (lfo 2)))
+    #((+ num= num= num~) -> num~
+      trace (+ 1 2 (lfo 2)): <num~ 4.0>
+      trace (+ 1 2 (lfo 2)): <num~ 3.9882585630406>)
+
+    (trace (+ 1 2 (every 1 3)))
+    #((+ num= num= num!) -> num!
+      trace (+ 1 2 (every 2 3)): <num! 6>
+      trace (+ 1 2 (every 2 3)): <num! 6>)
+
+    (trace (+ 1 (lfo 2) (every 1 3)))
+    #((+ num= num~ num!) -> num!
+      trace (+ 1 (lfo 2) (every 2 3)): <num! 4.9950529446967>
+      trace (+ 1 (lfo 2) (every 2 3)): <num! 4.9950529446967>)
+
+Sometimes a *Pure Op* will require additional constraints on the *kinds* of
+some of its inputs. These will be specified in the documentation.