gojo 1;

let $space = carrier();
let $x = carrier();
let $y = carrier(unit_of($x));
let $index = carrier();
let $cells = group($index, ?cell_support);
let $a = group_on($space, at($x, 1), at($y, 1));
let $b = group_on($space, at($x, 4), at($y, 1));
let $c = group_on($space, at($x, 2), at($y, 3));
let $motif = group($a -> $b, $b -> $c, $c -> $a);

// The two coordinate calibrations remain separate and explicitly ordered.
// T(x,y) = (x+12,y); G(x,y) = (x+6,-y). Hence G followed by G is T.
let $period_tick = tick(12);
let $period = span($x, 0, $period_tick);
let $translate_x = $period -> span($x, $period_tick, 24);
let $preserve_y = span($y, 0, 1) -> span($y, 0, 1);
let $glide_x = span($x, 0, 6) -> span($x, 6, $period_tick);
let $reflect_y = span($y, 0, 1) -> span($y, 0, -1);
let $coordinate_basis = ports(span($x, 0, 1), span($y, 0, 1));

// A pointwise extension to the whole motif is an exposed, still-open obligation.
// This pass represents the instruction and its missing correspondence; no expander runs.
let $translation = action(ports(?current_motif),
    group($coordinate_basis, ports($translate_x, $preserve_y), ?translation_correspondence),
    ports(?next_motif), ?translation_residue, $period);
let $glide = action(ports(?current_motif),
    group($coordinate_basis, ports($glide_x, $reflect_y), ?glide_correspondence),
    ports(?next_motif), ?glide_residue, $period);
let $feedback = frame(?next_motif -> ?current_motif);
let $translates = repeat($motif, $cells, $translation,
    $feedback, ?repeat_boundary, ?translation_history);
let $glides = repeat($motif, $cells, $glide,
    $feedback, ?repeat_boundary, ?glide_history);

// A finite observation window is not the support of the entire pattern.
let $window = span($index, -2, 2);
root group($translates, $glides, $window, $period, $translate_x,
    $preserve_y, $glide_x, $reflect_y, $motif, $coordinate_basis);

// A selected period may be partial without introducing a zero-length transform.
let $open_step = action(ports(?current_motif),
    group($coordinate_basis, ports(?x_calibration, $reflect_y), ?open_correspondence),
    ports(?next_motif), ?open_residue, ?period_evidence);
root group(repeat($motif, $cells, $open_step, $feedback,
    ?repeat_boundary, ?open_history), bind(?x_calibration, $glide_x));

// A selected pointwise read fills the correspondence obligation above. All
// triangle sites are explicitly exposed; the repeat's support remains open.
let $target_basis = group_on($space, span($x, 0, 1), span($y, 0, 1));
let $exposure = ports($a, $b, $c);
let $map_glide = group($motif, $exposure, ports($glide_x, $reflect_y), $target_basis);
let $map_translate = group($motif, $exposure, ports($translate_x, $preserve_y), $target_basis);
let $inverse_x = span($x, 6, 12) -> span($x, 0, 6);
root group($map_glide, $map_translate, ports($inverse_x, $reflect_y),
    $glide, $translation, $window, $cells);