Calculus Constructio

Calculus Constructio is a programming language involving the construction of lines, circles, polynomial and parametric curves, and intersections.

Syntax

Each program is a series of newline separated instructions. Each instruction looks like this:

variable_name:instruction arg,arg,...

• The instruction is applied...
• ...to the arg,arg,... (arguments), which must be variables...
• ...and the result is assigned to the variable called variable_name.

Constants

There are two default constants that every module, function and program has access to:

• zero, which is the point (0, 0).
• one, which is the point (1, 0).

Input

Input is given through the input variable. When no input is given, it will be an empty list.

Output

The program can output through three ways:

• Assigning to the output variable: This is the preferred method as it is the only output method where flags are able to modify the output. The other two instructions are meant for debugging purposes. A program will error at the end if this variable has not been assigned to.
• The Halt or H instruction: This accepts one argument, prints the argument to STDOUT, and terminates the program, printing Program has halted. to STDERR.
• The Print or > instruction: This accepts one argument and prints the argument to STDOUT. It does not terminate the program.

Valid Variable Names

All variable names are valid apart from those which contain :. Note that this also means that variables with zero-length names are valid (e.g. you can provide the arguments ,arg1,,arg2, to an instruction, meaning the first, third, and last arguments are of the zero-length variable). It is also worth noting that it is possible to assign a value to variables containing ,, but then these cannot be used inside arguments, as the comma will be interpreted as separating two variable names.

Modules

Modules can be imported using the Import or ! instruction, assigning it to a variable name. The only argument to it is the module name. It is given as a filepath, or as a relative directory (probably). You should omit the file extension, and it is assumed that it is a .cns file. Then, the functions and other things inside can be used as the variable variable_name.function_or_other_variable_name.

Functions

Functions can be defined starting with the Define or $ instruction, followed by its arguments as comma-separated names, assigning it to the variable name. The body of the function is just normal syntax, except the return value of the function should be assigned to the return variable. The function should be ended by using the same variable name with the EndDefine or % function, with no arguments following. Functions can be applied using the Apply or Y instruction. Functions must have at least one argument, however that argument can just be a dummy argument that isn't used if necessary. Functions cannot access any external variables apart from modules, other functions, and arguments passed in to it.

Types

Here is a list of types and what they mean:

• A CModule represents a module imported into a program. It is also what the main program is turned into before being run.
• A CFunction is a custom function defined in a program.
• A List is just a list.
• A Construction is an object created using points, or one of:
  • Line
  • Circle
  • Polynomial
  • Parametric

List of instructions

It is worth noting that each instruction has a long form and a short form, and when a Point is given to a function that should seemingly accept a number, the number is taken from the point's x coordinate.

Long Form	Short Form	Arguments	Behaviour Description
Line	L	Point, Point	Constructs a line from the two given points. Can sometimes be treated as a line segment.
Circle	C	Point, Point	Constructs a circle, with the center as the first point, and the second point being on the circumference.
Intersect	X	Construction, Construction	Returns a list of points where the two constructions intersect.
Unfurl	^	Circle, Construction	Unfurls the circumference of a circle such that one end of the line touches the center of the circle and the other end touches a given construction.
Collapse	V	Line, Point	Collapses a line into a circle with the given point as its center.
Index	I	List, Point	Returns the item in the list with the given index.
Slice	S	List, Point, Point	Returns a slice of the list from the start index up to but not including the end index.
Polynomial	P	Point, ...	Returns the minimal polynomial that goes through all the points.
Parametric	A	Point, ...	Returns the minimal parametric curve that gives the given points when t is equal to 0, 1, 2, etc.
Concat	+	List, Any	Adds the value onto the list, if it is not a list. Otherwise, concatenates the lists together.
SwapXY	~	Point	Returns another point with swapped X and Y coordinates.
NewList	*	Any, ...	Returns a new list containing all of the arguments.
Apply	Y	CFunction, List	Applies the function, with the given list as arguments to that function.
Closer	@	Point, Point, Point	Returns which of the last two points is closer to the first point.
Equal	=	Any, Any	Returns if the two objects are equal.
ToList	/	Point | Construction	If it is a point, returns a list with the X and Y coordinates, as two points with those as X coordinates. If it is a construction, returns a list of the points that form it.
ToPoint	.	List	Returns a point with the X and Y coordinates given in the list, taken from the X coordinates of the two points in the list.
If	?	Point, CFunction, CFunction, List	If the given point is truthy (non-zero X coordinate), applies the first function to the given arguments, otherwise, applies the second function to the given arguments.
While	W	CFunction, CFunction, List	While the second function returns a truthy value for the current list, changes the current list to a new list from the result of applying the first function to the old list.
Transfer	T	Any	Returns the value given to it, intended for if you need to set a variable equal to another variable.
Halt	H	Any	Prints the given value to STDOUT, prints Program has halted. to STDERR, and terminates the program. Useful for debugging.
Print	>	Any	Prints the given value to STDOUT. Does not terminate the program. Useful for debugging.
Ternary	{	Point, Any, Any	If the given point is truthy, return the second argument, otherwise, return the third.

Links

• GitHub Repository