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- library(yall): Lambda expressions

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## A.51 library(yall): Lambda expressions

- author
- Paulo Moura and Jan Wielemaker
- To be done
- Extend optimization support

Prolog 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/2-5
family or foldl/4-7.

The *closure* concept used here is somewhat different from the
closure concept from functional programming. The latter is a function
that is always evaluated in the context that existed at function
creation time. Here, a closure is a term of arity *0 =<
L =< K*. The term's functor is the name of a
predicate of arity

*K*and the term's

*L*arguments (where

*L*could be 0) correspond to

*L*leftmost arguments of said predicate, bound to parameter values. For example, a closure involving atom_concat/3 might be the term

`atom_concat(prefix)`

. In order of
increasing *L*, one would have increasingly more complete closures that could be passed to call/3, all giving the same result:

call(atom_concat,prefix,suffix,R). call(atom_concat(prefix),suffix,R). call(atom_concat(prefix,suffix),R). call(atom_concat(prefix,suffix,R)).

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(atom_concat(Postfix),ListIn,ListOut)`

calls
`atom_concat(Postfix,In,Out)`

. This is where `library(yall)`

comes in, where the module name, *yall*, stands for *Yet Another
Lambda Library*.

The library allows us to write a lambda expression that *wraps
around* the (possibly complex) goal to call:

?- maplist([In,Out]>>atom_concat(In,'_p',Out), [a,b], ListOut). ListOut = [a_p, b_p].

A bracy list `{...}`

specifies which variables are *shared*
between the wrapped goal and the surrounding context. This allows us to
write the code below. Without the `{Postfix}`

a fresh
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 confine variables to the called goal's context. This
features shines when combined with bagof/3
or setof/3 where
one normally has to list those variables whose bindings one is *not*
interested in using the
`Var^Goal`

construct (marking `Var` as existentially
quantified and confining it to the called goal's context). Lambda
expressions allow you to do the converse: specify the variables which
one *is* interested in. These variables are common to the context
of the called goal and the surrounding context.

Lambda expressions use the syntax below

{...}/[...]>>Goal.

The `{...}`

optional part is used for lambda-free
variables (the ones shared between contexts). 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 betweenâ€™()'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.

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`)- Calls a copy of
`Lambda`. This is similar to`call(Lambda,A1,...)`

, but arguments are reordered according to the list`Parameters`:- The first
`length(Parameters)`

arguments from`A1`, ... are unified with (a copy of)`Parameters`, which*may*share them with variables in`Lambda`. - Possible excess arguments are passed by position.

`Parameters`is either a plain list of parameters or a term `{Free}/List`

.`Free`represents variables that are shared between the context and the`Lambda`term. This is needed for compiling`Lambda`expressions. - The first
`+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`)- Shorthand for
`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 examplep(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)

- [semidet]
**is_lambda**(`@Term`) - True if
`Term`is a valid Lambda expression. - [det]
**lambda_calls**(`+LambdaExpression, -Goal`) - [det]
**lambda_calls**(`+LambdaExpression, +ExtraArgs, -Goal`) `Goal`is the goal called if call/N is applied to`LambdaExpression`, where`ExtraArgs`are the additional arguments to call/N.`ExtraArgs`can be an integer or a list of concrete arguments. This predicate is used for cross-referencing and code highlighting.