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.
def 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 a primitive function io.
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.