Array kernels and primitives

This page lists the array-oriented primitives supported by Hydrangea today. For each entry, the syntax matches the surface language, and the argument descriptions follow the compiler’s current naming.

Core combinators

Kernel	Syntax	Arguments	Result
`generate`	`generate [shape] fn`	`shape`: array shape; `fn`: index function (`[i, j, ...] -> value`)	Array of the requested shape
`fill`	`fill [shape] value`	`shape`: array shape; `value`: element value	Array of the requested shape
`map`	`map fn array`	`fn`: unary function; `array`: input array	Array with the same shape
`zipwith`	`zipwith fn array1 array2`	`fn`: binary function; `array1`, `array2`: same-shaped arrays	Array with the same shape
`reduce`	`reduce fn init array`	`fn`: accumulator function; `init`: initial accumulator; `array`: input array	Array with the trailing/rightmost dimension removed
`reduce_generate`	`reduce_generate combine init shape gen`	`combine`: accumulator function; `init`: initial accumulator; `shape`: generated shape; `gen`: generator function	Reduced array without materializing the intermediate
`foldl`	`foldl fn init array`	`fn`: strict left-fold function; `init`: accumulator; `array`: 1-D array	Final accumulator value
`foldl_while`	`foldl_while pred fn init array`	`pred`: continuation predicate; `fn`: step function; `init`: accumulator; `array`: 1-D array	Final accumulator value

Scans and segmented reduction

Kernel	Syntax	Arguments	Result
`scan`	`scan fn init array`	`fn`: step function; `init`: initial state; `array`: 1-D array	Exclusive prefix-scan array
`scan_inclusive`	`scan_inclusive fn init array`	`fn`: step function; `init`: initial state; `array`: 1-D array	Inclusive prefix-scan array
`scanr`	`scanr fn init array`	`fn`: step function; `init`: initial state; `array`: 1-D array	Exclusive right-to-left scan
`scanr_inclusive`	`scanr_inclusive fn init array`	`fn`: step function; `init`: initial state; `array`: 1-D array	Inclusive right-to-left scan
`segmented_reduce`	`segmented_reduce fn init offsets vals`	`fn`: step function; `init`: initial state; `offsets`, `vals`: 1-D arrays	One reduced value per segment

Indexing, scattering, and gathering

Kernel	Syntax	Arguments	Result
`sort_indices`	`sort_indices keys`	`keys`: 1-D integer array	Permutation array that sorts `keys`
`iota`	`iota n`	`n`: integer length	`Array[n, Int]` containing `0..n-1`
`make_index`	`make_index n idxs`	`n`: bound for valid indices; `idxs`: integer array	Index-annotated integer array; identity at runtime
`permute`	`permute combine defaults perm_fn src`	`combine`: combining function; `defaults`: destination array; `perm_fn`: index-mapping function; `src`: source array	Permuted destination-shaped array
`scatter`	`scatter combine defaults idxs vals`	`combine`: combining function; `defaults`: destination array; `idxs`: index array; `vals`: values array	Destination-shaped array
`scatter_guarded`	`scatter_guarded combine defaults idxs vals guard`	`combine`: combining function; `defaults`: destination array; `idxs`: index array; `vals`: values array; `guard`: boolean array	Destination-shaped array
`gather`	`gather idxs array`	`idxs`: index array; `array`: source array	Array shaped like `idxs`
`index`	`index idx array`	`idx`: index value; `array`: source array	Element at `idx`
`check_index`	`check_index idx default array`	`idx`: index value; `default`: fallback element; `array`: source array	Element at `idx`, or `default` if out of bounds

Shape and array layout helpers

Kernel	Syntax	Arguments	Result
`shape_of`	`shape_of array`	`array`: input array	Shape vector for the array
`replicate`	`replicate [spec] array`	`spec`: shape specification; `array`: source array	Replicated array
`slice`	`slice [spec] array`	`spec`: slice specification; `array`: source array	Sliced array
`reshape`	`reshape new_shape array`	`new_shape`: shape value; `array`: source array	Same elements with a new shape
`stencil`	`stencil boundary fn array`	`boundary`: `clamp`, `wrap`, `mirror`, or `(constant x)`; `fn`: accessor function; `array`: source array	Array of stencil results

Sparse and structured-array helpers

Kernel	Syntax	Arguments	Result
`coo_sum_duplicates`	`coo_sum_duplicates nrows ncols nnz rows cols vals`	Scalar dimensions plus integer arrays for `rows`, `cols`, and `vals`	COO record with duplicate entries summed
`csr_from_sorted_coo`	`csr_from_sorted_coo nrows ncols nnz rows cols vals`	Scalar dimensions plus sorted integer arrays for `rows`, `cols`, and `vals`	CSR record

I/O helpers

Kernel	Syntax	Arguments	Result
`read_array`	`read_array shape "file.csv"`	`shape`: expected shape; `file.csv`: path string	Array read from CSV
`read_array_float`	`read_array_float shape "file.csv"`	`shape`: expected shape; `file.csv`: path string	Float array read from CSV
`write_array`	`write_array array "file.csv"`	`array`: data to write; `file.csv`: path string	Unit
`write_array_float`	`write_array_float array "file.csv"`	`array`: float data to write; `file.csv`: path string	Unit

Compiler-internal derived helper

Kernel	Syntax	Arguments	Result
`scatter_generate`	`scatter_generate combine defaults idxs fn`	`combine`: combining function; `defaults`: destination array; `idxs`: index array; `fn`: value generator	Equivalent to scattering over `generate (shape_of idxs) fn`