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apply.pl -- Apply predicates on a list
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This module defines meta-predicates that apply a predicate on all members of a list.

All predicates support partial application in the Goal argument. This means that these calls are identical:

?- maplist(=, [foo, foo], [X, Y]).
?- maplist(=(foo), [X, Y]).
See also
- apply_macros.pl provides compile-time expansion for part of this library.
- http://www.cs.otago.ac.nz/staffpriv/ok/pllib.htm
- Unit test code in src/Tests/library/test_apply.pl
To be done
- Add include/4, include/5, exclude/4, exclude/5
Source include(:Goal, +List1, ?List2) is det
Filter elements for which Goal succeeds. True if List2 contains those elements Xi of List1 for which call(Goal, Xi) succeeds.
See also
- exclude/3, partition/4, convlist/3.
Compatibility
- Older versions of SWI-Prolog had sublist/3 with the same arguments and semantics.
Source exclude(:Goal, +List1, ?List2) is det
Filter elements for which Goal fails. True if List2 contains those elements Xi of List1 for which call(Goal, Xi) fails.
See also
- include/3, partition/4
Source partition(:Pred, +List, ?Included, ?Excluded) is det
Filter elements of List according to Pred. True if Included contains all elements for which call(Pred, X) succeeds and Excluded contains the remaining elements.
See also
- include/3, exclude/3, partition/5.
Source partition(:Pred, +List, ?Less, ?Equal, ?Greater) is semidet
Filter List according to Pred in three sets. For each element Xi of List, its destination is determined by call(Pred, Xi, Place), where Place must be unified to one of <, = or >. Pred must be deterministic.
See also
- partition/4
Source maplist(:Goal, ?List1)
Source maplist(:Goal, ?List1, ?List2)
Source maplist(:Goal, ?List1, ?List2, ?List3)
Source maplist(:Goal, ?List1, ?List2, ?List3, ?List4)
True if Goal is successfully applied on all matching elements of the list. The maplist family of predicates is defined as: 
maplist(G, [X_11, ..., X_1n],
           [X_21, ..., X_2n],
           ...,
           [X_m1, ..., X_mn]) :-
   call(G, X_11, ..., X_m1),
   call(G, X_12, ..., X_m2),
   ...
   call(G, X_1n, ..., X_mn).

This family of predicates is deterministic iff Goal is deterministic and List1 is a proper list, i.e., a list that ends in [].

Source convlist(:Goal, +ListIn, -ListOut) is det
Similar to maplist/3, but elements for which call(Goal, ElemIn, _) fails are omitted from ListOut. For example (using library(yall)): 
?- convlist([X,Y]>>(integer(X), Y is X^2),
            [3, 5, foo, 2], L).
L = [9, 25, 4].
Compatibility
- Also appears in YAP library(maplist) and SICStus library(lists).
Source foldl(:Goal, +List, +V0, -V)
Source foldl(:Goal, +List1, +List2, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +List4, +V0, -V)
Fold an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("fold-left"), using columns of m list elements as arguments for Goal. The foldl family of predicates is defined as follows, with V0 an initial value and V the final value of the folding operation: 
foldl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, V) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, V).

No implementation for a corresponding foldr is given. A foldr implementation would consist in first calling reverse/2 on each of the m input lists, then applying the appropriate foldl. This is actually more efficient than using a properly programmed-out recursive algorithm that cannot be tail-call optimized.

Source scanl(:Goal, +List, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +List4, +V0, -Values)
Scan an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("scan-left"), using columns of m list elements as arguments for Goal. The scanl family of predicates is defined as follows, with V0 an initial value and V the final value of the scanning operation: 
scanl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, [V0, V1, ..., Vn] ) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, Vn).

scanl behaves like a foldl that collects the sequence of values taken on by the Vx accumulator into a list.

Re-exported predicates

The following predicates are exported from this file while their implementation is defined in imported modules or non-module files loaded by this module.

Source maplist(:Goal, ?List1)
Source maplist(:Goal, ?List1, ?List2)
Source maplist(:Goal, ?List1, ?List2, ?List3)
Source maplist(:Goal, ?List1, ?List2, ?List3, ?List4)
True if Goal is successfully applied on all matching elements of the list. The maplist family of predicates is defined as: 
maplist(G, [X_11, ..., X_1n],
           [X_21, ..., X_2n],
           ...,
           [X_m1, ..., X_mn]) :-
   call(G, X_11, ..., X_m1),
   call(G, X_12, ..., X_m2),
   ...
   call(G, X_1n, ..., X_mn).

This family of predicates is deterministic iff Goal is deterministic and List1 is a proper list, i.e., a list that ends in [].

Source maplist(:Goal, ?List1)
Source maplist(:Goal, ?List1, ?List2)
Source maplist(:Goal, ?List1, ?List2, ?List3)
Source maplist(:Goal, ?List1, ?List2, ?List3, ?List4)
True if Goal is successfully applied on all matching elements of the list. The maplist family of predicates is defined as: 
maplist(G, [X_11, ..., X_1n],
           [X_21, ..., X_2n],
           ...,
           [X_m1, ..., X_mn]) :-
   call(G, X_11, ..., X_m1),
   call(G, X_12, ..., X_m2),
   ...
   call(G, X_1n, ..., X_mn).

This family of predicates is deterministic iff Goal is deterministic and List1 is a proper list, i.e., a list that ends in [].

Source maplist(:Goal, ?List1)
Source maplist(:Goal, ?List1, ?List2)
Source maplist(:Goal, ?List1, ?List2, ?List3)
Source maplist(:Goal, ?List1, ?List2, ?List3, ?List4)
True if Goal is successfully applied on all matching elements of the list. The maplist family of predicates is defined as: 
maplist(G, [X_11, ..., X_1n],
           [X_21, ..., X_2n],
           ...,
           [X_m1, ..., X_mn]) :-
   call(G, X_11, ..., X_m1),
   call(G, X_12, ..., X_m2),
   ...
   call(G, X_1n, ..., X_mn).

This family of predicates is deterministic iff Goal is deterministic and List1 is a proper list, i.e., a list that ends in [].

Source foldl(:Goal, +List, +V0, -V)
Source foldl(:Goal, +List1, +List2, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +List4, +V0, -V)
Fold an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("fold-left"), using columns of m list elements as arguments for Goal. The foldl family of predicates is defined as follows, with V0 an initial value and V the final value of the folding operation: 
foldl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, V) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, V).

No implementation for a corresponding foldr is given. A foldr implementation would consist in first calling reverse/2 on each of the m input lists, then applying the appropriate foldl. This is actually more efficient than using a properly programmed-out recursive algorithm that cannot be tail-call optimized.

Source foldl(:Goal, +List, +V0, -V)
Source foldl(:Goal, +List1, +List2, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +List4, +V0, -V)
Fold an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("fold-left"), using columns of m list elements as arguments for Goal. The foldl family of predicates is defined as follows, with V0 an initial value and V the final value of the folding operation: 
foldl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, V) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, V).

No implementation for a corresponding foldr is given. A foldr implementation would consist in first calling reverse/2 on each of the m input lists, then applying the appropriate foldl. This is actually more efficient than using a properly programmed-out recursive algorithm that cannot be tail-call optimized.

Source foldl(:Goal, +List, +V0, -V)
Source foldl(:Goal, +List1, +List2, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +V0, -V)
Source foldl(:Goal, +List1, +List2, +List3, +List4, +V0, -V)
Fold an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("fold-left"), using columns of m list elements as arguments for Goal. The foldl family of predicates is defined as follows, with V0 an initial value and V the final value of the folding operation: 
foldl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, V) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, V).

No implementation for a corresponding foldr is given. A foldr implementation would consist in first calling reverse/2 on each of the m input lists, then applying the appropriate foldl. This is actually more efficient than using a properly programmed-out recursive algorithm that cannot be tail-call optimized.

Source scanl(:Goal, +List, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +List4, +V0, -Values)
Scan an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("scan-left"), using columns of m list elements as arguments for Goal. The scanl family of predicates is defined as follows, with V0 an initial value and V the final value of the scanning operation: 
scanl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, [V0, V1, ..., Vn] ) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, Vn).

scanl behaves like a foldl that collects the sequence of values taken on by the Vx accumulator into a list.

Source scanl(:Goal, +List, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +List4, +V0, -Values)
Scan an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("scan-left"), using columns of m list elements as arguments for Goal. The scanl family of predicates is defined as follows, with V0 an initial value and V the final value of the scanning operation: 
scanl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, [V0, V1, ..., Vn] ) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, Vn).

scanl behaves like a foldl that collects the sequence of values taken on by the Vx accumulator into a list.

Source scanl(:Goal, +List, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +V0, -Values)
Source scanl(:Goal, +List1, +List2, +List3, +List4, +V0, -Values)
Scan an ensemble of m (0 <= m <= 4) lists of length n head-to-tail ("scan-left"), using columns of m list elements as arguments for Goal. The scanl family of predicates is defined as follows, with V0 an initial value and V the final value of the scanning operation: 
scanl(G, [X_11, ..., X_1n],
         [X_21, ..., X_2n],
         ...,
         [X_m1, ..., X_mn], V0, [V0, V1, ..., Vn] ) :-
   call(G, X_11, ..., X_m1, V0, V1),
   call(G, X_12, ..., X_m2, V1, V2),
   ...
   call(G, X_1n, ..., X_mn, V<n-1>, Vn).

scanl behaves like a foldl that collects the sequence of values taken on by the Vx accumulator into a list.