Is the Nat LessOrEqualOrGreater than a given number?

lowest can be a number <= the minimum.

giveAPresent { age } =
    case age |> MinNat.is nat18 { lowest = nat0 } of
        Nat.Less age ->
            toy { age = age }


        Nat.Greater age ->
            experience { age = age }


        Nat.Equal () ->
            bigPresent


toy : { age : Nat (ArgIn Nat0 Nat17 ifN_) } -> Toy


experience : { age : Nat (ArgIn Nat19 max ifN_) } -> Experience

Is the Nat BelowOrAtLeast a given number?

factorial : Nat (ArgIn min max ifN_) -> Nat (Min Nat1)
factorial =
    factorialBody


factorialBody : -- as in factorial
factorialBody =
    case x |> MinNat.isAtLeast nat1 { lowest = nat0 } of
        Nat.Below _ ->
            MinNat.value nat1


        Nat.EqualOrGreater atLeast1 ->
            Nat.mul atLeast1
                (factorial
                    (atLeast1 |> MinNat.sub nat1)
                )

Is the Nat AtMostOrAbove a given number?

goToU18Party : { age : Nat (ArgIn min Nat17 ifN_) } -> Snack


tryToGoToU18Party { age } =
    case age |> MinNat.isAtMost nat17 { lowest = nat0 } of
        EqualOrLess age ->
            Just (goToU18Party { age = age })


        Greater _ ->
            Nothing

Subtract an exact Nat (N ...).

atLeast7 |> MinNat.sub nat2
--> : Nat (Min Nat5)

Add a fixed Nat (N ...) value.

atLeast70 |> InNat.add nat7
--> : Nat (Min Nat77)

Subtract a Nat (In ...). The second argument is the maximum of the subtracted Nat.

atLeast6 |> MinNat.subMax nat5 between0And5
--> : Nat (Min Nat1)

Add a Nat (In ...). The second argument is the minimum added value.

atLeast5 |> MinNat.addMin nat2 atLeast2
--> : Nat (Min Nat7)

Convert a Nat (ArgIn min ...) to a Nat (Min min).

between3And10 |> MinNat.value
--> : Nat (Min Nat4)

There is only 1 situation you should use this.

To make these the same type.

[ atLeast1, between1And10 ]

Elm complains:

But all the previous elements in the list are: Nat (Min Nat1)

[ atLeast1
, between1And10 |> MinNat.value
]

A Codec to serialize Nats with a lower bound.

import Serialize


serializeNaturalNumber :
    Serialize.Codec
        String
        (Nat (Min Nat0))
serializeNaturalNumber =
    MinNat.serialize nat0


encode : Nat (ArgIn min max ifN_) -> Bytes
encode =
    MinNat.value
        >> Serialize.encodeToBytes serializeNaturalNumber


decode :
    Bytes
    -> Result (Serialize.Error String) (Nat (Min Nat0))
decode =
    Serialize.decodeFromBytes serializeNaturalNumber