# Glossary¶

Apply
Instances of `Apply` represent the application of an Op to some input Variable (or variables) to produce some output Variable (or variables). They are like the application of a [symbolic] mathematical function to some [symbolic] inputs.

Broadcasting is a mechanism which allows tensors with different numbers of dimensions to be used in element-by-element (i.e. element-wise) computations. It works by (virtually) replicating the smaller tensor along the dimensions that it is lacking.

Constant

A variable with an immutable value. For example, when you type

```>>> x = at.ivector()
>>> y = x + 3
```

Then a `constant` is created to represent the `3` in the graph.

See also: `graph.basic.Constant`

Elemwise

An element-wise operation `f` on two tensor variables `M` and `N` is one such that:

```f(M, N)[i, j] == f(M[i, j], N[i, j])
```

In other words, each element of an input matrix is combined with the corresponding element of the other(s). There are no dependencies between elements whose `[i, j]` coordinates do not correspond, so an element-wise operation is like a scalar operation generalized along several dimensions. Element-wise operations are defined for tensors of different numbers of dimensions by broadcasting the smaller ones. The `Op` responsible for performing element-wise computations is `Elemwise`.

Expression
See Apply
Expression Graph

A directed, acyclic set of connected Variable and Apply nodes that express symbolic functional relationship between variables. You use Aesara by defining expression graphs, and then compiling them with aesara.function.

Destructive

An Op is destructive–of particular input(s)–if its computation requires that one or more inputs be overwritten or otherwise invalidated. For example, inplace`Op`s are destructive. Destructive `Op`s can sometimes be faster than non-destructive alternatives. Aesara encourages users not to put destructive `Op`s into graphs that are given to aesara.function, but instead to trust the rewrites to insert destructive `Op`s judiciously.

Destructive `Op`s are indicated via a `Op.destroy_map` attribute. (See `Op`.

Graph
see expression graph
Inplace
Inplace computations are computations that destroy their inputs as a side-effect. For example, if you iterate over a matrix and double every element, this is an inplace operation because when you are done, the original input has been overwritten. `Op`s representing inplace computations are destructive, and by default these can only be inserted by rewrites, not user code.
A `Linker` instance responsible for “running” the compiled function. Among other things, the linker determines whether computations are carried out with C or Python code.
Mode
A `Mode` instance specifying an optimizer and a linker that is passed to aesara.function. It parametrizes how an expression graph is converted to a callable object.
Op

The `.op` of an Apply, together with its symbolic inputs fully determines what kind of computation will be carried out for that `Apply` at run-time. Mathematical functions such as addition (i.e. `aesara.tensor.add()`) and indexing `x[i]` are `Op`s in Aesara. Much of the library documentation is devoted to describing the various `Op`s that are provided with Aesara, but you can add more.

Rewriter
A function or class that transforms an Aesara graph.
Optimizer
An instance of a rewriter that has the capacity to provide an improvement to the performance of a graph.
Pure
An Op is pure if it has no destructive side-effects.
Storage
The memory that is used to store the value of a `Variable`. In most cases storage is internal to a compiled function, but in some cases (such as constant and shared variable the storage is not internal.
Shared Variable
A Variable whose value may be shared between multiple functions. See `shared` and `aesara.function`.
aesara.function
The interface for Aesara’s compilation from symbolic expression graphs to callable objects. See `function.function()`.
Type

The `.type` of a Variable indicates what kinds of values might be computed for it in a compiled graph. An instance that inherits from `Type`, and is used as the `.type` attribute of a Variable.

Variable

The the main data structure you work with when using Aesara. For example,

```>>> x = at.ivector()
>>> y = -x**2
```

`x` and `y` are both `Variable`s, i.e. instances of the `Variable` class.

Some tensor `Op`s (such as `Subtensor` and `DimShuffle`) can be computed in constant time by simply re-indexing their inputs. The outputs of such `Op`s are views because their storage might be aliased to the storage of other variables (the inputs of the `Apply`). It is important for Aesara to know which `Variable`s are views of which other ones in order to introduce Destructive `Op`s correctly.
`Op`s that are views have their `Op.view_map` attributes set.