yall.pl -- Lambda expressionsyall.pl -- Lambda expressionsProlog realizes high-order programming with meta-calling. The core predicate of this is call/1, which simply calls its argument. This can be used to define higher-order predicates such as ignore/1 or forall/2. The call/N construct calls a closure with N-1 additional arguments. This is used to define higher-order predicates such as the maplist/N family or foldl/N.
The problem with higher order predicates based on call/N is that the
additional arguments are always added to the end of the closure's
argument list. This often requires defining trivial helper predicates to
get the argument order right. For example, if you want to add a common
postfix to a list of atoms you need to apply
atom_concat(In,Postfix,Out), but maplist(x(PostFix),ListIn,ListOut)
calls x(PostFix,In,Out). This is where this library comes in, which
allows us to write
?- maplist([In,Out]>>atom_concat(In,'_p',Out), [a,b], ListOut). ListOut = [a_p, b_p].
The {...} specifies which variables are shared between the lambda
and the context. This allows us to write the code below. Without the
{PostFix} a free variable would be passed to atom_concat/3.
add_postfix(PostFix, ListIn, ListOut) :-
maplist({PostFix}/[In,Out]>>atom_concat(In,PostFix,Out),
ListIn, ListOut).
This introduces the second application area of lambda expressions: the
ability to stop binding variables in the context. This features shines
when combined with bagof/3 or setof/3 where you normally have to specify
the the variables in whose binding you are not interested using the
Var^Goal construct (marking Var as existential quantified). Lambdas
allow doing the reverse: specify the variables in which you are
interested.
Lambda expressions use the syntax below
{...}/[...]>>Goal.
The {...} optional part is used for lambda-free variables. The order
of variables doesn't matter hence the {...} set notation.
The [...] optional part lists lambda parameters. Here order of
variables matters hence the list notation.
As / and >> are standard infix operators, no new operators are added
by this library. An advantage of this syntax is that we can simply
unify a lambda expression with Free/Parameters>>Lambda to access each of
its components. Spaces in the lambda expression are not a problem
although the goal may need to be written between ()'s. Goals that are
qualified by a module prefix also need to be wrapped inside parentheses.
Combined with library(apply_macros), library(yall) allows writing one-liners for many list operations that have the same performance as hand written code.
The module name, yall, stands for Yet Another Lambda Library.
This module implements Logtalk's lambda expressions syntax. The development of this module was sponsored by Kyndi, Inc.
+Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
is_lambda(@Term) is semidet lambda_calls(+LambdaExpression, -Goal) is det lambda_calls(+LambdaExpression, +ExtraArgs, -Goal) is det +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Parameters >> +Lambda >>(+Parameters, +Lambda, ?A1) >>(+Parameters, +Lambda, ?A1, ?A2) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) >>(+Parameters, +Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)call(Lambda,A1,...),
but arguments are reordered according to the list Parameters:
length(Parameters) arguments from A1, ... are
unified with (a copy of) Parameters, which may share
them with variables in Lambda. +Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
+Free / :Lambda /(+Free, :Lambda, ?A1) /(+Free, :Lambda, ?A1, ?A2) /(+Free, :Lambda, ?A1, ?A2, ?A3) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6) /(+Free, :Lambda, ?A1, ?A2, ?A3, ?A4, ?A5, ?A6, ?A7)Free/[]>>Lambda. This is the same as applying
call/N on Lambda, except that only variables appearing in Free
are bound by the call. For example
p(1,a).
p(2,b).
?- {X}/p(X,Y).
X = 1;
X = 2.
This can in particularly be combined with bagof/3 and setof/3 to select particular variables to be concerned rather than using existential quantification (^/2) to exclude variables. For example, the two calls below are equivalent.
setof(X, Y^p(X,Y), Xs)
setof(X, {X}/p(X,_), Xs)
lambda_calls(+LambdaExpression, -Goal) is det lambda_calls(+LambdaExpression, +ExtraArgs, -Goal) is det