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Start with the structure of a value. A tuple groups fields; a vector adds an array dimension. Parentheses can also group an expression, so the trailing comma distinguishes a one-field tuple. The examples print selected fields and compare tuple structure with vector rank.

Forms in this category

• scalar literals
• boolean and null values
• complex values
• tuples and records
• fixed and dynamic vectors
• repeated vectors
• multisets — design or partial support
• generic type and shape handles

Values and types

identity(x:T)->T:x
first(x:[T:n])->T:x.(0)
pair_sum(x:(num,num))->num:x.0+x.1
::identity(3)
::first([1,2])
::pair_sum((3,4))

3
1
7

pairs:[(1,2),(3,4)]_a
matrix:[[1,2],[3,4]]_ab
::pairs
::matrix

[(1, 2), (3, 4)]
[[1, 2], [3, 4]]

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Give an expression a name with name:. Prefix an existing name with a dot to update its binding. An inner scope can shadow a name; an update searches for an existing binding. The example makes that distinction observable through printed values.

Forms in this category

• binding declaration
• nearest-binding update
• lexical shadowing
• comments and output
• semicolon logical rows

Bindings and scopes

x:3
.x:x+1
num y:x/2
::x
::y

4
2

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A function connects named parameters to an expression or an indented body. Call it with parentheses. Scopes can return their final expression or expose a record with a bare colon. Expand the examples to see default arguments, captured values, callable selection and forward declarations independently.

Forms in this category

• function definition
• typed parameters and return type
• expression-valued scopes
• scope-record result
• lambdas
• closures
• first-class callable values
• forward declarations

Bindings and scopes

make(x):
    y:x+1
    (x:x,y:y)
result:make(2)
::result.y

3

make(c):((x):str(c)&str(x))
f:make(2)
g:make("A")
::f(3)
::g(4)

23
A4

run(i:int):
 ::[+,*].(i)(2,3)
 0
run(0)
run(1)

5
6

f:make(2)
::f(3)
make(c:int):((x):x+c)

5

add(x,y=1):x+y
f(x:int)->int:x+1
twice:((x):2*x)
::add(2,y:3)
::f(2)
::twice(3)

5
3
6

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Choose an argument by name in a call, or bind it in square brackets to create another function. power[n:3] fixes the exponent while leaving the input open. Parameter binding and dimension selection have different roles; inspect the examples before combining them.

Forms in this category

• named call arguments
• default arguments
• partial application
• fully bound zero-argument calls
• operator specialization

Bound arguments and structural selectors

L(x,n,m):x+n+m
G:L[n:0,m:3]
::G(4)
f(x):x
::f(4)

7
4

f(x,step):x+step
g:f[step:2]
::g(3)

5

power(x,n):x^n
cube:power[n:3]
::cube(2)

8

f(x,n,step):x+n*step
g:f[step:2]
::g(3,4)
h:f[x:3,n:4,step:2]
::h()

11
11

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Use a leading colon to bring named fields into the receiving scope. In an argument list, a spilled record supplies named arguments. This lets a configuration record feed an ordinary function without manually repeating every field. A scope-ending bare colon is a separate record-return form.

Forms in this category

• record-to-scope spill
• call argument spill
• nominal backing spill — design or partial support

Spill record fields

record:(x:2,y:3)
:record
::x+y

5

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A dotted module name produces a module handle. Keep it under an alias, such as m:.math, for qualified calls, or spill its exports with :.math. The small example uses both forms. Available modules and target restrictions are listed separately in the library reference.

Forms in this category

• qualified module handles
• module-export spill
• local and nested modules — design or partial support

Import and call a qualified module

m:.math
::m.sqrt(81)

9

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Reach a named field through record.field, a tuple slot through tuple.0, and an indexed selection through value.(selector). A colon retains an axis in a multidimensional selection. The slicing example shows exactly which elements the browser preview returns.

Forms in this category

• named and positional members
• computed member selection
• multidimensional index selection
• slices
• axis preservation markers
• singleton-axis insertion

Indexing and slicing

A:[[1,2],[3,4]]
::A.(1,:)
::A.(...,0)
::A.(::,:,:)

[3, 4]
[1, 3]
[[[1, 2], [3, 4]]]

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Attach dimension names where the relationship between axes matters. A function subscript states which dimensions it consumes; other dimensions remain in the result. Repeated labels can express diagonal selection. Work through the reduction and contraction examples to see how labels differ from storage positions.

Forms in this category

• named dimensions
• anonymous dimensions
• repeated-axis diagonal
• structural ellipsis
• explicit contraction

Named dimensions and reductions

A:[[1,2],[3,4]]_ij
::sum_j(A)
::A_ii

[3, 7]
[1, 4]

A:[[1,2],[3,4]]_ij
B:[[5,6],[7,8]]_jk
::sum_j(A*B)

[[19, 22], [43, 50]]

run():
 A_ij:[[num(1,1),num(2,-1),num(3,0)],[num(4,2),num(5,0),num(6,-2)]]
 B_jk:[[7,8],[9,10],[11,12]]
 C_ik:sum_j(A_ij * B_jk)
 :: C
 0
run()

[[58 - 2i, 64 - 2i], [139 - 8i, 154 - 8i]]

A:[[1,2],[3,4]]_ij
::A
B:[[[1,2],[3,4]],[[5,6],[7,8]]]_i...k
::B

[[1, 2], [3, 4]]
[[[1, 2], [3, 4]], [[5, 6], [7, 8]]]

A:[[1,2],[3,4]]_ij
B:[[5,6],[7,8]]_jk
C:sum_j(A*B)
diagonal:A_ii
::C
::diagonal

[[19, 22], [43, 50]]
[1, 4]

Specific example sources are checked separately from the complete category. Coverage and specification mapping

An ordinary numerical function can act over compatible vector dimensions. A structural call instead presents selected dimensions to the function as a container. In the span example, changing the selected axis changes which values participate in each maximum-minus-minimum calculation.

Forms in this category

• ordinary lifting
• selected-axis structural calls
• dimension alignment

Lifting and structural calls

max(a:num,b:num)->num:
    a>b? @:a
    b
ReLU(x:num)->num:max(0,x)
::ReLU([-1,2,3]_i)

[0, 2, 3]

stat:.stat
span(x):stat.max(x)-stat.min(x)
A:[[1,4],[2,8]]_ij
::span_i(A)

[1, 4]

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Operators express arithmetic and relationships, while concatenation and function composition build larger values and callables. Their meaning depends on the operand structure. The examples make the distinction concrete with printed results rather than treating every operator as a scalar-only operation.

Forms in this category

• elementwise arithmetic
• elementwise comparison and logic
• whole-value equality
• operator values
• concatenation
• function composition
• pointwise function operations
• implicit multiplication

Concatenation

left:[1,2]_i
right:[3,4]_i
::left &_i right

[1, 2, 3, 4]

add(x):x+1
double(x):2*x
F_i:[add,double]_i
::F_i(3)
h:add&double
::h(3)

[4, 6]
8

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Range endpoints are inclusive. A bounded observation can request a finite part of an unbounded range. The preview example demonstrates selected demand and empty work on small inputs. It does not establish disk-backed arrays, bounded memory for arbitrary datasets, or HDF5 access.

Forms in this category

• inclusive finite ranges
• descending ranges
• unbounded ranges
• finite consumer demand
• typed empty work — design or partial support

Lazy demand

values:..
values.(0..3) >> ::$

0
1
2
3

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A reduction combines a dimension; an ordered fold carries a value from one step to the next. Recurrence expresses values in terms of earlier values. These operations have different ordering requirements. Use the examples to compare their results before selecting one for an analysis.

Forms in this category

• ordered reduction
• multidimensional reduction
• sum product chain
• indexed specialization recurrence

Ordered folds

step(z,c):z+c
c:[1,2,3]_i
::reduce_i(step,c,0)

6

step(z,c):z+c
::reduce_i(step,[1,2,3]_i,0)

6

step(z,n,c):z^2+c
n_i:..10
F_i:step[n:n_i,c:num(0.1,0.2)]
::chain_i(F)(0)

0.052808601763274413 + 0.22361225622108541i

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A pipe introduces a scope for the current value. $ refers to that value, additional dollar signs reach outer pipe scopes, and named coordinates refer to selected indices. Indentation controls nesting. The example keeps a short pipeline visible so each observation can be traced.

Forms in this category

• value pipes
• nested pipes
• named coordinates
• numbered loop indices

Pipes and loop coordinates

[10,20]_i >>
    ::$i
    ::$0
    ::$

0
0
10
1
1
20

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A question mark guards an expression or suite. The repeating conditional form continues while its condition holds. Return, continue and break forms transfer control within their surrounding function, loop or pipe. The runnable counter is deliberately finite and exposes the values at each step.

Forms in this category

• conditional expressions and suites
• condition loops
• return
• continue
• break

Repeat while a condition holds

x:0
x<3?>
    ::x
    .x:x+1

0
1
2

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Matching selects a result from pattern arms. Errors can be raised, caught and matched; assertions check a relationship and can attach a message. The examples below demonstrate matching and typed raise/catch. For assertions, run the path checks and change an expected value to observe a failure. The browser output reports the actual program result.

Forms in this category

• value and type matching
• fallback arms
• match loops
• assertions
• typed raise
• typed catch and propagation

Conditions, matching and errors

value:2
label:value ??
    0 => "zero"
    1 => "one"
    "many"
::label

many

:.errors
(Error("message")!)!?
    Error => ::$.message

message

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A constructor can give a value a nominal identity in addition to its fields. Reflection and reconstruction describe how that structure is inspected or rebuilt. The point example tests field access after an operation; it is a bounded example rather than proof of every reconstruction rule.

Forms in this category

• nominal construction and reconstruction
• postfix type reflection
• field-name and field-type reflection — design or partial support
• operator and dotted-access overloads — design or partial support

Nominal reconstruction

Point(x:num,y:num):
    : [x,y]
p:Point(1,2)
q:p+1
::q.x
::q.y

2
3

Point(x:num,y:num):
    :[x,y]
p:Point(1,2)
::(p+1).x

2

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Transform a function into another function, then call the result. The derivative and integral examples exercise the forms supported by this preview. General symbolic-domain manipulation is a broader design area; the presence of symbolic library source does not make every transformation a verified browser feature.

Forms in this category

• exact function differentiation
• function integration
• transform specialization
• symbolic domains and assumptions — design or partial support
• shared semantic graph — design or partial support

Exact derivatives

square(x):x^2
slope:square'x
::slope(3)

6

f(x):x^2
slope:f'x
::slope(3)
I:integ_x(f)
F:I[from:0]
::F(3)

6
9

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A physical quantity carries dimensional meaning as well as a numerical value. Unit names provide scales, while physical dimensions describe compatibility. Import the SI catalog, combine compatible quantities and convert them explicitly. The examples show conversions; they do not qualify all dimension-exponent combinations.

Forms in this category

• physical dimension expressions
• unit literals
• quantity conversion
• dimensional arithmetic

Physical domains and units

: .units
x:2m+30cm
v:[1,2,3]m
::x.to(cm)
::v.to(cm)

230 cm
[100, 200, 300] cm

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Double-quoted strings are immediate values; single-quoted templates defer formatting. A template can name fields and specify formatting when it is applied to a record. The runnable example prints a formatted pair, keeping formatting behavior separate from numerical computation.

Forms in this category

• immediate strings
• deferred templates
• field and formatting interpolation

Templates

x:1.26
::"x = $x.1f"
s:(x:1.26,y:2.5)
::'[$x.1f, $y.1f]'.format(:s)

x = 1.3
[1.3, 2.5]

s:(x:1.23,y:4.56)
::'[$x.1f, $y.1f]'.format(:s)

[1.2, 4.6]

Specific example sources are checked separately from the complete category. Coverage and specification mapping

A viewport receives coordinate data as layers and displays the resulting scene. The example creates a connected curve. Broader physical laws, embeddings and geometry topology remain design or partial implementation areas; a rendered curve does not establish a complete simulation or automatic GPU execution contract.

The table describes the intended interface. The checked examples establish add, push and show; set, append and plot remain unqualified in this browser package.

Forms in this category

• viewport construction
• coordinate properties
• connected topology
• explicit topology
• retained state push
• physical laws and prescribed state — design or partial support

Connected geometry

u:0.0009765625*[0..1024]
frame:.ui.viewport
frame.add(x:u_u,y:u_u^2,color:[0.25,0.72,1,1])
frame.show()

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Queues, isolated processes, broadcast subscriptions and shared values coordinate event-oriented work. They are distinct from the compiler's numerical execution choices. The example starts a producer, handles queued messages and joins the producer. Host filesystem and OS command capabilities have their own target restrictions.

Forms in this category

• isolated process call
• blocking queue
• broadcast subscriptions
• immutable shared values

Event and I/O concurrency

concurrent:.concurrent
MouseEvent:1
KeyEvent:2
Stop:0
handle_mouse(event): ::event
handle_key(event): ::event
produce(events,key:int,stop:int):
    events.put(key)
    events.put(stop)
events:concurrent.queue()
events.put(MouseEvent)
p:concurrent.process(produce,events,KeyEvent,Stop)
(event:events.get())??>
    MouseEvent => handle_mouse(event)
    KeyEvent => handle_key(event)
    Stop => @|
p.join()

1
2

Specific example sources are checked separately from the complete category. Coverage and specification mapping

Some language decisions remain unsettled. The list below is explicit so incomplete cleanup, sharing, control-binding and declaration forms are not mistaken for usable syntax. No fabricated runnable example is supplied for an undecided construct.

• deterministic external-resource cleanup
• publishing shared generations
• complete UI control binding grammar
• complete unit-literal/suffix precedence combinations
• final process variadic declaration

Coverage and specification mapping