8.2) Metapredicates

Metapredicates are built-in predicates that are applied on predicates. They are represented by superscript letters and directly follow the predicate on which you want to apply them.

Just like built-in predicates, metapredicates also have an additional parameter called the superscript that directly follows the metapredicate name. It can either be a series of superscript digits or one of ⁽ and ⁾ to indicate that the first/last element of the input must be used as superscript (like built-in predicates and subscripts).

For example, the code pᶠ⁴² can be read as "find the first 42 permutations of the input".

Metapredicates can be applied to inline predicates and predicate compositions as well. For example {p}ᶠ⁴² would work as well.

↖ Superscript arrow

You can use the subscript arrow ↖ to pass the immediately following variable as a superscript to a metapredicate (like ⁽ and ⁾, in a shorter way that does not require the input to contain that variable).

For example, 13+₁ⁱ↖7 will output 20.

Note that if you want to use both subscript and superscript arrows, they must both be used after the predicate and metapredicate combo.

For example, 13+ⁱ↙2↖7 or 13+ⁱ↖7↙2 will output 27.

List of built-in metapredicates

Symbol	Name	Superscript	Description
ᵃ	Accumulate	Default = 1 I	Same as ⁱ but the Input at each step is the list of accumulated results.
ᵇ	Bagof	Default I	Same as ᶠ but uses bagof instead of findall under the hood
ᶜ	Count	Default = 0 1	Count all outputs of the predicate for ? Count all unique outputs of the predicate for ?
ᵈ	Declare	Default 0 1 2	? = [A,B], . = B, call the pred. with A as input and B as output ? = . = [A,B], call the pred. with A as input and B as output ? = [A,B], . = A, call the pred. with B as input and A as output ? = . = [A,B], call the pred. with B as input and A as output
ᵉ	Existence	Default I	The output of the pred. for at least one element of ? is . The output of the pred. for at least one element of ? = . is I
ᶠ	Find	Default I	Find all outputs of the predicate for ? Find the first I outputs of the predicate for ?
ᵍ	Group by	Default	Groups elements of ? together into . if they generate the same output to the predicate.
ʰ	Head	Default = 1 I	Apply the predicate only to the head of ? Apply the predicate only to the first I elements of ?
ⁱ	Iterate	Default I	Same as with superscript I with I > 0 not set Apply I times the predicate to ?
ʲ		Default
ᵏ		Default
ˡ	Left fold	Default	. is the left fold of the predicate on ?
ᵐ	Map	Default = 1 I	Map the predicate to each element of ? Nested map I times on ?
ⁿ	Nonexistence	Default I	The output of the pred. for each element of ? is never . The output of the pred. for each element of ? = . is never I
ᵒ	Order by	Default = 0 1 2 3	. is ? ordered asc. by mapping the predicate . is ? ordered desc. by mapping the predicate Same as 0 but . contains the elements of the map Same as 1 but . contains the elements of the map
ᵖ		Default
ʳ	Right fold	Default	Not implemented
ˢ	Select	Default	Find outputs of the predicate for each element of ?
ᵗ	Tail	Default = 1 I	Apply the predicate only to the tail of ? Apply the predicate only to the last I elements of ?
ᵘ	Unique	Default I	Find all unique outputs of the pred. for ? Find the first I unique outputs of the pred. for ?
ᵛ	Verify	Default I	The output of the pred. for each element of ? is always . The output of the pred. for each element of ? = . is always I
ʷ		Default
ˣ		Default
ʸ		Default
ᶻ	Zip	Default 0 1 2	Zip the input with the result of ᵐ on the pred. Zip the input with the result of ᶠ on the pred. Zip the result of ᵐ on the pred. with the input Zip the result of ᶠ on the pred. with the input