gojo 1;

let $space = carrier();
let $x = carrier();
let $y = carrier(unit_of($x));
let $p0 = group_on($space, at($x, 0), at($y, 0));
let $p1 = group_on($space, at($x, 4), at($y, 8));
let $p2 = group_on($space, at($x, 8), at($y, 0));
let $p3 = group_on($space, at($x, 12), at($y, 4));

// 0. Existing GojoCAD recipes: chord -> control; chord -> control span.
let $quadratic = ($p0 -> $p2) -> $p1;
let $cubic = ($p0 -> $p3) -> ($p1 -> $p2);
root group($quadratic, $cubic, $p0, $p1, $p2, $p3);

// 1. A construction carries the shared parameter and every interpolation edge.
// Parsing retains requests. AffineFrame selects their explicit local contract.
let $t = carrier();
let $domain = span($t, 0, 1000);
let $basis = group_on($space, span($x, 0, 1), span($y, 0, 1));
let $grade = group(?sample, $domain, $domain, $basis);
let $ab = ports(?start, ?control_a, $grade) -> ?q0;
let $bc = ports(?control_a, ?control_b, $grade) -> ?q1;
let $cd = ports(?control_b, ?end, $grade) -> ?q2;
let $abc = ports(?q0, ?q1, $grade) -> ?r0;
let $bcd = ports(?q1, ?q2, $grade) -> ?r1;
let $result = ports(?r0, ?r1, $grade) -> ?curve_point;
let $construction = action(
    ports(?start, ?control_a, ?control_b, ?end, $grade),
    frame($ab, $bc, $cd, $abc, $bcd, $result),
    ports(?curve_point), ?interpolation_residue_policy, $domain);
let $partial = frame(bind(?start, $p0), bind(?control_a, $p1), bind(?end, $p3));
let $complete = frame(bind(?start, $p0), bind(?control_a, $p1),
    bind(?control_b, $p2), bind(?end, $p3), bind(?sample, at($t, 500)));
root group($construction, $partial, $complete, $grade);

// 2. Legal degeneracies expose ambiguity in the old pair-of-spans recipe.
let $closed_pair = ($p0 -> $p0) -> ($p1 -> $p2);
let $joined_pair = ($p0 -> $p3) -> ($p3 -> $p2);
let $closed_bindings = frame(bind(?start, $p0), bind(?control_a, $p1),
    bind(?control_b, $p2), bind(?end, $p0));
let $repeated_bindings = frame(bind(?start, $p0), bind(?control_a, $p0),
    bind(?control_b, $p0), bind(?end, $p0));
root group($closed_pair, $joined_pair, $construction, $closed_bindings,
    $repeated_bindings);

// 3. Reversing a curve requires reversing control order, not swapping chord/control roles.
let $reversed_controls = frame(bind(?start, $p3), bind(?control_a, $p2),
    bind(?control_b, $p1), bind(?end, $p0));
root group($construction, $reversed_controls, reverse($cubic));