This module contains an implementation of set functions. The general idea of set functions is described in:
S. Antoy, M. Hanus: Set Functions for Functional Logic Programming Proc. 11th International Conference on Principles and Practice of Declarative Programming (PPDP'09), pp. 7382, ACM Press, 2009
Intuition: If f
is an nary function, then (setn f)
is a setvalued
function that collects all nondeterminism caused by f (but not
the nondeterminism caused by evaluating arguments!) in a set.
Thus, (setn f a1 ... an)
returns the set of all
values of (f b1 ... bn)
where b1
,...,bn
are values
of the arguments a1
,...,an
(i.e., the arguments are
evaluated "outside" this capsule so that the nondeterminism
caused by evaluating these arguments is not captured in this capsule
but yields several results for (setn...)
.
Similarly, logical variables occuring in a1
,...,an
are not bound
inside this capsule (in PAKCS they cause a suspension until
they are bound).
The set of values returned by a set function is represented
by an abstract type Values
on which several operations are
defined in this module. Actually, it is a multiset of values,
i.e., duplicates are not removed.
The handling of failures and nested occurrences of set functions is not specified in the previous paper. Thus, a detailed description of the semantics of set functions as implemented in this library can be found in the paper
J. Christiansen, M. Hanus, F. Reck, D. Seidel: A Semantics for Weakly Encapsulated Search in Functional Logic Programs Proc. 15th International Conference on Principles and Practice of Declarative Programming (PPDP'13), pp. 4960, ACM Press, 2013
Restrictions of the PAKCS implementation of set functions:
Author: Michael Hanus, Fabian Reck
Version: September 2018
set0
:: a > Values a
Combinator to transform a 0ary function into a corresponding set function. 
set1
:: (a > b) > a > Values b
Combinator to transform a unary function into a corresponding set function. 
set2
:: (a > b > c) > a > b > Values c
Combinator to transform a binary function into a corresponding set function. 
set3
:: (a > b > c > d) > a > b > c > Values d
Combinator to transform a function of arity 3 into a corresponding set function. 
set4
:: (a > b > c > d > e) > a > b > c > d > Values e
Combinator to transform a function of arity 4 into a corresponding set function. 
set5
:: (a > b > c > d > e > f) > a > b > c > d > e > Values f
Combinator to transform a function of arity 5 into a corresponding set function. 
set6
:: (a > b > c > d > e > f > g) > a > b > c > d > e > f > Values g
Combinator to transform a function of arity 6 into a corresponding set function. 
set7
:: (a > b > c > d > e > f > g > h) > a > b > c > d > e > f > g > Values h
Combinator to transform a function of arity 7 into a corresponding set function. 
isEmpty
:: Values a > Bool
Is a multiset of values empty? 
notEmpty
:: Values a > Bool
Is a multiset of values not empty? 
valueOf
:: Eq a => a > Values a > Bool
Is some value an element of a multiset of values? 
choose
:: Eq a => Values a > (a,Values a)
Chooses (nondeterministically) some value in a multiset of values and returns the chosen value and the remaining multiset of values. 
chooseValue
:: Eq a => Values a > a
Chooses (nondeterministically) some value in a multiset of values and returns the chosen value. 
select
:: Values a > (a,Values a)
Selects (indeterministically) some value in a multiset of values and returns the selected value and the remaining multiset of values. 
selectValue
:: Values a > a
Selects (indeterministically) some value in a multiset of values and returns the selected value. 
mapValues
:: (a > b) > Values a > Values b
Maps a function to all elements of a multiset of values. 
foldValues
:: (a > a > a) > a > Values a > a
Accumulates all elements of a multiset of values by applying a binary operation. 
filterValues
:: (a > Bool) > Values a > Values a
Keeps all elements of a multiset of values that satisfy a predicate. 
minValue
:: Ord a => Values a > a
Returns the minimum of a nonempty multiset of values according to the given comparison function on the elements. 
minValueBy
:: (a > a > Ordering) > Values a > a
Returns the minimum of a nonempty multiset of values according to the given comparison function on the elements. 
maxValue
:: Ord a => Values a > a
Returns the maximum of a nonempty multiset of values according to the given comparison function on the elements. 
maxValueBy
:: (a > a > Ordering) > Values a > a
Returns the maximum of a nonempty multiset of values according to the given comparison function on the elements. 
values2list
:: Values a > IO [a]
Puts all elements of a multiset of values in a list. 
printValues
:: Show a => Values a > IO ()
Prints all elements of a multiset of values. 
sortValues
:: Ord a => Values a > [a]
Transforms a multiset of values into a list sorted by the standard term ordering. 
sortValuesBy
:: (a > a > Bool) > Values a > [a]
Transforms a multiset of values into a list sorted by a given ordering on the values. 
Abstract type representing multisets of values.
Constructors:
Combinator to transform a unary function into a corresponding set function. 
Combinator to transform a binary function into a corresponding set function. 
Combinator to transform a function of arity 3 into a corresponding set function. 
Combinator to transform a function of arity 4 into a corresponding set function. 
Combinator to transform a function of arity 5 into a corresponding set function. 
Combinator to transform a function of arity 6 into a corresponding set function. 
Combinator to transform a function of arity 7 into a corresponding set function. 
Chooses (nondeterministically) some value in a multiset of values
and returns the chosen value and the remaining multiset of values.
Thus, if we consider the operation chooseValue x = fst (choose x)
then 
Chooses (nondeterministically) some value in a multiset of values
and returns the chosen value.
Thus, 
Selects (indeterministically) some value in a multiset of values
and returns the selected value and the remaining multiset of values.
Thus, NOTE: The usage of this operation is only safe (i.e., does not destroy completeness) if all values in the argument set are identical.

Selects (indeterministically) some value in a multiset of values
and returns the selected value.
Thus, NOTE: The usage of this operation is only safe (i.e., does not destroy completeness) if all values in the argument set are identical.

Maps a function to all elements of a multiset of values. 
Accumulates all elements of a multiset of values by applying a binary operation. This is similarly to fold on lists, but the binary operation must be commutative so that the result is independent of the order of applying this operation to all elements in the multiset. 
Keeps all elements of a multiset of values that satisfy a predicate. 
Returns the minimum of a nonempty multiset of values according to the given comparison function on the elements. 
Returns the minimum of a nonempty multiset of values according to the given comparison function on the elements. 
Returns the maximum of a nonempty multiset of values according to the given comparison function on the elements. 
Returns the maximum of a nonempty multiset of values according to the given comparison function on the elements. 
Puts all elements of a multiset of values in a list. Since the order of the elements in the list might depend on the time of the computation, this operation is an I/O action. 
Prints all elements of a multiset of values. 
Transforms a multiset of values into a list sorted by the standard term ordering. As a consequence, the multiset of values is completely evaluated. 
Transforms a multiset of values into a list sorted by a given ordering on the values. As a consequence, the multiset of values is completely evaluated. In order to ensure that the result of this operation is independent of the evaluation order, the given ordering must be a total order. 