SliP Language Reference

Version 2.3.0, 2026-08-21. SliP is a programmable symbolic calculator. Implementation in C++/ is authoritative. See also the Tutorial and changelog.

1. Two modes

Both modes use a fresh context on every RUN. Bindings from earlier forms or lines in the source are visible to later ones during that run. The source is the complete, reproducible program; bindings are not carried from one RUN to the next.

2. Calculator (sugared) mode

Line wrapping

Each non-empty line expr (trimmed, comment stripped) is evaluated as:

( expr )

Implicit multiply

2 3 4   →  24
2πr     →  2 × π × r
cosπ    →  cos(π)

Function calls

sin(0)        sin applied to 0
atan2[ 1 1 ]  two-argument form
max[ 3 2 1 ]  list argument

Assignment

'r = 2

becomes ( 'r = 2 ) and binds r for the rest of that RUN.

3. Names and tokens

• Whitespace separates tokens.
• Solo characters (always alone): Greek letters, π 𝑒 ∞, operators like + - × ÷ == : …
• Names: letters/digits until space, solo char, or delimiter. abπcd → ab, π, cd.
• ASCII aliases exist for common hard-to-type constants: pi, euler, inf.
• ASCII e is a name. Napier's number is 𝑒 (keypad) or euler.
• ⊤ ⊥ ⊂ ⊃ ∩ ∪ are reserved solo names without builtin behaviour in the current interpreter.

4. Evaluation

Sentence ( … )

1. Infix split first: the lowest-priority operator splits the raw sentence; recurse both sides. Equal priority → rightmost wins, except right-associative = and ,.
2. Prefix / quote pass (right to left) runs inside infix-free segments. A prefix absorbs a following run of bare numerics: sin 2π → sin( 2 × π ), but sin(2) π → sin( 2 ) × π.
3. Adjacent numerics with no operator → multiply

Operands evaluate left to right, and && || ¿ short-circuit: the right side is untouched when the left side decides the result.

Blocks

Parallel ∥

∥ '[ s₁ s₂ … ] evaluates the elements concurrently, each isolated in its own child context, and collects the results in source order:

( ∥ '[ ( 1 + 1 ) ( 2 + 2 ) ( 3 + 3 ) ]  )  →  [ 2 4 6 ]

( 'z = 1 )
( ∥ '[ ( 'z = 99 ) ( z ) ] )               →  [ 99 1 ]   second branch still sees 1
( z )                                      →  1          caller untouched

( 5 : '( ∥ '[ ( @ + 1 ) ( @ × 2 ) ] ) )    →  [ 6 10 ]   @ is seeded per branch

Branches cannot observe each other, so the value equals sequential evaluation; when several branches fail, the earliest in source order reports. Use « » when the sentences must share bindings.

On this page ∥ runs sequentially. Browser threads need SharedArrayBuffer, which needs COOP/COEP headers the static host cannot send. The native CLI build uses real threads. The value is the same either way — only elapsed time differs.

Truth

5. Context

• 'name = value — assign in current context
• ¶ — snapshot bindings as Dictionary
• ¤ — random float in [0, 1), not context snapshot

6. Operators (summary)

Primitives

Quote / prefix / unary

Infix (priority low → loose)

Comparisons bind tighter than && || ^^, so x > 0 && y > 0 reads as ( x > 0 ) && ( y > 0 ).

Apply :

arg : f pushes arg on the argument stack, evaluates f, then pops the stack. Use @ inside quoted functions to read the stack top.

Math (prefix)

sin cos tan log exp sqrt … — one arg.
atan2 pow random — two args via [ ].
hypot max min — list arg.

Random

¤                 →  uniform [0, 1)
random[ 1 2 ]     →  uniform [1, 2)

JSON

operand:toJSON · `` literal`:byJSON ``

7. Web graphics

The WASM build adds Canvas/WebGL operators (canvas, fill, stroke, path2D, shader helpers, …). They are not available in the CLI or native apps. Existing canvases are removed at the start of each RUN.

The top bar includes editable SliP graphics programs: Mandelbrot (WebGL), Koch, Complex orbit, Barnsley fern, and Lorenz attractor (Canvas 2D). The graphics surface is currently sample-driven rather than specified operator by operator.

8. Constants

∞  𝑒  π  γ  φ  log2e  log10e  ln2  ln10

ASCII e remains an ordinary name.