package baby

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in-package search v0.2.0

package baby

baby
- Baby
  - BASE_MAP
  - BASE_SET
  - Custom
    
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  - MAP
    
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  - OrderedType
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The signature Baby.OrderedType describes a type equipped with a total ordering function.

type t

The type of the set elements.

val compare : t -> t -> int

The function compare decides a relation $\leq$ over elements of type t.

The relation $\leq$ must be a total preorder: that is,

for all elements $x, y$ , it must be the case that $x \leq y$ or $y \leq x$ holds.
for all elements $x, y, z$ , it must be the case that $x \leq y$ and $y \leq z$ imply $x \leq z$ ;

Let us write $x \equiv y$ when $x \leq y$ and $y \leq x$ hold. In that case, we say that $x$ and $y$ are equivalent.

Let us write $x < y$ when $x \leq y$ and $\neg (y \leq x)$ hold.

compare must behave as follows:

if $x \equiv y$ holds then compare x y must be zero;
if $x < y$ holds then compare x y must be negative;
if $y < x$ holds then compare x y must be positive.

If equivalence implies equality (that is, if for all elements $x, y$ , $x \equiv y$ implies $x = y$ ) then we say that the relation $\leq$ is a total order.