Paper & Values

Every Beloch program starts the same way: with a sheet of paper. From there you name points and lines on that sheet, and Beloch computes where they land. This first tutorial builds the smallest possible program — a square with its two diagonals — and uses it to introduce the two ideas everything else rests on: the paper and values.

The sheet

Here is a complete, valid Beloch program. One line.

; paper.bel
paper square

paper square declares the sheet: a square. Every program needs exactly one paper declaration, and it comes first. On the right you can see the result — right now it is just the outline, because we have not creased anything yet.

The square comes with its four corners already named, going counter-clockwise from the bottom-left:

• .a — bottom-left
• .b — bottom-right
• .c — top-right
• .d — top-left

The leading dot is how you write a point in Beloch. .a is not a variable you defined — it is a value the paper handed you. The four edges are named too, by their endpoints: --ab is the bottom edge, --bc the right, --cd the top, --da the left. The -- prefix is how you write a line.

The first line

Let's draw a line across the sheet. We'll connect two opposite corners.

; diagonal.bel
paper square
mark through .a .c

Read the new line as an English sentence: mark a crease that goes through .a and .c. through .a .c is an expression — it takes two points and produces a line, the unique line passing through both. .a is the bottom-left corner and .c the top-right, so the line is the main diagonal, and it now shows up in the diagram.

mark is the verb: it records the line onto the paper as a crease you can see. (We are only marking here, not folding anything — the difference between marking and folding is the whole of a later tutorial. For now, mark just means "draw this line so I can see it.")

The second line

Add the other diagonal the same way:

1
2
3
4; diagonals.bel
paper square
mark through .a .c
mark through .b .d

through .b .d connects .b (bottom-right) to .d (top-left) — the other diagonal. The two creases cross right in the middle of the sheet.

What you learned

• Every program opens with paper square. It gives you a unit square with corners .a .b .c .d and edges --ab --bc --cd --da.
• A leading . writes a point; a leading -- writes a line.
• through .p .q is an expression that builds the line through two points.
• mark <line> records a crease onto the sheet.

Next, we'll give our own names to points and lines so we can build creases out of earlier ones: Naming Points & Lines.