Defining Ord in terms of lt vs lte

Almost immediately after 3.2 was cut I thought about how libraries (Sanctuary in particular) would implement it. I realized that either there were going to be extra equality checks (not performant) or an indirect definition in terms of gt (unnecessarily convoluted).

// with Ord defined by lte
// note double equality checks
// only define 'fantasy-land/lte' and 'fantasy-land/equals'
const lte = a => b => a.lte(b);
const lt = a => b => a.lte(b) && !a.equals(b);
const gt = a => b => !a.lte(b);
const gte = a => b => !a.lte(b) || a.equals(b)

// with Ord defined by lte and lte defined in terms of gt
// solves extra equality checks
// requires implementing gt, 'fantasy-land/equals', and 'fantasy-land/lte' in terms of gt
const gt = a => b => a.gt(b);
const lte = a => b => !a.gt(b);
const lt = a => b => !a.gt(b) && !a.equals(b);
const gte = a => b => a.gt(b) || a.equals(b);

An alternative would be to define Ord in terms of lt and equals.

// no extra equality checks
// only define 'fantasy-land/lt` and 'fantasy-land/equals'
const lt = a => b => a.lt(b);
const lte = a => b => a.lt(b) || a.equals(b);
const gt = a => b => !a.lt(b) && !a.equals(b);
const gte = a => b => !a.lt(b);

laws:

1. If a.lt(b) then b.lt(a) === false (irreflexivity)
2. a.lt(b) or b.lt(a) or a.equals(b) (trichotomy)
3. If a.lt(b) and b.lt(c), then a.lt(c) (transitivity)

An added bonus is that we could refer to lt as precedes which has no connotation of quantity.

[xgbuils]

I don’t really understand the root of the performance problem. I can take any Ord operator(lt, lte, gt, gte) and define the rest using only negation.

// based on .lte
const lte = a => b => a.lte(b);
const lt = a => b => !b.lte(a);
const gt = a => b => !a.lte(b);
const gte = a => b => b.lte(a);

// based on .gt
const lte = a => b => !a.gt(b);
const lt = a => b => b.gt(a); // edit: before const lt = a => b => b.lte(a);
const gt = a => b => a.gt(b);
const gte = a => b => !b.gt(a); // edit: before const gte = a => b => !b.lte(a);

[i-am-tom]

@davidchambers … Today, you have legitimately and significantly improved my life.