Merge pull request google#680 from jheek:lift-md

PiperOrigin-RevId: 345646943

docs/notes/lift.md

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+# Design Note: transformation lifting
+
+## Introduction
+
+JAX uses a functional api meaning that it deals only which pure functions only.
+A pure function is defined as a function where the output only depends on the function arguments.
+Therefore, mutable state outside the function should not affect the function itself and the function
+itself should not cause side effects in objects that live outside of the function.
+
+Python functions do not have to be pure because they allow side effects or mutations to occur.
+For JAX restricting the API to pure functions has a number of advantages:
+
+1. It becames easier to reason about functions locally
+2. Both stochasticity and determinism are explicit because a function can only return a different output if the arguments are changed.
+3. Functional transforms which would otherwise be ambigious. 
+
+## Functionalization
+
+TODO
+
+## Lifting
+
+TODO
+
+## Alternatives
+
+TODO