Flatland

The Flatland language operates on a 2D plane of instructions, but it is not grid-based (as opposed to Befunge and ><>). Rather, the execution paths are defined by geometric shapes, namely infinite lines and circles.

Inspired by ASCII-Only's chat message in PPCG.SE chat room:

possibly lines could be execution paths, and points and circles used to indicate control structures/literals. possibly

Synopsis

• A program consists of a set of points, lines and circles.
• Each point contains an instruction.
• A line represents a sequential execution path.
• A circle represents a loop.
• There is one instruction pointer (IP), moving along the specified lines and circles.
• An intersection represents a conditional; the IP transfers to another path if a certain condition is met.

Details

• The language is stack-based, and the instruction set (likely) resembles one of Befunge or ><>, except the routing commands.
• Points are defined by (x,y) coords.
• Lines are defined by two points on it.
• Circles are defined by its center and radius.
• Point-on-line relationships are automatically detected with a tolerance value.
• When the program starts, IP is at the first point specified, facing positive X direction (if ambiguous, positive Y).
• The program terminates when the IP is on a line and no more points are left in the current direction.
• On an intersection, the IP turns left if the top of the stack is negative, turns right if positive, and keeps moving in its current path if zero.
• The following cases give undefined behavior (or forbidden, depending on implementation):

- No points or no paths are specified at all.

- The first point is not on any path.

- Two points in a program share the same position.

- A point in a program coincides with an intersection of two paths.

- Three or more paths intersect at the same position.

- Two paths are identical.

Instructions

TBD.

Syntax

TBD.

Turing-completeness

Although it is not proven yet, it is believed to be Turing-complete by reduction from a Minsky machine given that the language has basic arithmetic (+-*/) instructions (looping and state transition are naturally represented by circles and intersections, respectively).