Addition of generic / introductory glossary

docs/src/glossary.md

@@ -0,0 +1,81 @@
+# ChainRules Glossary
+
+This glossary serves as a quick reference for common terms used in the field of Automatic Differentiation, as well as those used throughout the documentation relating specifically to ChainRules.
+
+##Definitions:
+
+###Adjoint:
+
+The conjugate transpose of the Jacobian for a given function `f`.
+
+###Derivative:
+
+The derivative of a function `y = f(x)` with respect to the independent variable `x` denoted `f'(x)` or `dy/dx` is the rate of change of the dependent variable `y` with respect to the change of the independent variable `x`. In multiple dimensions, we may refer to the gradient of a function.
+
+###Differential:
+
+The differential of a given function `y = f(x)` denoted `dy` is the product of the derivative function `f'(x)` and the increment of the independent variable `dx`. In multiple dimensions, it is the sum of these products across each dimension (using the partial derivative and the given independent variable's increment).
+
+In ChainRules, differentials are types ("differential types") and correspond to primal types. A differential should represent a difference between two primal values.
+
+####Natural Differential:
+
+A natural differential type for a given primal type is the type people would intuitively associate with representing the difference between two values of the primal type.
+
+####Structural Differential:
+
+If a given primal type `P` does not have a natural differential, we need to come up with one that makes sense. These are called structural differentials and are represented as `Composite{P, <:NamedTuple}`.
+
+####Semi-Structural Differential:
+
+A structural differential that contains at least one natural differential field.
+
+####Thunk:
+
+An "unnatural" differential type. If we wish to delay the computation of a derivative for whatever reason, we wrap it in a `Thunk` or `ImplaceableThunk`. It holds off on computing the wrapped derivative until it is needed.
+
+####Zero:
+
+`Zero()` can also be a differential type. If you have trouble understanding the rules enforced upon differential types, consider this one first, as `Zero()` is the trivial vector space.
+
+###Directional Derivative:
+
+The directional derivative of a function `f` at any given point in any given unit-direction is the gradient multiplied by the direction. It represents the rate of change of `f` in that direction.
+
+###F-rule:
+
+A function used in forward-mode differentiation. For a given function `f`, it takes in the positional and keyword arguments of `f` and returns the primal result and the pushforward.
+
+###Gradient:
+
+The gradient of a scalar function `f` represented by `∇f` is a vector function whose components are the partial derivatives of `f` with respect to each dimension of the domain of `f`.
+
+###Jacobian:
+
+The Jacobian of a vector-valued function `f` is the matrix of `f`'s first-order partial derivatives.
+
+###Jacobian Transpose Vector Product (j'vp):
+
+The product of the adjoint of the Jacobian and the vector in question. A description of the pullback in terms of its Jacobian.
+
+###Jacobian Vector Product (jvp):
+
+The product of the Jacobian and the vector in question. It is a description of the pushforward in terms of its Jacobian.
+
+###Primal:
+
+Something relating to the original problem, as opposed to relating to the derivative. In ChainRules, primals are types ("primal types").
+
+###Pullback:
+
+`Pullback(f)` describes the sensitivity of the input of `f` as a function of (for the relative change to) the sensitivity of the output of `f`. Can be represented as the dot product of a vector (left) the adjoint Jacobian (right).
+
+###Pushforward:
+
+`Pushforward(f)` describes the sensitivity of the output of `f` as a function of (for the relative change to) the sensitivity of the input of `f`. Can be represented as the dot product of the Jacobian (left) and a vector (right).
+
+###R-rule:
+
+A function used in reverse-mode differentiation. For a given function `f`, it takes in the positional and keyword arguments of `f` and returns the primal result and the pullback.
+
+