SliP Language Reference

Draft 2026-07-04. SliP is a programmable symbolic calculator. Implementation in C++/ is authoritative. See also Tutorial.

1. Two modes

Mode	Checkbox	Input
Calculator	Programming mode off	One expression per line (§2)
Programming	Programming mode on	Full SliP; `//` comments stripped

Both modes share one session context on the web until Reset context or reload.

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 in the session.

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 `( … )`

Prefix / quote pass (right to left)
Infix pass (lowest priority operator splits first)
Adjacent numerics with no operator → multiply

Blocks

Form	Context	Effect
`{ … }`	New child context	Sequential; returns list of results
`« … »`	Same context	Sequential (not parallel threads); bindings persist

Truth

Value	Meaning	Printed
`[]`	Nil / false	`[]`
non-empty	Truthy	own REPR
from `==` etc.	true	`T`

5. Context

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

6. Operators (summary)

Primitives

Sym	Meaning
`@`	Stack top (for `:` apply)
`£`	Stack as list
`¶`	Context → Dict
`∅`	Empty list
`¤`	Random [0, 1)

Quote / prefix / unary

Sym	Meaning
`'`	Quote
`!`	Eval
`#` `*` `$`	Length / CDR / last
`;` `¦`	Stdout / stderr print
`~` `¬`	Bit / logical NOT
`¡`	Throw

Infix (priority low → loose)

Pri	Operators
0	`=` assign
10	`?` `¿` if
30	`∈` `∋` `==` `<>` `<` `>` `<=` `>=`
40	`&&` `\|\|` `^^`
50	`§` `,`
60	`+` `-`
70	`·` `×` `÷` `/` `%`
80	`&` `\|` `^`
90	`:` apply
100	`±` `.` matrix cols / index

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

WASM build adds Canvas/WebGL operators (canvas, fill, stroke, …). Not in CLI. Canvases are removed on each CALCULATE. The graphics surface is currently sample-driven rather than specified operator by operator.

8. Constants

∞  𝑒  π  γ  φ  log2e  log10e  ln2  ln10

ASCII alias	Constant
`pi`	`π`
`euler`	`𝑒`
`inf`	`∞`

ASCII e remains an ordinary name.