Triangularity

Triangularity is a stack-based esoteric programming language created in early 2018 by PPCG user Mr. Xcoder.

Language Description
Any valid Triangularity program must have a padding made out of dots, laid out in 2 triangles. That is, the Kth line in the program (counting from the bottom upwards) must have K - 1 dots on both sides, and each line of a program must consist of exactly 2L - 1 characters (including the dots), where L is the number of lines in the program. Therefore, the character count of a program in this language must be listed in OEIS A056220.

Commands
! – Logical negation. The falsy values are 0, 0.0, 0j, "" (the empty string), [], {},, None, False, set (the empty set). " – Begins and ends a string literal. Note that the whole string must be on a single line of code. ) – Push a 0 onto the stack. 0123456789 – All these characters take the previous stack entry, multiply it by 10 and add their decimal digit value. + – Addition. / – Division. =>< – Comparison functions. @ – Increment the top of the stack (add 1 to its value). ^ – Exponentiation. _ – Negative. Multiplies the top of the stack by -1. ` – Cast to string. C – Counts the number of occurrences of an element in a sequence (either string or list) E – Evaluate. eval in Python. I – Input at that index (modular, 0-based). J – Join a sequence with a certain separator. L – Length. O – Sort. R – Reverse. c – Character from ASCII value. d – Positive divisors. e – Dump the contents of a sequence separately onto the stack. f – Cast to int. Trims decimals. h – Retrieves the first N elements of a sequence. i – Reads all STDIN and returns a list of lines. l – Return the 0-based indices in a sequence at which a certain element occurs. m – Retrieve the element at index N (0-based) into a sequence. o – Character to ASCII value. p – Primality test. r – Range (half-inclusive). t – Trims the first N elements of a sequence. u – Sum. w – Wrap into a singleton list.

Stack Manipulation
D – Duplicate. Push two copies of the argument. P – Pop. Discards the top of the stack. W – Wrap the whole stack into a list. s – Swap the top two stack entries.

Operators
There are two operators in Triangularity: Map and Filter. The former is denoted by the character  and is closed with , and it lets you iterate over a sequence and runs a set of commands on a separate stack, for each element of that collection. The latter does the same, but instead of returning the results of the mapping, it returns the elements that yield a truthy value when ran through the given block of code. It is denoted by the character  and is closed using.

"Hello, World!"
The classic "Hello, World!" program looks like this:

....... ....... ......  ...... .....     ..... ....       .... ...         ... ..           .. .             . "Hello, World!"

That's because the whole string must be on a single line of code. The shortest known program for this task is, however:

.... .... ..."!"... .."rld".. ."o, Wo". "Hell"+++

Which uses multiple strings concatenated together, to avoid / minimise the one-line problem.

Automatic padding adder
.......)....... ......2)1...... ...../)IL^..... ....f)rMD@_.... ...)2)1/)IL^... ..f+`"'.'*"+E.. .DWReD)2s^)Its. D+@sh+s+})10cJ.

This is a program that adds padding to a single-line string given as input, such that the output is a validly-structured Triangularity program. Disclaimer: This doesn't handle string literals.

Online Interpreter
Thanks to Dennis, there is a free online interpreter available at Try it online!

Resources

 * Github repository (the source code is in )
 * Stack Exchange chat room
 * Documentation