Language Reference

Everything Tilde accepts. The language itself has very few words; nearly all of what a program says comes from definitions, most of them in the prelude.

General

• One statement per line. A line that starts at the left edge is a statement or the start of a definition; indented lines belong to the definition above.
• -- starts a comment, to the end of the line.
• Names are letters, digits and _, may end in primes (l', A''), and may be paths into a shape's parts (t.point1).
• Text is written in double quotes: "hello".
• Numbers may be negative and have a decimal point: -2.5.
• Brackets group: what is inside is worked out first.
• A line is read left to right — see Reading a Line.

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The language's own words

Word	Use
import m	use the definitions module m exports
export import m	use them, and pass them on to whoever imports this file
define …:	a new definition
define type T:	a new kind of shape, made of named parts
return x	the last line of a definition: what it gives back
tsx	a definition body written in TypeScript, for what the solver does itself

Definitions

define right triangle (t: new Triangle) with legs (u: Scalar) (v: Scalar) => Triangle:
    triangle t with a b c
    a at 0 0
    b at u 0
    c at 0 v
    return t

The words outside brackets are the pattern; each (name: Type) is a slot. => T says what the definition gives back, and return on the last line says which thing that is. A definition with no => T gives back nothing.

Slot type	Takes
Point, Line, Circle, Scalar, Text, or a define type	a thing of that kind, by name, by bracket, or as a number or text
new T	a new name: the definition makes something under it and hands it back
Name	a plain word, passed on as itself (a setting's name)
Type	the name of a type
Any	anything

Types

define type Triangle:
    Point point1
    Point point2
    Point point3

Each part is written type, then name. new Triangle t makes a triangle and its parts, reached as t.point1 and so on.

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The prelude

import prelude brings in all of these.

Making things

point p                               line l
circle c                              scalar k
scalar k = 5                          scalar k is 5
point p = 3 5                         point p = (3, 5)
line l through p q
circle c with center p and radius r
triangle t with a b c
(x, y)                                a point, unnamed

Saying things about them

p at x y                              -- position
p = q                                 -- the same point
p = x y                               -- p at (x, y)
k = 5                                 k is 5
distance between p and q is d         -- also draws the segment
p on l                                p on c
l through p
c with center p                       c with radius r
l parallel m                          l parallel m at d
l perpendicular m                     l perpendicular m at p

Each of these gives back what it was said about, so they chain: line l parallel m through p.

Numbers and text

a + b     a - b     a * b     a / b   -- on numbers written out
"a" + "b"                             -- joins text

Other

print x                               -- shown below the figure, once solved
segment p q                           -- draws the segment
set grid on     set axes off     set origin on     set subscripts off
new Triangle t                        -- make a shape and its parts
call x n                              -- give x a second name, n

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What is not valid

• Giving a name to something when the name is already taken.
• Using a name before the line that makes it.
• A line that no definition can read — or that two can read equally well, with nothing to choose between them.
• Two different values for the same number, or two different places for the same point: these are contradictions, not changes.