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 use a fresh context on each CALCULATE by default. Bindings from earlier lines in the source are visible to later lines in the same run. Check Keep session between runs in the settings panel to retain bindings across runs.

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 CALCULATE 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 `( … )`

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.