# Built-in Data¶

## Boolean¶

`True`

and `False`

are booleans.

## Scalar Values¶

In Egison, numeric scalar values (except for floats) are treated as polynomials and represented in the mathematical canonical form.

### Integer¶

```
1
0
-100
```

### Rational number¶

```
1 / 3
4 / 6 ---> 2 / 3
```

### Symbols¶

Unbound variables are interpreted as symbols.

```
> x + 1
x + 1
> f 2 -- uninterpreted functions
f 2
```

Mathematical expressions with symbols are automatically normalized into the normal form.

```
> (x + 1) ^ 2
x^2 + 2 * x + 1
```

#### Special symbols¶

Egison implements normalization algorithm for some of the common mathematical symbols.

`i`

(imaginary unit):

```
> i * i
-1
> (1 + i)^2
2 * i
```

`sqrt`

and `rt`

(`sqrt n`

denotes \(\sqrt{n}\) and `rt m n`

denotes \(\sqrt[m]{n}\)):

```
> (sqrt 2) ^ 2
2
> (rt 3 2) ^ 3
2
```

`sin`

and `cos`

:

```
> (sin x)^2 + (cos x)^2
1
```

## Float¶

```
1.0
1e-1 ---> 0.1
2e3 ---> 2000.0
```

## Inductive data¶

A variable starting with an upper-case letter is interpreted as a constructor of inductive data. You don’t need to define the inductive data before using it.

```
Leaf
Node 1 Leaf (Node 2 Leaf Leaf)
```

## Tuple (Multiple values)¶

A tuple is denoted as a sequence of elements enclosed in parentheses and separated by `,`

.
Tuples of single element cannot be written.

```
() -- zero-element tuple
(1, 2)
(2, "foo", True)
```

## Collection¶

A collection is a sequence of elements that are enclosed in brackets and separated by `,`

.

```
[]
[1]
[1, 2]
[1, 2, 3]
```

## Tensor¶

A tensor is a sequence of elements enclosed in double brackets `[|`

`|]`

and separated by `,`

.
The \(i\)-th element of a tensor `t`

can be retrieved by `t_i`

. Note that it is 1-indexed.

```
t := [| 1, 2, 3, 4, 5 |]
t_1 ---> 1
-- The index can be any expression that evaluates to an integer.
t_(2+3) ---> 5
t_6 ---> Error: Tensor index out of bounds
```

You can get the shape of a tensor with `tensorShape`

.

```
tensorShape [| 1, 2, 3, 4, 5 |] ---> [5]
```

Multi-dimensional tensors can be defined by nesting tensors.

```
[| [| 1, 2, 3 |], [| 4, 5, 6 |], [| 7, 8, 9 |] |]_1 ---> [| 1, 2, 3 |]
[| [| 1, 2, 3 |], [| 4, 5, 6 |], [| 7, 8, 9 |] |]_2_3 ---> 6
```

Egison prepares special syntax for tensors. See Syntax for Tensor Computation for detail.

## Hash Maps¶

A hash map is a sequence of key-value pairs enclosed in double braces `{|`

`|}`

.
The value of a key `k`

in a hash map `h`

can be retrieved by `h_k`

.
If the key is not included in the keys of the hash map, the result will be `undefined`

.

```
{| (1, 11) (2, 12) (3, 13) (4, 14) (5, 15) |}_1 ---> 11
{| (1, 11) (2, 12) (3, 13) (4, 14) (5, 15) |}_4 ---> 14
{| (1, 11) (2, 12) (3, 13) (4, 14) (5, 15) |}_8 ---> undefined
```

## IO Function¶

IO functions are functions that will yield IO operation when executed.

Any IO functions can be executed with io expressions.

```
print "foo" ---> #<io-function>
```

## Port¶

A port has information of a file and its access mode (input/output).
You can create a port with `openInputFile`

or `openOutputFile`

.

## Undefined¶

`undefined`

is a useful built-in data you can put where you have not written yet.