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Define and give an example of the Amb operator.

The Amb operator (short for "ambiguous") expresses nondeterminism. This doesn't refer to randomness (as in "nondeterministic universe") but is closely related to the term as it is used in automata theory ("non-deterministic finite automaton").

The Amb operator takes a variable number of expressions (or values if that's simpler in the language) and yields a correct one which will satisfy a constraint in some future computation, thereby avoiding failure.

Problems whose solution the Amb operator naturally expresses can be approached with other tools, such as explicit nested iterations over data sets, or with pattern matching. By contrast, the Amb operator appears integrated into the language. Invocations of Amb are not wrapped in any visible loops or other search patterns; they appear to be independent.

Essentially Amb(x, y, z) splits the computation into three possible futures: a future in which the value x is yielded, a future in which the value y is yielded and a future in which the value z is yielded. The future which leads to a successful subsequent computation is chosen. The other "parallel universes" somehow go away. Amb called with no arguments fails.

For simplicity, one of the domain values usable with Amb may denote failure, if that is convenient. For instance, it is convenient if a Boolean false denotes failure, so that Amb(false) fails, and thus constraints can be expressed using Boolean expressions like Amb(x * y == 8) which unless x and y add to four.

A pseudo-code program which satisfies this constraint might look like:

let x = Amb(1, 2, 3)
let y = Amb(7, 6, 4, 5)
Amb(x * y = 8)
print x, y

The output is 2 4 because Amb(1, 2, 3) correctly chooses the future in which x has value 2, Amb(7, 6, 4, 5) chooses 4 and consequently Amb(x * y = 8) produces a success.

Alternatively, failure could be represented using strictly Amb():

unless x * y = 8 do Amb()

Or else Amb could take the form of two operators or functions: one for producing values and one for enforcing constraints:

let x = Ambsel(1, 2, 3)
let y = Ambsel(4, 5, 6)
Ambassert(x * y = 8)
print x, y

where Ambassert behaves like Amb() if the Boolean expression is false, otherwise it allows the future computation to take place, without yielding any value.

The task is to somehow implement Amb, and demonstrate it with a program which chooses one word from each of the following four sets of character strings to generate a four-word sentence:

"the" "that" "a"
"frog" "elephant" "thing"
"walked" "treaded" "grows"
"slowly" "quickly"

The constraint to be satisfied is that the last character of each word (other than the last) is the same as the first character of its successor.

The only successful sentence is "that thing grows slowly"; other combinations do not satisfy the constraint and thus fail.

The goal of this task isn't to simply process the four lists of words with explicit, deterministic program flow such as nested iteration, to trivially demonstrate the correct output. The goal is to implement the Amb operator, or a facsimile thereof that is possible within the language limitations.

11l

Translation of: Nim

<lang 11l>F amb(comp, options, prev = ‘’) -> Array[String]

  I options.empty
     R []

  L(opt) options[0]
     // If this is the base call, prev is empty and we need to continue.
     I prev != ‘’ & !comp(prev, opt)
        L.continue

     // Take care of the case where we have no options left.
     I options.len == 1
        R [opt]

     // Traverse into the tree.
     V res = amb(comp, options[1..], opt)

     // If it was a failure, try the next one.
     if !res.empty
        R opt [+] res // We have a match

  R []

V sets = [[‘the’, ‘that’, ‘a’],

         [‘frog’, ‘elephant’, ‘thing’],
         [‘walked’, ‘treaded’, ‘grows’],
         [‘slowly’, ‘quickly’]]

V result = amb((s, t) -> s.last == t[0], sets) print(result.join(‘ ’))</lang>

Output:

that thing grows slowly

Ada

<lang ada>with Ada.Strings.Unbounded; use Ada.Strings.Unbounded; with Ada.Text_IO; use Ada.Text_IO;

procedure Test_Amb is

  type Alternatives is array (Positive range <>) of Unbounded_String;

  type Amb (Count : Positive) is record
     This : Positive := 1;
     Left : access Amb; 
     List : Alternatives (1..Count);
  end record;
  
  function Image (L : Amb) return String is
  begin
     return To_String (L.List (L.This));
  end Image;

  function "/" (L, R : String) return Amb is
     Result : Amb (2);
  begin
     Append (Result.List (1), L);
     Append (Result.List (2), R);
     return Result;
  end "/";
  
  function "/" (L : Amb; R : String) return Amb is
     Result : Amb (L.Count + 1);
  begin
     Result.List (1..L.Count) := L.List ;
     Append (Result.List (Result.Count), R);
     return Result;
  end "/";

  function "=" (L, R : Amb) return Boolean is
     Left : Unbounded_String renames L.List (L.This);
  begin
     return Element (Left, Length (Left)) = Element (R.List (R.This), 1);
  end "=";
  
  procedure Failure (L : in out Amb) is
  begin
     loop
        if L.This < L.Count then
           L.This := L.This + 1;
        else
           L.This := 1;
           Failure (L.Left.all);
        end if;
        exit when L.Left = null or else L.Left.all = L;
     end loop;
  end Failure;

  procedure Join (L : access Amb; R : in out Amb) is
  begin
     R.Left := L;
     while L.all /= R loop
        Failure (R);
     end loop;
  end Join;

  W_1 : aliased Amb := "the" / "that" / "a";
  W_2 : aliased Amb := "frog" / "elephant" / "thing";
  W_3 : aliased Amb := "walked" / "treaded" / "grows";
  W_4 : aliased Amb := "slowly" / "quickly";

begin

  Join (W_1'Access, W_2);
  Join (W_2'Access, W_3);
  Join (W_3'Access, W_4);
  Put_Line (Image (W_1) & ' ' & Image (W_2) & ' ' & Image (W_3) & ' ' & Image (W_4));

end Test_Amb;</lang> The type Amb is implemented with the operations "/" to construct it from strings. Each instance keeps its state. The operation Failure performs back tracing. Join connects two elements into a chain. The implementation propagates Constraint_Error when matching fails.

Output:

that thing grows slowly

ALGOL 68

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d

Note: This program violates ALGOL 68's scoping rules when a locally scoped procedure is returned to a more global scope. ELLA ALGOL 68RS misses this violation, but ALGOL 68 Genie spots it at run time and then produces an assert. However ELLA ALGOL 68RS does produce the desired result, but may potentially suffer from "mysterious" stack problems. <lang algol68>MODE PAGE = FLEX[0]STRING; MODE YIELDPAGE = PROC(PAGE)VOID; MODE ITERPAGE = PROC(YIELDPAGE)VOID;

OP INITITERPAGE = (PAGE self)ITERPAGE:

 (YIELDPAGE yield)VOID: # scope violation #
   FOR i TO UPB self DO
     yield(self[i])
   OD;

OP + = (ITERPAGE for strings, PAGE b)ITERPAGE:

 (YIELDPAGE yield)VOID: # scope violation #
   for strings((PAGE amb)VOID:(
     [UPB amb + 1]STRING joined; 
     joined[:UPB amb] := amb;
     STRING last string := amb[UPB amb];
     CHAR last char := last string[UPB last string];
     FOR i TO UPB b DO
       IF last char = b[i][1] THEN
         joined[UPB joined] := b[i];
         yield(joined)
       FI
     OD
   ));

OP + = (PAGE a, PAGE b)ITERPAGE: INITITERPAGE a + b;

ITERPAGE gen amb :=

  PAGE("the", "that", "a") +
  PAGE("frog", "elephant", "thing") +
  PAGE("walked", "treaded", "grows") +
  PAGE("slowly", "quickly");

PAGE sep;

FOR PAGE amb IN # gen amb( # ) DO #
1. (PAGE amb)VOID:

   print((amb[1]+" "+amb[2]+" "+amb[3]+" "+amb[4], new line))

OD# )</lang>

Output:

that thing grows slowly

ATS

<lang ATS> (* ****** ****** *) //

include

"share/atspre_staload.hats"

include

"share/HATS/atspre_staload_libats_ML.hats" // (* ****** ****** *) // staload "libats/ML/SATS/monad_list.sats" staload _ = "libats/ML/DATS/monad_list.dats" // (* ****** ****** *) // datatype words =

 | Sing of stringGt(0)
 | Comb of (words, words)

// (* ****** ****** *) // extern fun words_get_beg(words): char extern fun words_get_end(words): char // (* ****** ****** *) // implement words_get_beg(w0) = ( case+ w0 of | Sing(cs) => cs[0] | Comb(w1, w2) => words_get_beg(w1) ) // implement words_get_end(w0) = ( case+ w0 of | Sing(cs) => cs[pred(length(cs))] | Comb(w1, w2) => words_get_end(w2) ) // (* ****** ****** *) // fun words_comb (

 w1: words, w2: words

) : list0(words) =

 if (words_get_end(w1)=words_get_beg(w2))
   then list0_sing(Comb(w1, w2)) else list0_nil()

// (* ****** ****** *) // extern fun fprint_words: fprint_type(words) // overload fprint with fprint_words // implement fprint_words(out, ws) = ( case+ ws of | Sing(w) => fprint(out, w) | Comb(w1, w2) => fprint!(out, w1, ' ', w2) ) // implement fprint_val<words> = fprint_words // (* ****** ****** *) // typedef a = stringGt(0) and b = words // val ws1 =

 $list{a}("this", "that", "a")

val ws1 =

 list_map_fun<a>(ws1, lam(x) => Sing(x))

val ws1 = monad_list_list(list0_of_list_vt(ws1)) // val ws2 =
$list{a}("frog", "elephant", "thing")
val ws2 =
list_map_fun<a>(ws2, lam(x) => Sing(x))
val ws2 = monad_list_list(list0_of_list_vt(ws2)) // val ws3 =
$list{a}("walked", "treaded", "grows")
val ws3 =
list_map_fun<a>(ws3, lam(x) => Sing(x))
val ws3 = monad_list_list(list0_of_list_vt(ws3)) // val ws4 =
$list{a}("slowly", "quickly")
val ws4 =
list_map_fun<a>(ws4, lam(x) => Sing(x))
val ws4 = monad_list_list(list0_of_list_vt(ws4)) // (* ****** ****** *) // val ws12 = monad_bind2<b,b>
(ws1, ws2, lam (w1, w2) => monad_list_list(words_comb(w1, w2)))
val ws123 = monad_bind2<b,b>
(ws12, ws3, lam (w12, w3) => monad_list_list(words_comb(w12, w3)))
val ws1234 = monad_bind2<b,b>
(ws123, ws4, lam (w123, w4) => monad_list_list(words_comb(w123, w4)))
// (* ****** ****** *)
implement main0 () = {
val () = fprintln! (stdout_ref, "ws1234 = ", ws1234)
}
(* ****** ****** *) </lang>
AutoHotkey
Search autohotkey.com: [1]

Source: AMB - Ambiguous selector by infogulch <lang autohotkey>set1 := "the that a" set2 := "frog elephant thing" set3 := "walked treaded grows" set4 := "slowly quickly"
MsgBox % amb( "", set1, set2, set3, set4 )
this takes a total of 17 iterations to complete
amb( char = "", set1 = "", set2 = "", set3 = "", set4 = "" ) { ; original call to amb must leave char param blank
Loop, Parse, set1, %A_Space% If (char = (idxchar := SubStr(A_LoopField, 1, 1)) && set2 = "" || (char = idxchar || char = "") && ((retval:= amb(SubStr(A_LoopField, 0, 1), set2, set3, set4)) != "")) Return A_LoopField " " retval Return ""
}</lang>
Bracmat
<lang bracmat>( ( Amb
= first last list words word solution . !arg:(?first.?list) & ( !list: | !list:(.?words) ?list & !words : ? %( @(?word:!first ? @?last) & Amb$(!last.!list):?solution & !word !solution:?solution ) ? & !solution ) )
& Amb
$ ( . (.the that a) (.frog elephant thing) (.walked treaded grows) (.slowly quickly) )
)</lang>
that thing grows slowly
C
Note: This uses the continuations code from https://web.archive.org/web/20120619201518/http://homepage.mac.com:80/sigfpe/Computing/continuations.html
<lang c>typedef const char * amb_t;
amb_t amb(size_t argc, ...) {
amb_t *choices; va_list ap; int i; if(argc) { choices = malloc(argc*sizeof(amb_t)); va_start(ap, argc); i = 0; do { choices[i] = va_arg(ap, amb_t); } while(++i < argc); va_end(ap); i = 0; do { TRY(choices[i]); } while(++i < argc); free(choices); } FAIL;
}
int joins(const char *left, const char *right) { return left[strlen(left)-1] == right[0]; }
int _main() {
const char *w1,*w2,*w3,*w4; w1 = amb(3, "the", "that", "a"); w2 = amb(3, "frog", "elephant", "thing"); w3 = amb(3, "walked", "treaded", "grows"); w4 = amb(2, "slowly", "quickly"); if(!joins(w1, w2)) amb(0); if(!joins(w2, w3)) amb(0); if(!joins(w3, w4)) amb(0); printf("%s %s %s %s\n", w1, w2, w3, w4); return EXIT_SUCCESS;
}</lang>
C#
The implementation of the Amb class <lang csharp>using System; using System.Collections.Generic;
public class Amb : IDisposable {
List<IValueSet> streams = new List<IValueSet>(); List<IAssertOrAction> assertsOrActions = new List<IAssertOrAction>(); volatile bool stopped = false;
public IAmbValue<T> DefineValues<T>(params T[] values) { return DefineValueSet(values); }
public IAmbValue<T> DefineValueSet<T>(IEnumerable<T> values) { ValueSet<T> stream = new ValueSet<T>(); stream.Enumerable = values; streams.Add(stream); return stream; }
public Amb Assert(Func<bool> function) { assertsOrActions.Add(new AmbAssert() { Level = streams.Count, IsValidFunction = function }); return this; }
public Amb Perform(Action action) { assertsOrActions.Add(new AmbAction() { Level = streams.Count, Action = action }); return this; }
public void Stop() { stopped = true; }
public void Dispose() { RunLevel(0, 0); if (!stopped) { throw new AmbException(); } }
void RunLevel(int level, int actionIndex) { while (actionIndex < assertsOrActions.Count && assertsOrActions[actionIndex].Level <= level) { if (!assertsOrActions[actionIndex].Invoke() || stopped) return; actionIndex++; } if (level < streams.Count) { using (IValueSetIterator iterator = streams[level].CreateIterator()) { while (iterator.MoveNext()) { RunLevel(level + 1, actionIndex); } } } }
interface IValueSet { IValueSetIterator CreateIterator(); }
interface IValueSetIterator : IDisposable { bool MoveNext(); }
interface IAssertOrAction { int Level { get; } bool Invoke(); }
class AmbAssert : IAssertOrAction { internal int Level; internal Func<bool> IsValidFunction;
int IAssertOrAction.Level { get { return Level; } }
bool IAssertOrAction.Invoke() { return IsValidFunction(); } }
class AmbAction : IAssertOrAction { internal int Level; internal Action Action;
int IAssertOrAction.Level { get { return Level; } }
bool IAssertOrAction.Invoke() { Action(); return true; } }
class ValueSet<T> : IValueSet, IAmbValue<T>, IValueSetIterator { internal IEnumerable<T> Enumerable; private IEnumerator<T> enumerator;
public T Value { get { return enumerator.Current; } }
public IValueSetIterator CreateIterator() { enumerator = Enumerable.GetEnumerator(); return this; }
public bool MoveNext() { return enumerator.MoveNext(); }
public void Dispose() { enumerator.Dispose(); } }
}
public interface IAmbValue<T> {
T Value { get; }
}
public class AmbException : Exception {
public AmbException() : base("AMB is angry") { }
}</lang>
Usage: <lang csharp> // original problem
using (Amb amb = new Amb()) { var set1 = amb.DefineValues("the", "that", "a"); var set2 = amb.DefineValues("frog", "elephant", "thing"); var set3 = amb.DefineValues("walked", "treaded", "grows"); var set4 = amb.DefineValues("slowly", "quickly");
amb.Assert(() => IsJoinable(set1.Value, set2.Value)); amb.Assert(() => IsJoinable(set2.Value, set3.Value)); amb.Assert(() => IsJoinable(set3.Value, set4.Value));
amb.Perform(() => { System.Console.WriteLine("{0} {1} {2} {3}", set1.Value, set2.Value, set3.Value, set4.Value); amb.Stop(); }); } // problem from http://www.randomhacks.net/articles/2005/10/11/amb-operator using (Amb amb = new Amb()) { IAmbValue<int> x = amb.DefineValues(1, 2, 3); IAmbValue<int> y = amb.DefineValues(4, 5, 6); amb.Assert(() => x.Value * y.Value == 8); amb.Perform(() => { System.Console.WriteLine("{0} {1}", x.Value, y.Value); amb.Stop(); }); }</lang>
The following is a more idiomatic and not (or less) idiosyncratic C# version of Amb. The above uses a clever but unorthodox use of Dispose() to launch the backtracking (and a few other interesting quirks). Interesting but it can throw an exception in Dispose() which is strongly discouraged in C#.
The following was written independently but borrows some ideas/help from the previous solution. There are still limitations compared to the spirit of Amb, requiring an explicit run (called Disambiguate() normally but RequireFinal() - which calls Disambiguate() internally -is used to get closer to the spirit here) but, compared to many other language solutions here, it does have the explicit Require, meaning it is a general solution, not tied to the specific example in this task.(I suggest the task description is updated to ensure that a general amb operator is provided rather than a custom one for the single provided example). It uses a ToString override to return Value.ToString(), again to help in the spirit of things, but if the variables were used directly, one would have to be use the Value property instead.
Also the internal algorithm allows manual external tuning minimising the verification steps required. This is shown in the ordering of the choices and requirements in the problem to be solved. This, I think, is closer to the spirit of Amb, as defined here, although really this is quite different to McCarthy's class of ambiguous functions.
Works with: C# version 7.1
<lang csharp>using System; using System.Collections.Generic;
namespace Amb {
public interface IValue<T> { T Value { get; } string ToString(); }
public sealed class Amb { public IValue<T> Choose<T>(params T[] choices) { var array = new ChoiceArray<T> { Values = choices }; _itemsChoices.Add(array); return array; }
public void Require(Func<bool> predicate) => _constraints.Add(new Constraint { Predicate = predicate, AppliesForItems = _itemsChoices.Count });
public bool RequireFinal(Func<bool> predicate) { Require(predicate); return Disambiguate(); }
public bool Disambiguate() { try { Disambiguate(0, 0); return false; } catch (Exception ex) when (ex.Message == "Success") { return true; } }
interface IChoices { int Length { get; } int Index { get; set; } }
interface IConstraint { int AppliesForItems { get; } bool Invoke(); }
List<IChoices> _itemsChoices = new List<IChoices>(); List<IConstraint> _constraints = new List<IConstraint>();
void Disambiguate(int itemsTracked, int constraintIndex) { while (constraintIndex < _constraints.Count && _constraints[constraintIndex].AppliesForItems <= itemsTracked) { if (!_constraints[constraintIndex].Invoke()) return; constraintIndex++; }
if (itemsTracked == _itemsChoices.Count) { throw new Exception("Success"); } for (var i = 0; i < _itemsChoices[itemsTracked].Length; i++) { _itemsChoices[itemsTracked].Index = i; Disambiguate(itemsTracked + 1, constraintIndex); } }
class Constraint : IConstraint { internal int AppliesForItems; int IConstraint.AppliesForItems => AppliesForItems;
internal Func<bool> Predicate; public bool Invoke() => Predicate?.Invoke() ?? default; }
class ChoiceArray<T> : IChoices, IValue<T> { internal T[] Values;
public int Index { get; set; }
public T Value { get { return Values[Index]; } }
public int Length => Values.Length;
public override string ToString() => Value.ToString(); } }
}</lang> Usage: <lang csharp>using System.Linq; using static System.Console;
namespace Amb {
class Program { static void Main(string[] args) {
var amb = new Amb();
var set1 = amb.Choose("the", "that", "a"); var set2 = amb.Choose("frog", "elephant", "thing"); amb.Require(() => set1.Value.Last() == set2.Value[0]); var set3 = amb.Choose("walked", "treaded", "grows"); amb.Require(() => set2.Value.Last() == set3.Value[0]); var set4 = amb.Choose("slowly", "quickly"); amb.RequireFinal(() => set3.Value.Last() == set4.Value[0]);
WriteLine($"{set1} {set2} {set3} {set4}"); Read();
// problem from http://www.randomhacks.net/articles/2005/10/11/amb-operator amb = new Amb();
var x = amb.Choose(1, 2, 3); var y = amb.Choose(4, 5, 6); amb.RequireFinal(() => x.Value* y.Value == 8);
WriteLine($"{x} * {y} = 8"); Read(); Read(); } }
}</lang> Output:
that thing grows slowly 2 * 4 = 8
This is a compact solution using Csharp script (.csx) and LINQ query format: <lang csharp> using static System.Console; using System.Linq;
string[] w1 = { "the", "that", "a" }; string[] w2 = { "frog", "elephant", "thing" }; string[] w3 = { "walked", "treaded", "grows" }; string[] w4 = { "slowly", "quickly" };
var result = from a in w1
join b in w2 on a?.LastOrDefault() equals b?.FirstOrDefault() join c in w3 on b?.LastOrDefault() equals c?.FirstOrDefault() join d in w4 on c?.LastOrDefault() equals d?.FirstOrDefault() select new [] {a, b, c, d};
WriteLine(string.Join(" ", result.SelectMany(x => x)));
double[] x = { 1, 2, 3 }; double[] y = { 7, 6, 4, 5 };
var result2 = from a in x
join b in y on a equals 8 / b select new[] { a, b };
WriteLine(string.Join(" ", result2.SelectMany(x => x))); </lang> Output:
that thing grows slowly 2 4
Clojure
<lang clojure>(ns amb
(:use clojure.contrib.monads))
(defn amb [wss]
(let [valid-word (fn [w1 w2] (if (and w1 (= (last w1) (first w2))) (str w1 " " w2)))] (filter #(reduce valid-word %) (with-monad sequence-m (m-seq wss)))))
amb> (amb '(("the" "that" "a") ("frog" "elephant" "thing") ("walked" "treaded" "grows") ("slowly" "quickly"))) (("that" "thing" "grows" "slowly")) </lang>
Common Lisp
Common Lisp lacks the call/cc present in Scheme, and so the straightforward implementation using continuations would require a full-blown code walker (and could still have some issues with dynamically bound variables). A workable compromise uses the condition system and some convenience macros to define amblet a binding construct like let except that if a variable's init-form is of the form (amb {form}*) the amblet's body will be evaluated with the variable bound to successive values produced by each form until some evaluation does not signal an amb-error.
<lang lisp>(define-condition amb-failure () ()
(:report "No amb alternative succeeded."))
(defun invoke-ambiguously (function thunks)
"Call function with successive values produced by successive
functions in thunks until some invocation of function does not signal an amb-failure."
(do ((thunks thunks (rest thunks))) ((endp thunks) (error 'amb-failure)) (let ((argument (funcall (first thunks)))) (handler-case (return (funcall function argument)) (amb-failure ())))))
(defmacro amblet1 ((var form) &body body)
"If form is of the form (amb {form}*) then amblet1 is a convenient
syntax for invoke-ambiguously, by which body is evaluated with var bound the results of each form until some evaluation of body does not signal an amb-failure. For any other form, amblet binds var the result of form, and evaluates body."
(if (and (listp form) (eq (first form) 'amb)) `(invoke-ambiguously #'(lambda (,var) ,@body) (list ,@(loop for amb-form in (rest form) collecting `#'(lambda () ,amb-form)))) `(let ((,var ,form)) ,@body)))
(defmacro amblet (bindings &body body)
"Like let, except that if an init-form is of the form (amb {form}*),
then the corresponding var is bound with amblet1."
(if (endp bindings) `(progn ,@body) `(amblet1 ,(first bindings) (amblet ,(rest bindings) ,@body))))</lang>
Example:
> (flet ((string-adjacent (s1 s2) (char= (char s1 (1- (length s1))) (char s2 0)))) (amblet ((w1 (amb "the" "that" "a")) (w2 (amb "frog" "elephant" "thing")) (w3 (amb "walked" "treaded" "grows")) (w4 (amb "slowly" "quickly"))) (if (and (string-adjacent w1 w2) (string-adjacent w2 w3) (string-adjacent w3 w4)) (list w1 w2 w3 w4) (signal 'amb-failure)))) ("that" "thing" "grows" "slowly")
Macro with dynamic variables
<lang lisp>(defparameter *amb-ops* nil) (defparameter *amb-hist* nil)
(setf *random-state* (make-random-state t)) (defun shuffle (items)
(loop for i from 0 with r = items with l = (length r) while (< i l) do
(rotatef (elt r i) (elt r (+ i (random (- l i))))) finally (return r)))
(assert '(mess in, mess out))
(defmacro amb (a &rest rest)
(let ((f (first rest))
(rest (rest rest)))
(if (not f) `(let ((items (shuffle ,a)))
(let ((y (car (last *amb-hist*))) (o (car (last *amb-ops*)))) (loop for x in items do (if (or (not *amb-ops*) (funcall o y x)) (return (append *amb-hist* (list x)))) (elt items (random (length items))))))
`(let ((items (shuffle ,a)))
(let ((y (car (last *amb-hist*))) (o (car (last *amb-ops*)))) (loop for x in items do (if (or (not *amb-ops*) (funcall o y x)) (let ((*amb-hist* (append *amb-hist* (list x))) (*amb-ops* (append *amb-ops* (list ,f)))) (let ((r ,@rest)) (if r (return r)))))))))))
test cases
(defun joins (a b)
(char= (char a (1- (length a))) (char b 0)))
(defun w34()
(amb '("walked" "treaded" "grows") #'joins (amb '("slowly" "quickly"))))
(print
(amb '("the" "that" "a") #'joins (amb '("frog" "elephant" "thing") #'joins
(w34))))
(print (amb '(1 2 5) #'< (amb '(2 3 4) #'= (amb '(3 4 5))))) ; 1 4 4, 2 3 3, etc</lang>
D
<lang d>import std.stdio, std.array;
/** This amb function takes a comparison function and the possibilities that need to be checked.*/ //string[] amb(in bool function(in string, in string) pure comp, const(string)[] amb(in bool function(in string, in string) pure comp,
in string[][] options, in string prev = null) pure { if (options.empty) return null;
foreach (immutable opt; options.front) { // If this is the base call, prev is null and we need to // continue. if (!prev.empty && !comp(prev, opt)) continue;
// Take care of the case where we have no options left. if (options.length == 1) return [opt];
// Traverse into the tree. const res = amb(comp, options[1 .. $], opt);
// If it was a failure, try the next one. if (!res.empty) return opt ~ res; // We have a match! }
return null; // No matches.
}
void main() {
immutable sets = [["the", "that", "a"], ["frog", "elephant", "thing"], ["walked", "treaded", "grows"], ["slowly", "quickly"]];
// Pass in the comparator and the available sets. // (The comparator is not nothrow because of UTF.) const result = amb((s, t) => s.back == t.front, sets);
if (result.empty) writeln("No matches found!"); else writefln("%-(%s %)", result);
}</lang>

Output:
that thing grows slowly
E

Some lines in this example are too long (more than 80 characters). Please fix the code if it's possible and remove this message.
E does not currently have any kind of backtracking control flow (though there is a proposal in the works to backtrack upon exceptions, for the sake of consistency). However, since (Almost) Everything Is Message Passing, we can create an object which represents a set of possible values.
This is complicated, however, by the fact that any given amb must appear to produce only one result; that is, def x := amb(["a", "b"]); x + x produces aa or bb, not aa,bb,ab,ba as amb(["a", "b"]) + amb(["a", "b"]) would. Therefore, each choice is associated with the decisions which produced it: a map from amb objects to which member of them was chosen; any combination of two ambs discards any combination of choices which have inconsistent decisions.
Note that the choices are not evaluated lazily; this is a breadth-first rather than depth-first search through possibilities. Also, every amb remembers all of the ambs which produced it. As such, this is probably not a practical system for large problems.
<lang e>pragma.enable("accumulator")
def [amb, unamb] := { # block hides internals
def Choice := Tuple[any, Map]
def [ambS, ambU] := <elib:sealing.makeBrand>("amb") var counter := 0 # Used just for printing ambs
/** Check whether two sets of decisions are consistent */ def consistent(decA, decB) { def overlap := decA.domain() & decB.domain() for ambObj in overlap { if (decA[ambObj] != decB[ambObj]) { return false } } return true }
/** From an amb object, extract the possible choices */ def getChoices(obj, decisions) :List[Choice] { if (decisions.maps(obj)) { return [[decisions[obj], decisions]] } else if (ambU.amplify(obj) =~ choices, _) { return accum [] for [chosen, dec] ? (consistent(decisions, dec)) in choices { _ + getChoices(chosen, (decisions | dec).with(obj, chosen)) } } else { return obj, decisions } } /** Construct an amb object with remembered decisions */ def ambDec(choices :List[Choice]) { def serial := (counter += 1) def ambObj { to __printOn(out) { out.print("<amb(", serial, ")") for [chosen, decisions] in choices { out.print(" ", chosen) for k => v in decisions { out.print(";", ambU.amplify(k)[0][1], "=", v) } } out.print(">") } to __optSealedDispatch(brand) { if (brand == ambS.getBrand()) { return ambS.seal([choices, serial]) } } match [verb, args] { var results := [] for [rec, rdec] in getChoices(ambObj, [].asMap()) { def expandArgs(dec, prefix, choosing) { switch (choosing) { match [] { results with= [E.call(rec, verb, prefix), dec] } match [argAmb] + moreArgs { for [arg, adec] in getChoices(argAmb, dec) { expandArgs(adec, prefix.with(arg), moreArgs) } } } } expandArgs(rdec, [], args) } ambDec(results) } } return ambObj } /** Construct an amb object with no remembered decisions. (public interface) */ def amb(choices) { return ambDec(accum [] for c in choices { _.with([c, [].asMap()]) }) }
/** Get the possible results from an amb object, discarding decision info. (public interface) */ def unamb(ambObj) { return accum [] for [c,_] in getChoices(ambObj, [].asMap()) { _.with(c) } } [amb, unamb]
}</lang>
<lang e>def join(a, b) {
# This must not use the builtin if, since it coerces to boolean rather than passing messages. # false.pick(x, y) returns y and true.pick(x, y) returns x; we protect the amb([]) from causing # unconditional failure by putting both options in functions. # <=> is the comparison operator that happens to be message-based. return (a.last() <=> b[0]).pick(fn { a + " " + b }, fn { amb([]) })()
}
def w1 := amb(["the", "that", "a" ]) def w2 := amb(["frog", "elephant", "thing" ]) def w3 := amb(["walked", "treaded", "grows" ]) def w4 := amb(["slowly", "quickly" ])
unamb(join(join(join(w1, w2), w3), w4))</lang>

Comparison with Haskell

This can be compared with the Haskell use of lists as a monad to represent choice.
Haskell uses lazy evaluation; E does not. This implementation does not simulate lazy evaluation with thunks; it is eager (computes every intermediate choice before continuing) and therefore inefficient if you only need one successful result.

Haskell does not need to track decisions. This is because when using a monad in Haskell, the points of choice are explicitly written, either by monadic operators or combinators. The analogues to the two "ab" operations given above are: do x <- ["a","b"]; return (x ++ x) and do x <- ["a","b"]; y <- ["a","b"]; return (x ++ y) — the relevant difference being the number of <- operators. In this implementation, we instead absorb the choice into normal method calls; the Haskell analogue would be something like instance Monoid a => Monoid (Amb a) where Amb ... `mconcat` Amb ... = ..., which would have a similar need to track decisions.
Egison
<lang egison>
We don't need 'amb' in the code since pattern-matching of Egison automatically do backtracking.
(match-all {{"the" "that" "a"} {"frog" "elephant" "thing"} {"walked" "treaded" "grows"} {"slowly" "quickly"}} (list (multiset string))
[<cons <cons (& <snoc $c_1 _> $w_1) _> (loop $i [2 $n] <cons <cons (& <cons ,c_(- i 1) <snoc $c_i _>> $w_i) _> ...> <nil>)> (map (lambda [$i] w_i) (between 1 n))])
</lang>

Output:
<lang egison> Template:"that" "thing" "grows" "slowly" </lang>
Ela

This example is incorrect. Please fix the code and remove this message.
Details: The comparison is hard-coded into amb

<lang ela>open list core
amb xs = x where
(Some x) = & join xs "" join (x::xs) = amb' x (join xs) join [] = \_ -> Some "" eq' [] x = true eq' w x = last w == head x amb' [] _ _ = None amb' (x::xs) n w | eq' w x = match n x with Some v = Some (x ++ " " ++ v) _ = amb' xs n w | else = amb' xs n w</lang>
Usage:
<lang ela>amb [
["the","that","a"] ,["frog","elephant","thing"] ,["walked","treaded","grows"] ,["slowly","quickly"] ]</lang>
Elena
ELENA 5.0 : <lang elena>import system'routines; import extensions; import extensions'routines;
joinable(former,later) = (former[former.Length - 1] == later[0]);
dispatcher = new {
eval(object a, Func2 f) { ^ f(a[0],a[1]) }
eval(object a, Func3 f) { ^ f(a[0], a[1],a[2]) } eval(object a, Func4 f) { ^ f(a[0],a[1],a[2],a[3]) } eval(object a, Func5 f) { ^ f(a[0],a[1],a[2],a[3],a[4]) }
};
class AmbValueCollection {
object theCombinator; constructor new(params object[] args) { theCombinator := SequentialEnumerator.new(params args) }
seek(cond) { theCombinator.reset();
theCombinator.seekEach:(v => dispatcher.eval(v,cond)) } do(f) { var result := theCombinator.get(); if (nil != result) { dispatcher.eval(result,f) } else { InvalidArgumentException.raise() } }
}
singleton ambOperator {
for(params object[] args) = AmbValueCollection.new(params args);
}
public program() {
try { ambOperator .for( new object[]{"the","that","a"}, new object[]{"frog", "elephant", "thing"}, new object[]{"walked", "treaded", "grows"}, new object[]{"slowly", "quickly"}) .seek:(a,b,c,d => joinable(a,b) && joinable(b,c) && joinable(c,d) ) .do:(a,b,c,d) { console.printLine(a," ",b," ",c," ",d) } } catch(Exception e) { console.printLine:"AMB is angry" }; console.readChar()
}</lang>

Output:
that thing grows slowly
ERRE

This example is incorrect. Please fix the code and remove this message.
Details: Conditional is hard-coded into amb

<lang ERRE> PROGRAM AMB
! ! for rosettacode.org !
!$KEY
DIM SET1$[2],SET2$[2],SET3$[2],SET4$[2]
FUNCTION WORDS_OK(STRING1$,STRING2$)
WORDS_OK=(RIGHT$(STRING1$,1)=LEFT$(STRING2$,1))
END FUNCTION
PROCEDURE AMB(SET1$[],SET2$[],SET3$[],SET4$[]->RESULT$)
RESULT$="" ! Empty string, e.g. fail FOR A=0 TO 2 DO FOR B=0 TO 2 DO FOR C=0 TO 2 DO FOR D=0 TO 2 DO IF WORDS_OK(SET1$[A],SET2$[B]) AND WORDS_OK(SET2$[B],SET3$[C]) AND WORDS_OK(SET3$[C],SET4$[D]) THEN RESULT$=SET1$[A]+" "+SET2$[B]+" "+SET3$[C]+" "+SET4$[D] EXIT PROCEDURE END IF END FOR END FOR END FOR END FOR
END PROCEDURE
BEGIN
PRINT(CHR$(12);) ! CLS SET1$[0]="the" SET1$[1]="that" SET1$[2]="a" SET2$[0]="frog" SET2$[1]="elephant" SET2$[2]="thing" SET3$[0]="walked" SET3$[1]="treaded" SET3$[2]="grows" SET4$[0]="slowly" SET4$[1]="quickly" SET4$[2]=""
AMB(SET1$[],SET2$[],SET3$[],SET4$[]->TEXT$) IF TEXT$<>"" THEN PRINT("Correct sentence would be:") PRINT(TEXT$) ELSE PRINT("Failed to fine a correct sentence.") END IF PRINT PRINT("Press any key to exit.") REPEAT GET(Z$) UNTIL LEN(Z$)<>0
END PROGRAM </lang>
F#
Translation of: Haskell
Important differences to the Haskell solution:
The list monad is not predefined in F#. (But it is easy to define it.)

F# is not lazy, so this will check all combinations even if we just want one solution.
Both problems could be addressed by using sequence expressions instead.
<lang fsharp>// define the List "workflow" (monad) type ListBuilder() =
member o.Bind( lst, f ) = List.concat( List.map (fun x -> f x) lst ) member o.Return( x ) = [x] member o.Zero() = []
let list = ListBuilder()
let amb = id
// last element of a sequence let last s = Seq.nth ((Seq.length s) - 1) s
// is the last element of left the same as the first element of right? let joins left right = last left = Seq.head right
let example = list { let! w1 = amb ["the"; "that"; "a"]
let! w2 = amb ["frog"; "elephant"; "thing"] let! w3 = amb ["walked"; "treaded"; "grows"] let! w4 = amb ["slowly"; "quickly"] if joins w1 w2 && joins w2 w3 && joins w3 w4 then return String.concat " " [w1; w2; w3; w4] }
printfn "%s" (List.head example)</lang>
Factor
<lang factor>USING: backtrack continuations kernel prettyprint sequences ; IN: amb
CONSTANT: words {
{ "the" "that" "a" } { "frog" "elephant" "thing" } { "walked" "treaded" "grows" } { "slowly" "quickly" }
}
letters-match? ( str1 str2 -- ? ) [ last ] [ first ] bi* = ;
sentence-match? ( seq -- ? ) dup rest [ letters-match? ] 2all? ;
select ( seq -- seq' ) [ amb-lazy ] map ;
search ( -- )
words select dup sentence-match? [ " " join ] [ fail ] if . ;
MAIN: search</lang>
Running it from the listener :
( scratchpad ) "amb" run "that thing grows slowly"
Go
Solution with goroutines. See description on talk page. <lang go>package main
import (
"fmt" "sync"
)
func ambStrings(ss []string) chan []string {
c := make(chan []string) go func() { for _, s := range ss { c <- []string{s} } close(c) }() return c
}
func ambChain(ss []string, cIn chan []string) chan []string {
cOut := make(chan []string) go func() { var w sync.WaitGroup for chain := range cIn { w.Add(1) go func(chain []string) { for s1 := range ambStrings(ss) { if s1[0][len(s1[0])-1] == chain[0][0] { cOut <- append(s1, chain...) } } w.Done() }(chain) } w.Wait() close(cOut) }() return cOut
}
func main() {
s1 := []string{"the", "that", "a"} s2 := []string{"frog", "elephant", "thing"} s3 := []string{"walked", "treaded", "grows"} s4 := []string{"slowly", "quickly"} c := ambChain(s1, ambChain(s2, ambChain(s3, ambStrings(s4)))) for s := range c { fmt.Println(s) }
}</lang>

Output:
[that thing grows slowly]
Alternative solution: <lang go>package main import "fmt"
func amb(wordsets [][]string, res []string) bool { if len(wordsets) == 0 { return true }
var s string
l := len(res) if l > 0 { s = res[l - 1] }
res = res[0:len(res) + 1]
for _, res[l] = range(wordsets[0]) { if l > 0 && s[len(s) - 1] != res[l][0] { continue }
if amb(wordsets[1:len(wordsets)], res) { return true } }
return false }
func main() { wordset := [][]string { { "the", "that", "a" }, { "frog", "elephant", "thing" }, { "walked", "treaded", "grows" }, { "slowly", "quickly" } } res := make([]string, len(wordset))
if amb(wordset, res[0:0]) { fmt.Println(res) } else { fmt.Println("No amb found") } }</lang>
Haskell
Haskell's List monad returns all the possible choices. Use the "head" function on the result if you just want one. <lang haskell>import Control.Monad
amb = id
joins left right = last left == head right
example = do
w1 <- amb ["the", "that", "a"] w2 <- amb ["frog", "elephant", "thing"] w3 <- amb ["walked", "treaded", "grows"] w4 <- amb ["slowly", "quickly"] guard (w1 `joins` w2) guard (w2 `joins` w3) guard (w3 `joins` w4) pure $ unwords [w1, w2, w3, w4]
</lang>
Note that "amb" is defined as a no-op and is written only to help show the analogy with other implementations; ordinary style is to write e.g. w1 <- ["the", "that", "a"].
It may also be illuminating to show how this desugars (dropping the do notation) if we express it directly in terms of the list monad bind function (>>=) (or >>= without brackets as in infix operator), which is possibly more familiar (or more directly intelligible) as concatMap with its arguments flipped.
The function of amb can then be seen in the return of a list of bound values, if a predicate is matched, or the return of an empty list, if the predicate fails:
<lang haskell>joins :: String -> String -> Bool joins left right = last left == head right
-- First desugaring (dropping the do notation) -- in terms of the bind operator (>>=) for the list monad
exampleBind :: String exampleBind =
["the", "that", "a"] >>= (\w1 -> ["frog", "elephant", "thing"] >>= \w2 -> ["walked", "treaded", "grows"] >>= \w3 -> ["slowly", "quickly"] >>= (\w4 -> if joins w1 w2 then (if joins w2 w3 then (if joins w3 w4 then unwords [w1, w2, w3, w4] else []) else []) else []))
-- Second desugaring (still dropping the do notation) -- in terms of the concatMap, which is >>= with its arguments flipped
exampleConcatMap :: String exampleConcatMap =
concatMap (\w1 -> concatMap (\w2 -> concatMap (\w3 -> concatMap (\w4 -> if joins w1 w2 then (if joins w2 w3 then (if joins w3 w4 then unwords [w1, w2, w3, w4] else []) else []) else []) ["slowly", "quickly"]) ["walked", "treaded", "grows"]) ["frog", "elephant", "thing"]) ["the", "that", "a"]
main :: IO () main = do
print exampleBind print exampleConcatMap</lang>

Output:
"that thing grows slowly" "that thing grows slowly"
Or, immediately pairing each indeterminate value with a predicate (rather concluding with a compound predicate). <lang haskell>example :: [String] example =
["the", "that", "a"] >>= \w1 -> when True ["frog", "elephant", "thing"] >>= \w2 -> when (joins w1 w2) ["walked", "treaded", "grows"] >>= \w3 -> when (joins w2 w3) ["slowly", "quickly"] >>= \w4 -> when (joins w3 w4) [w1, w2, w3, w4]
joins :: String -> String -> Bool joins left right = last left == head right
when :: Bool -> [a] -> [a] when p xs =
if p then xs else []
main :: IO () main = print $ unwords example</lang>
"that thing grows slowly"

And a familar resugaring of a list monad wrapping of indeterminate values and constraints is, of course, the list comprehension notation, which has a semantics directly equivalent to that of amb tuples and contraints, and provides quite a clean and natural notation for their expression.
<lang haskell>joins :: String -> String -> Bool joins left right = last left == head right
example :: [String] example =
[ unwords [w1, w2, w3, w4] | w1 <- ["the", "that", "a"] , w2 <- ["frog", "elephant", "thing"] , w3 <- ["walked", "treaded", "grows"] , w4 <- ["slowly", "quickly"] , joins w1 w2 , joins w2 w3 , joins w3 w4 ]
main :: IO () main = print example</lang>

Output:
["that thing grows slowly"]
Haxe
<lang haxe>class RosettaDemo { static var setA = ['the', 'that', 'a']; static var setB = ['frog', 'elephant', 'thing']; static var setC = ['walked', 'treaded', 'grows']; static var setD = ['slowly', 'quickly'];
static public function main() { Sys.print(ambParse([ setA, setB, setC, setD ]).toString()); }
static function ambParse(sets : Array<Array<String>>) { var ambData : Dynamic = amb(sets);
for (data in 0...ambData.length) { var tmpData = parseIt(ambData[data]); var tmpArray = tmpData.split(' '); tmpArray.pop(); if (tmpArray.length == sets.length) { return tmpData; } }
return ; }
static function amb(startingWith : String = , sets : Array<Array<String>>) : Dynamic { if (sets.length == 0 || sets[0].length == 0) return;
var match : Dynamic = []; for (reference in sets[0]) { if (startingWith == || startingWith == reference.charAt(0)) { var lastChar = reference.charAt(reference.length-1); if (Std.is(amb(lastChar, sets.slice(1)), Array)) { match.push([ reference, amb(lastChar, sets.slice(1))]); } else { match.push([ reference ]); } } } return match; }
static function parseIt(data : Dynamic) { var retData = ; if (Std.is(data, Array)) { for (elements in 0...data.length) { if (Std.is(data[elements], Array)) { retData = retData + parseIt(data[elements]); } else { retData = retData + data[elements] + ' '; } } } return retData; } }</lang>
Icon and Unicon
<lang icon>procedure main()
s1 := ["the","that","a"] s2 := ["frog","elephant","thing"] s3 := ["walked","treaded","grows"] s4 := ["slowly","quickly"]
write(amb(!s1,!s2,!s3,!s4))
end
procedure amb(exprs[])
s := "" every e := !exprs do { if \c ~== e[1] then fail c := e[-1] s ||:= e || " " } return s
end</lang>
J
<lang j> amb=. ([ , ' ' , ])&>/&.>@:((({:@:[ = {.@:])&>/&> # ])@:,@:({@(,&<)))
>@(amb&.>/) ('the';'that';'a');('frog';'elephant';'thing');('walked';'treaded';'grows');(<'slowly';'quickly')
+-----------------------+ |that thing grows slowly| +-----------------------+</lang> amb is a dyadic verb: <lang j> ('the';'that';'a') amb ('frog';'elephant';'thing') amb ('walked';'treaded';'grows') amb ('slowly';'quickly') +-----------------------+ |that thing grows slowly| +-----------------------+</lang> A structured derivation of amb follows: <lang j> NB. Dynamic programming method...
o=. @: NB. Composing verbs success=. {:o[ = {.o] NB. Is the last letter of the left word equal to the first of the right? join=. [ , ' ' , ] NB. Joining the left and right words cp=. {@(,&<) NB. Cartesian product amb=. join&>/&.> o ((success&>/ &> # ]) o , o cp)f. amb NB. Showing the point-free code...
([ , ' ' , ])&>/&.>@:((({:@:[ = {.@:])&>/&> # ])@:,@:({@(,&<)))</lang>
Note that amb here is roughly equivalent to the Ambassert in the task description, and that the corresponding Ambsel is unnecessary and trivial (if needed, we could define Ambsel as the identity operation and make these examples slightly more verbose). However, this implementation should be refactored to extract the example logic from the implementation of amb (or you can do as was apparently suggested here, and use the definition of amb instead of the word - replacing success as needed).
JavaScript
Procedural
<lang javascript>function ambRun(func) {
var choices = []; var index;
function amb(values) { if (values.length == 0) { fail(); } if (index == choices.length) { choices.push({i: 0, count: values.length}); } var choice = choices[index++]; return values[choice.i]; }
function fail() { throw fail; }
while (true) { try { index = 0; return func(amb, fail); } catch (e) { if (e != fail) { throw e; } var choice; while ((choice = choices.pop()) && ++choice.i == choice.count) {} if (choice == undefined) { return undefined; } choices.push(choice); } }
}
ambRun(function(amb, fail) {
function linked(s1, s2) { return s1.slice(-1) == s2.slice(0, 1); }
var w1 = amb(["the", "that", "a"]); var w2 = amb(["frog", "elephant", "thing"]); if (!linked(w1, w2)) fail();
var w3 = amb(["walked", "treaded", "grows"]); if (!linked(w2, w3)) fail();
var w4 = amb(["slowly", "quickly"]); if (!linked(w3, w4)) fail();
return [w1, w2, w3, w4].join(' ');
}); // "that thing grows slowly"</lang>
Functional
Defining amb as the list monad bind/inject operator:
<lang javascript>(() => {
'use strict';
// amb :: [a] -> (a -> [b]) -> [b] const amb = xs => f => xs.reduce((a, x) => a.concat(f(x)), []);
// when :: Bool -> [a] -> [a] const when = p => xs => p ? ( xs ) : [];

// TEST ----------------------------------------------- const main = () => {
// joins :: String -> String -> Bool const joins = (a, b) => b[0] === last(a);
console.log( amb(['the', 'that', 'a']) (w1 => when(true)(
amb(['frog', 'elephant', 'thing']) (w2 => when(joins(w1, w2))(
amb(['walked', 'treaded', 'grows']) (w3 => when(joins(w2, w3))(
amb(['slowly', 'quickly']) (w4 => when(joins(w3, w4))(
unwords([w1, w2, w3, w4])
)) )) )) )) ); };
// GENERIC FUNCTIONS ----------------------------------
// last :: [a] -> a const last = xs => 0 < xs.length ? xs.slice(-1)[0] : undefined;
// unwords :: [String] -> String const unwords = xs => xs.join(' ');
// MAIN --- return main();
})();</lang>

Output:
that thing grows slowly
jq
Works with: jq version 1.4
Two solutions are given. The first follows the style of the Prolog example. The second perhaps hews more closely to the intended specification of "amb".
Solution using amb/0 <lang jq>def amb: .[];
def joins:
(.[0][-1:]) as $left | (.[1][0:1]) as $right | if $left == $right then true else empty end; </lang>
Example: <lang jq>(["the","that","a"] | amb) as $word1
| (["frog","elephant","thing"] | amb) as $word2 | [$word1, $word2] | joins | (["walked","treaded","grows"] | amb) as $word3 | [$word2, $word3] | joins | (["slowly","quickly"] | amb) as $word4 | [$word3, $word4] | joins | [$word1, $word2, $word3, $word4]</lang>

Output:
<lang sh>jq -n -f amb.jq [
"that", "thing", "grows", "slowly"
]</lang> Solution using amb(condition): <lang jq>def amb(condition): .[] | select(condition);
def joins:
(.[0][-1:]) as $left | (.[1][0:1]) as $right | $left == $right ;</lang>
Example: <lang jq>(["the","that","a"] | amb(true)) as $word1
| (["frog","elephant","thing"] | amb( [$word1, .] | joins)) as $word2 | (["walked","treaded","grows"] | amb( [$word2, .] | joins)) as $word3 | (["slowly","quickly"] | amb( [$word3, .] | joins)) as $word4 | [$word1, $word2,$word3, $word4]</lang>

Output:
As above.
Julia
<lang Julia># This is a general purpose AMB function that takes a two-argument failure function and
arbitrary number of iterable objects and returns the first solution found as an array

this function is in essence an iterative backtracking solver
function amb(failure, itrs...)
n = length(itrs) if n == 1 return end states = Vector(n) values = Vector(n) # starting point, we put down the first value from the first iterable object states[1] = start(itrs[1]) values[1], states[1] = next(itrs[1], states[1]) i = 1 # main solver loop while true # test for failure if i > 1 && failure(values[i-1], values[i]) # loop for generating a new value upon failure # in fact this would be way more readable using goto, but Julia doesn't seem to have that :( while true # if we failed, we must generate a new value, but first we must check whether there is any if done(itrs[i], states[i]) # backtracking step with sanity check in case we ran out of values from the current generator if i == 1 return else i -= 1 continue end else # if there is indeed a new value, generate it values[i], states[i] = next(itrs[i], states[i]) break end end else # no failure branch # if solution is ready (i.e. all generators are used) just return it if i == n return values end # else start up the next generator i += 1 states[i] = start(itrs[i]) values[i], states[i] = next(itrs[i], states[i]) end end
end
Call our generic AMB function according to the task description and

form the solution sentence from the returned array of words
amb((s1,s2) -> s1[end] != s2[1], # failure function
["the", "that", "a"], ["frog", "elephant", "thing"], ["walked", "treaded", "grows"], ["slowly", "quickly"]) |> x -> join(x, " ") |> println
</lang>
Kotlin
This solves the problem using backtracking whenever amb() is executed. amb will probably have unexpected behavior if any variables are mutated. Using simple assignment for variables shouldn't be a problem.
<lang scala>// version 1.2.41 import kotlin.coroutines.experimental.* import kotlin.coroutines.experimental.intrinsics.*
fun main(args: Array<String>) = amb {
val a = amb("the", "that", "a") val b = amb("frog", "elephant", "thing") val c = amb("walked", "treaded", "grows") val d = amb("slowly", "quickly") if (a[a.lastIndex] != b[0]) amb() if (b[b.lastIndex] != c[0]) amb() if (c[c.lastIndex] != d[0]) amb() println(listOf(a, b, c, d)) val x = amb(1, 2, 3) val y = amb(7, 6, 4, 5) if (x * y != 8) amb() println(listOf(x, y))
}

class AmbException(): Exception("Refusing to execute") data class AmbPair<T>(val cont: Continuation<T>, val valuesLeft: MutableList<T>)
@RestrictsSuspension class AmbEnvironment {
val ambList = mutableListOf<AmbPair<*>>() suspend fun <T> amb(value: T, vararg rest: T): T = suspendCoroutineOrReturn { cont -> if (rest.size > 0) { ambList.add(AmbPair(clone(cont), mutableListOf(*rest))) } value } suspend fun amb(): Nothing = suspendCoroutine<Nothing> { }
}
@Suppress("UNCHECKED_CAST") fun <R> amb(block: suspend AmbEnvironment.() -> R): R {
var result: R? = null var toThrow: Throwable? = null val dist = AmbEnvironment() block.startCoroutine(receiver = dist, completion = object : Continuation<R> { override val context: CoroutineContext get() = EmptyCoroutineContext override fun resume(value: R) { result = value } override fun resumeWithException(exception: Throwable) { toThrow = exception } }) while (result == null && toThrow == null && !dist.ambList.isEmpty()) { val last = dist.ambList.run { this[lastIndex] } if (last.valuesLeft.size == 1) { dist.ambList.removeAt(dist.ambList.lastIndex) last.apply { (cont as Continuation<Any?>).resume(valuesLeft[0]) } } else { val value = last.valuesLeft.removeAt(last.valuesLeft.lastIndex) (clone(last.cont) as Continuation<Any?>).resume(value) } } if (toThrow != null) { throw toThrow!! } else if (result != null) { return result!! } else { throw AmbException() }
}
val UNSAFE = Class.forName("sun.misc.Unsafe")
.getDeclaredField("theUnsafe") .apply { isAccessible = true } .get(null) as sun.misc.Unsafe
@Suppress("UNCHECKED_CAST") fun <T: Any> clone(obj: T): T {
val clazz = obj::class.java val copy = UNSAFE.allocateInstance(clazz) as T copyDeclaredFields(obj, copy, clazz) return copy
}
tailrec fun <T> copyDeclaredFields(obj: T, copy: T, clazz: Class<out T>) {
for (field in clazz.declaredFields) { field.isAccessible = true val v = field.get(obj) field.set(copy, if (v === obj) copy else v) } val superclass = clazz.superclass if (superclass != null) copyDeclaredFields(obj, copy, superclass)
}</lang>

Output:
[that, thing, grows, slowly] [2, 4]
langur
Works with: langur version 0.8.11
This would build every valid set, but for the sample data, there's only one.
<lang langur>val .wordsets = [
w/the that a/, w/frog elephant thing/, w/walked treaded grows/, w/slowly quickly/,
]
val .alljoin = f(.words) for[=true] .i of len(.words)-1 {
if last(.words[.i]) != first(.words[.i+1]): break = false
}
.amb expects 2 or more arguments
val .amb = f(...[2 to -1] .words) if(.alljoin(.words): join " ", .words)
writeln join "\n", where(mapX(.amb, .wordsets...))</lang>

Output:
that thing grows slowly
Latitude
Latitude supports callCC natively, so `amb` can be implemented in a relatively straightforward fashion in terms of continuations.
<lang latitude>;; This is the exception that will be thrown if an amb expression is
unsatisfiable.
AmbError ::= Exception clone tap {
self message := "Amb expression failed".
AmbError := self.
}.
The Amb object itself is primarily for internal use. It stores the

"next" backtracking point if an amb expression outright fails or

exhausts its possibilities at some point.
Amb ::= Object clone tap {
;; The default "next" point is to throw an exception. This will be ;; overridden in many cases, if there is an actual next handler to ;; jump to. self nextHandler := { AmbError clone throw. }.
Amb := self.
}.
callAmb := {
;; We need an object which will be accessible from inside the ;; continuations that will store the next backtracking point which ;; will be called. backtracker := Amb clone. ;; We define the dynamically-scoped method $amb which will try each ;; possibility that it is given. If all of those possibilities fail, ;; it will call the next handler. $amb := { takes '[cases]. ;; This is the return point. We're going to try each element of ;; the cases variable (probably an array, but it could feasibly be ;; any collection type). For each element, we'll jump to this ;; point (which will wind up being the end of the $amb method). If ;; it ends up failing, the backtrack point will get called and ;; we'll try the next one. callCC { escapable. ;; Get the current backtrack point from the toplevel object and ;; store it within this continuation. The backtrack object's ;; current backtrack point will change as we make new attempts, ;; but this prevHandler variable is stored locally in this scope ;; and will not change, so we can always use it later. prevHandler := #'(backtracker nextHandler). ;; We iterate over the collection to try each element. cases visit { takes '[curr]. callCC { ;; This inner continuation will be our new backtrack point. ;; We store the continuation object itself in the backtrack ;; object so that future $amb calls know to return to this ;; point if something goes wrong. nextExit := #'$1. backtracker nextHandler := { nextExit call (Nil). }. ;; Now we actually try the value by jumping to the end of ;; the $amb method and returning control to the caller. return (curr). }. }. ;; If we exhaust each possibility, then that means every value ;; in the cases variable has been tried and has failed. So we ;; set the backtrack point back to what it was before we tried ;; all of these values, and then we jump back to that previous ;; backtrack point. backtracker nextHandler := #'(prevHandler). prevHandler. ;; prevHandler will always either perform a continuation jump ;; (if there is a new backtrack point to try) or throw an ;; exception (if we've exhausted all possibilities), so this ;; continuation block will never exit normally. }. }. ;; An instant failure at a point in an amb expression is equivalent ;; to an $amb call on an empty collection. $fail := { $amb (Nil). }. ;; Now that the dynamic variables are in place, let's call the ;; block. #'($1) call.
}.</lang>
Now, we can use this new method as follows.
<lang latitude>callAmb {
x := $amb [1, 2, 3, 4]. y := $amb [7, 6, 4, 5]. (x * y == 8 ) ifFalse { $fail. }. ;; Note: $fail is equivalent to $amb []. println [x, y]. ;; [2, 4]
}.</lang>
In the above implementation, $amb is a local construct which operates inside a callAmb block. We could just as easily have used a global Amb instance and forgone the callAmb block.
Lua
<lang lua>function amb (set)
local workset = {} if (#set == 0) or (type(set) ~= 'table') then return end if #set == 1 then return set end if #set > 2 then local first = table.remove(set,1) set = amb(set) for i,v in next,first do for j,u in next,set do if v:byte(#v) == u[1]:byte(1) then table.insert(workset, {v,unpack(u)}) end end end return workset end for i,v in next,set[1] do for j,u in next,set[2] do if v:byte(#v) == u:byte(1) then table.insert(workset,{v,u}) end end end return workset
end</lang> Usage example: <lang lua>result = amb({{'the','that','a'},{'frog','elephant','thing'},{'walked','treaded','grows'},{'slowly','quickly'}}) for i,v in next,result do
io.write (i,':\t') for j,u in next,v do io.write (u,' ') end io.write ('\n')
end</lang>
Mathematica / Wolfram Language
Make all the tuples of all the lists, then filter out the good ones: <lang Mathematica> CheckValid[i_List]:=If[Length[i]<=1,True,And@@(StringTake[#1,-1]==StringTake[#2,1]&/@Partition[i,2,1])]
sets={{"the","that","a"},{"frog","elephant","thing"},{"walked","treaded","grows"},{"slowly","quickly"}}; Select[Tuples[sets],CheckValid]</lang>
gives back: <lang Mathematica>Template:"that", "thing", "grows", "slowly"</lang> Note that it will return multiple values if multiple sentences match the requirement, that is why the returned value is a list of list (1 element, 4 elements).
Alternative algorithm (slightly faster on most data sets): <lang Mathematica>CheckValid2[i_List] := StringFreeQ[StringJoin[Riffle[i, ","]], a_ ~~ "," ~~ b_ /; a =!= b]</lang>
Mercury
Like Prolog, Mercury has built-in nondeterminacy; however, Mercury is explicit about it, and statically checks it.
<lang Mercury>:- module amb.
- interface.

- import_module io.

- pred main(io::di, io::uo) is cc_multi.

- implementation.

- import_module list, string, char, int.
main(!IO) :-
( solution(S) -> io.write_string(S, !IO), io.nl(!IO) ; io.write_string("No solutions found :-(\n", !IO) ).
- pred solution(string::out) is nondet.
solution(S) :-
member(A, ["the", "that", "a"]), member(N, ["frog", "elephant", "thing"]), member(V, ["walked", "treaded", "grows"]), member(E, ["slowly", "quickly"]), S = join_list(" ", [A, N, V, E]), rule1(A, N), rule1(N, V), rule1(V, E).
- pred rule1(string::in, string::in) is semidet.
rule1(A, B) :- last_char(A) = C, first_char(B, C, _).
- func last_char(string::in) = (char::out) is semidet.
last_char(S) = C :- index(S, length(S) - 1, C).</lang>
The Amb defined in the Prolog solution is similar to the use of list.member/2 above. Predicates could be used instead:
<lang Mercury>
- pred noun(string).

- mode noun(out) is multi. % provide any one noun.

- mode noun(in) is semidet. % fail if given string isn't a known noun.
noun("frog"). noun("elephant"). noun("thing").</lang>
NetRexx
<lang netrexx> /* REXX **************************************************************
* 25.08.2013 Walter Pachl derived from REXX version 2 *********************************************************************/ w= l=0 mm=0 mkset(1,'the that a if',w,mm,l) mkset(2,'frog elephant thing',w,mm,l) mkset(3,'walked treaded grows trots',w,mm,l) mkset(4,'slowly quickly',w,mm,l) show(w,mm,l)
Loop i=1 to 3 /* loop over sets */ k=i+1 /* the following set */ Loop ii=1 To 10 /* loop over elements in set k*/ If w[i,ii].words=i Then Do /* a sentence part found */ Loop jj=1 To 10 /* loop over following words */ If w[i,ii].right(1)=w[k,jj].left(1) Then Do /* fitting */ ns=w[i,ii]' 'w[k,jj] /* build new sentence (part) */ If ns.words=k Then /* 'complete' part */ add(w,k,ns) /* add to set k */ End End End End End Say 'Results:' Loop jj=1 To 10 /* show the results */ If w[4,jj].words=4 Then Say '-->' w[4,jj] End
method add(w,k,s) public static /********************************************************************* * add a fitting sentence (part) s to set w[k,*] *********************************************************************/ Loop i=1 To 10 While w[k,i]> /* look for an empty slot */ End w[k,i]=s /* add the sentence (part) */ Return
method mkset(n,arg,smp,mm,l) public static /********************************************************************* * create set smp[n,*] from data in arg * mm[0] maximum number of elements in any set * l[n] maximum word length in set n *********************************************************************/ loop i = 1 to arg.words smp[n,i] = arg.word(i) If smp[n,i].length>l[n] Then l[n]=smp[n,i].length end if i-1>mm[0] Then Do mm[0]=i-1 End return
method show(w,mm,l) public static /********************************************************************* * show the input *********************************************************************/ Say 'Input:' Loop j=1 To mm[0] /* output lines */ ol= Loop i=1 To 4 ol=ol w[i,j].left(l[i]) End Say ol.strip End; say Return</lang>

Output:
Input: the frog walked slowly that elephant treaded quickly a thing grows if trots Results: --> the elephant trots slowly --> that thing grows slowly --> if frog grows slowly
Note: the output of the input is truncated (columns three and four), but the results are correct for the data specified, but not for the input as specified for this task (ditto for the PL/I example and the REXX version 2 example).
length corrected. thanks. extraneous input: intentional and harmless !?!
This Rosetta Code task said: demonstrate it with a program which chooses one word from each of the following four sets,
and instead, used a different set (causing a different result).
Nim
Translation of: D
<lang nim>import future, strutils
proc amb(comp: proc(a, b: string): bool, options: seq[seq[string]],
prev: string = nil): seq[string] = if options.len == 0: return @[]
for opt in options[0]: # If this is the base call, prev is nil and we need to continue. if prev != nil and not comp(prev, opt): continue
# Take care of the case where we have no options left. if options.len == 1: return @[opt]
# Traverse into the tree. let res = amb(comp, options[1..options.high], opt)
# If it was a failure, try the next one. if res.len > 0: return opt & res # We have a match
return @[]
const sets = @[@["the", "that", "a"],
@["frog", "elephant", "thing"], @["walked", "treaded", "grows"], @["slowly", "quickly"]]
let result = amb((s, t: string) => (s[s.high] == t[0]), sets) if result.len == 0:
echo "No matches found!"
else:
echo result.join " "</lang>

Output:
that thing grows slowly
OCaml
There is no Amb operator in OCaml. So below are two solutions to solve the same task. The first one is the more idiomatic for OCaml (and is similar to the Haskell solution), it builds all possible combinations and then take the good result in it.
The second solution tries to be closer to the way of solving the problem of Amb. It does not build and accumulate the combinations, it iterates over these with a higher order function and it stops when it finds a solution that matches the predicate.
Filtering possible combinations
<lang ocaml>let set_1 = ["the"; "that"; "a"] let set_2 = ["frog"; "elephant"; "thing"] let set_3 = ["walked"; "treaded"; "grows"] let set_4 = ["slowly"; "quickly"]
let combs ll =
let rec aux acc = function | [] -> (List.map List.rev acc) | hd::tl -> let acc = List.fold_left (fun _ac l -> List.fold_left (fun _ac v -> (v::l)::_ac) _ac hd ) [] acc in aux acc tl in aux [[]] ll
let last s = s.[pred(String.length s)] let joined a b = (last a = b.[0])
let rec test = function
| a::b::tl -> (joined a b) && (test (b::tl)) | _ -> true
let print_set set =
List.iter (Printf.printf " %s") set; print_newline();

let () =
let sets = combs [set_1; set_2; set_3; set_4] in let sets = List.filter test sets in List.iter print_set sets;
</lang>
We can take all the good results with List.filter or just take the first one with List.find.
Higher order function
Here the function comb_search replaces the function combs and uses arrays instead of lists. This function takes successively all the possible results by their indicies (with the array nx). When a result satisfies the predicate p, it is returned
<lang ocaml>let set_1 = [| "the"; "that"; "a" |] let set_2 = [| "frog"; "elephant"; "thing" |] let set_3 = [| "walked"; "treaded"; "grows" |] let set_4 = [| "slowly"; "quickly" |]
let comb_search p aa =
let nx = Array.make (Array.length aa) 0 in let lx = Array.map Array.length aa in let la = Array.length aa in let rec loop() = let res = Array.mapi (fun i j -> aa.(i).(j)) nx in if p res then (res) else ( nx.(0) <- nx.(0) + 1; if nx.(0) < lx.(0) then loop() else ( nx.(0) <- 0; let rec roll n = if n >= la then raise Not_found else ( nx.(n) <- nx.(n) + 1; if nx.(n) >= lx.(n) then ( nx.(n) <- 0; roll (n+1) ) else loop() ) in roll 1 ) ) in loop()
let last s = s.[pred(String.length s)] let joined a b = (last a = b.[0])
let rec test = function
| a::b::tl -> (joined a b) && (test (b::tl)) | _ -> true
let test r = test(Array.to_list r)
let print_set set =
Array.iter (Printf.printf " %s") set; print_newline();

let () =
let result = comb_search test [| set_1; set_2; set_3; set_4 |] in print_set result;
</lang>
OpenEdge/Progress
<lang OpenEdge/Progress>DEF VAR cset AS CHAR EXTENT 4 INIT [
"the,that,a", "frog,elephant,thing", "walked,treaded,grows", "slowly,quickly"
].
FUNCTION getAmb RETURNS CHARACTER (
i_cwords AS CHAR, i_iset AS INT
):
DEF VAR cresult AS CHAR. DEF VAR ii AS INT. DEF VAR cword AS CHAR.
DO ii = 1 TO NUM-ENTRIES( cset [ i_iset ] ) WHILE NUM-ENTRIES( cresult, " " ) < EXTENT( cset ):
cword = ENTRY( ii, cset[ i_iset ] ). IF i_cwords = "" OR SUBSTRING( i_cwords, LENGTH( i_cwords ), 1 ) = SUBSTRING( cword, 1, 1 ) THEN DO: IF i_iset = EXTENT ( cset ) THEN cresult = i_cwords + " " + cword. ELSE cresult = getAmb( i_cwords + " " + cword, i_iset + 1 ). END.
END.
RETURN cresult.
END FUNCTION. /* getAmb */

MESSAGE getAmb( "", 1 ) VIEW-AS ALERT-BOX.</lang>

Output:
--------------------------- Message --------------------------- that thing grows slowly --------------------------- OK ---------------------------
Oz
Oz is, among other things, a logic programming language and has a choice operator. Using recursion we can easily build an Amb operator with it. <lang oz>declare
fun {Amb Xs} case Xs of nil then fail [] [X] then X [] X|Xr then choice X [] {Amb Xr} end end end
fun {Example} W1 = {Amb ["the" "that" "a"]} W2 = {Amb ["frog" "elephant" "thing"]} W3 = {Amb ["walked" "treaded" "grows"]} W4 = {Amb ["slowly" "quickly"]} in {List.last W1 W2.1} {List.last W2 W3.1} {List.last W3 W4.1} W1#" "#W2#" "#W3#" "#W4 end
in
{ForAll {SearchAll Example} System.showInfo}</lang>
In Oz, the programmer explicitly controls how a logic program is executed (search strategy, number of required solutions, laziness, which physical machines are used for the search process...). In this case we use the predefined function SearchAll to eagerly calculate all possible solution. All work is done within the current process.
PARI/GP
<lang parigp>Amb(V)={ amb(vector(#V,i,vector(#V[i],j,Vec(V[i][j]))),[]) }; amb(V,s)={ if (#V == 0, return(concat(s))); my(v=V[1],U=vecextract(V,2^#V-2),t,final=if(#s,s[#s])); if(#s, s = concat(s,[" "])); for(i=1,#v, if ((#s == 0 | final == v[i][1]), t = amb(U, concat(s, v[i])); if (t, return(t)) ) ); 0 }; Amb([["the","that","a"],["frog","elephant","thing"],["walked","treaded","grows"],["slowly","quickly"]])</lang>
Perl
Using fork
This first Perl implementation of the amb operator provides an interface which satisfies the terms of the task precisely. It shouldn't be used in real code though, unless you know for a fact that the computer you are using it on has a very lightweight fork() system call.
It is provided here simply to demonstrate that it can be done.
<lang perl>use strict; use warnings;
use constant EXIT_FAILURE => 1; use constant EXIT_SUCCESS => 0;
sub amb {
exit(EXIT_FAILURE) if !@_; for my $word (@_) { my $pid = fork; die $! unless defined $pid; return $word if !$pid; my $wpid = waitpid $pid, 0; die $! unless $wpid == $pid; exit(EXIT_SUCCESS) if $? == EXIT_SUCCESS; } exit(EXIT_FAILURE);
}
sub joined {
my ($join_a, $join_b) = @_; substr($join_a, -1) eq substr($join_b, 0, 1);
}
my $w1 = amb(qw(the that a)); my $w2 = amb(qw(frog elephant thing)); my $w3 = amb(qw(walked treaded grows)); my $w4 = amb(qw(slowly quickly));
amb() unless joined $w1, $w2; amb() unless joined $w2, $w3; amb() unless joined $w3, $w4;
print "$w1 $w2 $w3 $w4\n"; exit(EXIT_SUCCESS);</lang>
Using the regex engine
This version also stays relatively true to the spirit of the task description. The amb routine in this case generates regex alternations, which are then dynamically interpolated into a regex and iterated/backtracked over by the regex engine. Please note that this approach only works well for simple search problems; for more demanding ones it scales quite badly in both speed and memory usage.
<lang perl>#!/usr/bin/perl
use strict; use warnings; use feature 'say'; use re 'eval';
sub amb ($@) {
my $var = shift; join ' || ', map { "(?{ $var = '$_' })" } @_;
}
sub joins {
substr(shift,-1,1) eq substr(shift,0,1)
}
my ($a,$b,$c,$d); =~ m/
(??{ amb '$a', qw[the that a] }) (??{ amb '$b', qw[frog elephant thing] }) (??{ amb '$c', qw[walked treaded grows] }) (??{ amb '$d', qw[slowly quickly] }) (?(?{ joins($b, $c) })|(*FAIL)) (?(?{ joins($a, $b) })|(*FAIL)) (?(?{ joins($c, $d) })|(*FAIL)) (?{ say "$a $b $c $d" })
/x;</lang>
Using a higher-order function
In practice, one wouldn't try to squeeze such a search problem into the amb interface shown in the task description, when coding in Perl. The main purpose of the amb operator is backtracking, and a more conventional Perl idiom for that purpose is for the user to pass a subroutine of their own into a function which acts as a backtracking engine.
The following code does just that: the first arguments for amb(...) are one or more arrays of values, followed by a user-defined subroutine. The amb(...) function arbitrarily selects one value from each of the arrays, and calls the user's supplied sub with the selected values.
If the user's supplied sub calls amb() with no arguments, the outer amb(...) will pick the next set of values. If the user's supplied sub returns normally, then the return value from the sub will be the return value of amb(...).
This version uses vastly less memory, and is quite reusable.
<lang perl>use strict; use warnings;
sub amb {
if( @_ == 0 ) { no warnings 'exiting'; next AMB; } my $code = pop; my @words = @_; my @index = (0) x @words; AMB: while( 1 ) { my @w = map $words[$_][$index[$_]], 0 .. $#_; return $code->( @w ); } continue { my $i = 0; while( ++$index[$i] == @{$words[$i]} ) { $index[$i] = 0; return if ++$i == @index; } }
}
my @w1 = qw(the that a); my @w2 = qw(frog elephant thing); my @w3 = qw(walked treaded grows); my @w4 = qw(slowly quickly);
sub joined {
my ($join_a, $join_b) = @_; substr($join_a, -1) eq substr($join_b, 0, 1);
}
amb( \(@w1, @w2, @w3, @w4), sub {
my ($w1, $w2, $w3, $w4) = @_; amb() unless joined($w1, $w2); amb() unless joined($w2, $w3); amb() unless joined($w3, $w4); print "$w1 $w2 $w3 $w4\n";
});</lang>
All three versions produce the same output.

Output:
that thing grows slowly
Phix
Fairly simple recursive solution <lang Phix>function amb1(sequence sets, object res=0, integer idx=1) integer ch = 0 integer pass = 0
if idx>length(sets) then pass = 1 else if res=0 then res = repeat(0,length(sets)) else ch = sets[idx-1][res[idx-1]][$] end if for k=1 to length(sets[idx]) do if ch=0 or sets[idx][k][1]=ch then res[idx] = k {pass,res} = amb1(sets,res,idx+1) if pass then exit end if end if end for end if return {pass,res}
end function
sequence sets = {{"the","that","a"},
{"frog","elephant","thing"}, {"walked","treaded","grows"}, {"slowly","quickly"}}
integer pass sequence res
{pass,res} = amb1(sets) if pass then puts(1,"success: ") for i=1 to length(sets) do res[i] = sets[i][res[i]] end for ?res else puts(1,"failure\n") end if</lang>

Output:
success: {"that","thing","grows","slowly"}
To make things a bit more interesting/flexible, I factored out the inner test to a routine passed as an argument, and likewise added an optional result routine for multiple results. And to prove it the following solves three rather different problems instead of just one. <lang Phix>function amb(sequence sets, integer testrid, integer resrid=-1, object res=0, integer idx=1) integer flag = (res==0) integer pass = 0
if idx>length(sets) then pass = 1 if resrid!=-1 then call_proc(resrid,{sets,res}) end if else if flag then res = repeat(0,length(sets)) end if for k=1 to length(sets[idx]) do res[idx] = k if flag or call_func(testrid,{sets,res,idx}) then {pass,res} = amb(sets,testrid,resrid,res,idx+1) if pass and resrid=-1 then exit end if end if end for end if return {pass,res}
end function
function pairable(sequence sets, sequence res, integer idx)
return sets[idx-1][res[idx-1]][$] = sets[idx][res[idx]][1]
end function constant r_pairable = routine_id("pairable")
procedure AMB_Show(sequence sets, sequence res)
puts(1,"success: ") for i=1 to length(sets) do res[i] = sets[i][res[i]] end for ?res
end procedure constant r_show = routine_id("AMB_Show")
function pythagorean(sequence sets, sequence res, integer idx) -- (note that res[idx]==sets[idx][res[idx]] in all cases) integer x, y, z
if sequence(sets) then end if -- (suppress warning) {x,y,z} = res return idx<3 or (x*x+y*y=z*z)
end function constant r_pythagorean = routine_id("pythagorean")
procedure pythag_show(sequence sets, sequence res)
if sequence(sets) then end if -- (suppress warning) puts(1,"success: ") ?res
end procedure constant r_pythag_show = routine_id("pythag_show")
-- see http://www.randomhacks.net/articles/2005/10/11/amb-operator function not8(sequence sets, sequence res, integer idx) -- (note that idx==2 in all cases) -- (at the last moment, I flipped the test, after realising that -- someone had completely misunderstood the original article... -- ...and proved it by showing some strange output on rosetta.) -- return sets[1][res[1]]*sets[idx][res[idx]]!=8
return sets[1][res[1]]*sets[idx][res[idx]]=8
end function constant r_not8 = routine_id("not8")
procedure not8_show(sequence sets, sequence res)
puts(1,"success: ") ?{sets[1][res[1]],sets[2][res[2]]}
end procedure constant r_not8_show = routine_id("not8_show")
sequence sets = {{"the","that","a"},
{"frog","elephant","thing"}, {"walked","treaded","grows"}, {"slowly","quickly"}}
sequence sets2 = repeat(tagset(11),3) sequence sets3 = {{1, 2, 3}, {4, 5, 6}}
puts(1,"\nThe original:\n") {} = amb(sets,r_pairable,r_show) puts(1,"\nSmall Pythagorean triples problem:\n") {} = amb(sets2,r_pythagorean,r_pythag_show) puts(1,"\nSome strange not 8 problem:\n") -- (now fixed) {} = amb(sets3,r_not8,r_not8_show)</lang>

Output:
The original: success: {"that","thing","grows","slowly"} Small Pythagorean triples problem: success: {3,4,5} success: {4,3,5} success: {6,8,10} success: {8,6,10} Some strange not 8 problem: success: {2,4}
PicoLisp
For backtracking, Pilog (PicoLisp Prolog) is the natural choice.
Translation of: Prolog
<lang PicoLisp>(be amb (@E @Lst)
(lst @E @Lst) )
(be joins (@Left @Right)
(^ @T (last (chop (-> @Left)))) (^ @R (car (chop (-> @Right)))) (or ((equal @T @R)) ((amb @ NIL)) ) ) # Explicitly using amb fail as required
(be ambExample ((@Word1 @Word2 @Word3 @Word4))
(amb @Word1 ("the" "that" "a")) (amb @Word2 ("frog" "elephant" "thing")) (amb @Word3 ("walked" "treaded" "grows")) (amb @Word4 ("slowly" "quickly")) (joins @Word1 @Word2) (joins @Word2 @Word3) (joins @Word3 @Word4) )</lang>

Output:
: (? (ambExample @Result)) @Result=("that" "thing" "grows" "slowly") -> NIL
PL/I
<lang pli>*process or(!) source attributes xref;
amb: Proc Options(main); /********************************************************************* * 25.08.2013 Walter Pachl *********************************************************************/ Dcl w(4,10) Char(40) Var Init('the','that','a','if',(6)(1)' ', 'frog','elephant','thing',(7)(1)' ', 'walked','treaded','grows','trots',(6)(1)' ', 'slowly','quickly',(8)(1)' '); Dcl ns Char(40) Var; Dcl (i,k,j,ii,jj,m,n) Bin Fixed(31); n=hbound(w,1); /* number of sets */ m=hbound(w,2); /* max number of words in set */ Call show; /* show the input */ Do i=1 To n-1; /* loop over sets */ k=i+1; /* the following set */ Do ii=1 To m; /* loop over elements in set k*/ If words(w(i,ii))=i Then Do; /* a sentence part found */ Do jj=1 To m; /* loop over following words */ If right(w(i,ii),1)=left(w(k,jj),1) Then Do; /* fitting */ ns=w(i,ii)!!' '!!w(k,jj); /* build new sentence (part) */ If words(ns)=k Then /* 'complete' part */ Call add(k,ns); /* add to set k */ End; End; End; End; Do jj=1 To m; /* show the results */ If words(w(4,jj))=4 Then put edit('--> ',w(4,jj))(Skip,a,a); End;
add: Proc(ni,s); /********************************************************************* * add a sentence (part) to set ni *********************************************************************/ Dcl (i,ni) Bin Fixed(31); Dcl s Char(40) Var; Do i=1 To m While(w(ni,i)>); /* look for an empty slot */ End; w(ni,i)=s; /* add the sentence (part) */ End;
words: Proc(s) Returns(Bin Fixed(31)); /********************************************************************* * return the number of blank separated words in s *********************************************************************/ Dcl s Char(40) Var; Dcl nw Bin Fixed(31) Init(0); Dcl i Bin Fixed(31) Init(1); If s> Then Do; nw=1; Do i=1 To length(s); If substr(s,i,1)=' ' Then nw+=1; End; End; Return(nw); End;
show: Proc; /********************************************************************* * show the input sets *********************************************************************/ Dcl (i,j,mm) Bin Fixed(31) Init(0); Dcl l(4) Bin Fixed(31) Init((4)0); Do i=1 To n; Do j=1 To m; If w(i,j)> Then Do; mm=max(mm,j); /* max number of words in any set */ l(i)=max(l(i),length(w(i,j))); /* max word length in set i */ End; End; End; Put Edit('Input:')(Skip,a); Do j=1 To mm; /* output lines */ Put Skip; Do i=1 To n; Put Edit(w(i,j),' ')(a(l(i)),a); End; End; Put Skip; End;
End;</lang>

Output:
Input: (extended by 2 words!) the frog walked slowly that elephant treaded quickly a thing grows if trots --> the elephant trots slowly --> that thing grows slowly --> if frog grows slowly
Prolog
<lang prolog>amb(E, [E|_]). amb(E, [_|ES]) :- amb(E, ES).
joins(Left, Right) :-
append(_, [T], Left), append([R], _, Right), ( T \= R -> amb(_, []) % (explicitly using amb fail as required) ; true ).
amb_example([Word1, Word2, Word3, Word4]) :-
amb(Word1, ["the","that","a"]), amb(Word2, ["frog","elephant","thing"]), amb(Word3, ["walked","treaded","grows"]), amb(Word4, ["slowly","quickly"]), joins(Word1, Word2), joins(Word2, Word3), joins(Word3, Word4).</lang>
PureBasic
<lang PureBasic>Procedure Words_Ok(String1.s, String2.s)
If Mid(String1,Len(String1),1)=Mid(String2,1,1) ProcedureReturn #True EndIf ProcedureReturn #False
EndProcedure
Procedure.s Amb(Array A.s(1), Array B.s(1), Array C.s(1), Array D.s(1))
Protected a, b, c, d For a=0 To ArraySize(A()) For b=0 To ArraySize(B()) For c=0 To ArraySize(C()) For d=0 To ArraySize(D()) If Words_Ok(A(a),B(b)) And Words_Ok(B(b),C(c)) And Words_Ok(C(c),D(d)) ProcedureReturn A(a)+" "+B(b)+" "+C(c)+" "+D(d) EndIf Next Next Next Next ProcedureReturn "" ; Empty string, e.g. fail
EndProcedure
If OpenConsole()
Define Text.s Dim Set1.s(2) Dim Set2.s(2) Dim Set3.s(2) Dim Set4.s(1) Set1(0)="the": set1(1)="that": set1(2)="a" Set2(0)="frog": set2(1)="elephant": set2(2)="thing" Set3(0)="walked": set3(1)="treaded": set3(2)="grows" Set4(0)="slowly": set4(1)="quickly" text=Amb(set1(),set2(),Set3(),set4()) If Text<>"" PrintN("Correct sentence would be,"+#CRLF$+Text) Else PrintN("Failed to fine a correct sentence.") EndIf PrintN(#CRLF$+#CRLF$+"Press ENTER to exit."): Input() CloseConsole()
EndIf</lang>
Python
Procedural
(Note: The code is also imported and used as a module in the solution to this task).
Python does not have the amb function, but the declarative style of programming and the use of the one "function" to do all three tasks of:
Setting ranges

Setting the constraint

Iterating over all solutions
can be done in what appears to be a declarative manner with the following class Amb: <lang python>import itertools as _itertools
class Amb(object):
def __init__(self): self._names2values = {} # set of values for each global name self._func = None # Boolean constraint function self._valueiterator = None # itertools.product of names values self._funcargnames = None # Constraint parameter names def __call__(self, arg=None): if hasattr(arg, '__code__'): ## ## Called with a constraint function. ## globls = arg.__globals__ if hasattr(arg, '__globals__') else arg.func_globals # Names used in constraint argv = arg.__code__.co_varnames[:arg.__code__.co_argcount] for name in argv: if name not in self._names2values: assert name in globls, \ "Global name %s not found in function globals" % name self._names2values[name] = globls[name] # Gather the range of values of all names used in the constraint valuesets = [self._names2values[name] for name in argv] self._valueiterator = _itertools.product(*valuesets) self._func = arg self._funcargnames = argv return self elif arg is not None: ## ## Assume called with an iterable set of values ## arg = frozenset(arg) return arg else: ## ## blank call tries to return next solution ## return self._nextinsearch() def _nextinsearch(self): arg = self._func globls = arg.__globals__ argv = self._funcargnames found = False for values in self._valueiterator: if arg(*values): # Set globals. found = True for n, v in zip(argv, values): globls[n] = v break if not found: raise StopIteration return values def __iter__(self): return self def __next__(self): return self() next = __next__ # Python 2
if __name__ == '__main__':
if True: amb = Amb() print("\nSmall Pythagorean triples problem:") x = amb(range(1,11)) y = amb(range(1,11)) z = amb(range(1,11)) for _dummy in amb( lambda x, y, z: x*x + y*y == z*z ): print ('%s %s %s' % (x, y, z)) if True: amb = Amb() print("\nRosetta Code Amb problem:") w1 = amb(["the", "that", "a"]) w2 = amb(["frog", "elephant", "thing"]) w3 = amb(["walked", "treaded", "grows"]) w4 = amb(["slowly", "quickly"]) for _dummy in amb( lambda w1, w2, w3, w4: \ w1[-1] == w2[0] and \ w2[-1] == w3[0] and \ w3[-1] == w4[0] ): print ('%s %s %s %s' % (w1, w2, w3, w4)) if True: amb = Amb() print("\nAmb problem from " "http://www.randomhacks.net/articles/2005/10/11/amb-operator:") x = amb([1, 2, 3]) y = amb([4, 5, 6]) for _dummy in amb( lambda x, y: x * y != 8 ): print ('%s %s' % (x, y))</lang>

Output:
Small Pythagorean triples problem: 3 4 5 4 3 5 6 8 10 8 6 10 Rosetta Code Amb problem: that thing grows slowly Amb problem from http://www.randomhacks.net/articles/2005/10/11/amb-operator: 1 4 1 5 1 6 2 5 2 6 3 4 3 5 3 6
List Comprehension
Translation of: Haskell
The semantics of Python's list comprehension notation is also formally equivalent to that of the list monad structure in the Haskell versions above.
List comprehensions provide quite a clean and natural encoding of the amb relationship between sets of indeterminate values and sets of constraints:
<lang python># joins :: String -> String -> Bool def joins(a, b):
return a[-1] == b[0]

print (
[ ' '.join([w1, w2, w3, w4]) for w1 in ['the', 'that', 'a'] for w2 in ['frog', 'elephant', 'thing'] for w3 in ['walked', 'treaded', 'grows'] for w4 in ['slowly', 'quickly'] if joins(w1, w2) and joins(w2, w3) and joins(w3, w4) ]
)</lang>

Output:
['that thing grows slowly']
Rearranging this by pairing each indeterminate value with a predicate may foreground and clarify the way in which list comprehensions encode amb pairings:
<lang python>def main():
print ( unlines([ unwords([w1, w2, w3, w4])
for w1 in ['the', 'that', 'a'] if True
for w2 in ['frog', 'elephant', 'thing'] if joins(w1, w2)
for w3 in ['walked', 'treaded', 'grows'] if joins(w2, w3)
for w4 in ['slowly', 'quickly'] if joins(w3, w4) ]) )

joins :: String -> String -> Bool
def joins(a, b):
return a[-1] == b[0]

unlines :: [String] -> String
def unlines(xs):
return '\n'.join(xs)

unwords :: [String] -> String
def unwords(xs):
return ' '.join(xs)

if __name__ == '__main__':
main()</lang>

Output:
that thing grows slowly
List Monad
Defining amb directly as the list monad bind operator, and using it to enchain indeterminate values and predicates:
<lang python>from itertools import chain

amb :: [a] -> (a -> [b]) -> [b]
def amb(xs):
return lambda f: list( chain.from_iterable( map(f, xs) ) )

main :: IO ()
def main():
xs = enumFromTo(1)(10) print ('Pythagorean triples from integers 1-10:') print ( amb(xs)( lambda x: amb(xs) (lambda y: amb(xs) (lambda z: when( x * x + y * y == z * z )( (x, y, z) ) )) ) )
# joins :: String -> String -> Bool def joins(a, b): return a[-1] == b[0]
print ('\nRC problem given above:') print ( amb(['the', 'that', 'a'])( lambda w1: amb( ['frog', 'elephant', 'thing'] )(lambda w2: amb( ['walked', 'treaded', 'grows'] )(lambda w3: amb( ['slowly', 'quickly'] )(lambda w4: when( joins(w1, w2) and joins(w2, w3) and joins(w3, w4) )( (w1, w2, w3, w4) )))) ) ) print('\nAdditional problem reference in procedural version above:') print( amb([1, 2, 3]) ( lambda x: amb([4, 5, 6]) ( lambda y: when(x * y != 8) ( (x, y) ) ) ) )
GENERIC -------------------------------------------------

enumFromTo :: (Int, Int) -> [Int]
def enumFromTo(m):
return lambda n: list(range(m, 1 + n))

when :: Bool -> [a] -> [a]
def when(p):
return lambda x: [x] if p else []
MAIN ---
if __name__ == '__main__':
main()</lang>

Output:
Pythagorean triples from integers 1-10: [(3, 4, 5), (4, 3, 5), (6, 8, 10), (8, 6, 10)] RC problem given above: [('that', 'thing', 'grows', 'slowly')] Additional problem reference in procedural version above: [(1, 4), (1, 5), (1, 6), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)]
Or, if we prefer to pair each indeterminate value with its immediate predicate, rather than using a single compound predicate at the end of the expression:
<lang python>from itertools import chain

amb :: [a] -> (a -> [b]) -> [b]
def amb(xs):
return lambda f: list( chain.from_iterable( map(f, xs) ) )

when :: Bool -> [a] -> [a]
def when(p):
return lambda xs: xs if p else []

TEST ----------------------------------------------------
joins :: String -> String -> Bool
def joins(a, b):
return a[-1] == b[0]

print (
amb(['the', 'that', 'a'])( lambda w1: when(True)
(amb(['frog', 'elephant', 'thing']) (lambda w2: when(joins(w1, w2))
(amb(['walked', 'treaded', 'grows']) (lambda w3: when(joins(w2, w3))
(amb(['slowly', 'quickly']) (lambda w4: when(joins(w3, w4))(
[w1, w2, w3, w4] )))))) ) )
)</lang>

Output:
['that', 'thing', 'grows', 'slowly']
R
A brute force approach that depends on the expand.grid() function, which generates all possible paths through a list of vectors: <lang r>checkSentence <- function(sentence){
Input: character vector

Output: whether the sentence formed by the elements of the vector is valid
for (index in 1:(length(sentence)-1)){ first.word <- sentence[index] second.word <- sentence[index+1] last.letter <- substr(first.word, nchar(first.word), nchar(first.word)) first.letter <- substr(second.word, 1, 1) if (last.letter != first.letter){ return(FALSE) } } return(TRUE)
}
amb <- function(sets){
Input: list of character vectors containing all sets to consider

Output: list of character vectors that are valid
all.paths <- apply(expand.grid(sets), 2, as.character) all.paths.list <- split(all.paths, 1:nrow(all.paths)) winners <- all.paths.list[sapply(all.paths.list, checkSentence)] return(winners)
}</lang>

Output:
<lang r>sentence1 <- c("that", "thing", "grows", "slowly") sentence2 <- c("rosetta", "code", "is", "cool") sentence <- list(sentence1, sentence2) sapply(sentence, checkSentence) [1] TRUE FALSE
set1 <- c("the", "that", "a") set2 <- c("frog", "elephant", "thing") set3 <- c("walked", "treaded", "grows") set4 <- c("slowly", "quickly") sets <- list(set1, set2, set3, set4) amb(sets) $`26` [1] "that" "thing" "grows" "slowly"</lang>
Racket
<lang Racket>
lang racket
A quick `amb' implementation (same as in the Twelve Statements task)
(define failures null)
(define (fail)
(if (pair? failures) ((first failures)) (error "no more choices!")))
(define (amb/thunks choices)
(let/cc k (set! failures (cons k failures))) (if (pair? choices) (let ([choice (first choices)]) (set! choices (rest choices)) (choice)) (begin (set! failures (rest failures)) (fail))))
(define-syntax-rule (amb E ...) (amb/thunks (list (lambda () E) ...)))
(define (assert condition) (unless condition (fail)))
Problem solution
(define (joins? left right)
(regexp-match? #px"(.)\0\\1" (~a left "\0" right)))
(let ([result (list (amb "the" "that" "a")
(amb "frog" "elephant" "thing") (amb "walked" "treaded" "grows") (amb "slowly" "quickly"))]) (for ([x result] [y (cdr result)]) (assert (joins? x y))) result)
-> '("that" "thing" "grows" "slowly")
</lang>
Raku
(formerly Perl 6)
Using Junctions
Junctions are a construct that behave similarly to the wanted Amb operator. The only difference is, that they don't preserve the state that was True inside any control structure (like an if).
There is currently a trick, how you only get the "true" values from a Junction for any test: return from a subroutine. Because of DeMorgans Law, you'll have to switch and and or, since you want to return on falseness. Just look at 'all' in combination with the sub(){return unless test} as the amb operator.
<lang perl6>
| an array of four words, that have more possible values.

| Normally we would want `any' to signify we want any of the values, but well negate later and thus we need `all'
my @a = (all «the that a»), (all «frog elephant thing»), (all «walked treaded grows»), (all «slowly quickly»);
sub test (Str $l, Str $r) {
$l.ends-with($r.substr(0,1))
}
(sub ($w1, $w2, $w3, $w4){
# return if the values are false return unless [and] test($w1, $w2), test($w2, $w3),test($w3, $w4); # say the results. If there is one more Container layer around them this doesn't work, this is why we need the arguments here. say "$w1 $w2 $w3 $w4"
})(|@a); # supply the array as argumetns
</lang>
Using the Regex Engine
By using a reduction metaoperator to calculate all possible combinations, we can Amb any number of sets with no arbitrary limits. A simple regex pattern can find out if a certain combination is correct or not.
<lang perl6># The Task # my @firstSet = «the that a»; my @secondSet = «frog elephant thing»; my @thirdSet = «walked treaded grows»; my @fourthSet = «slowly quickly»;
.say for doAmb [@firstSet, @secondSet, @thirdSet, @fourthSet];

sub doAmb( @lol ) { # Takes out the correct sentences. my @sentences = map *.join(" "), [X] @lol; grep *.&isAmb, @sentences; }
sub isAmb( $sentence ) { # Checks `$sentence` for correctness. $sentence !~~ / (.) " " (.) <!{$0 eq $1}> / # <https://docs.raku.org/language/regexes#Regex_boolean_condition_check> }</lang>
REXX
version 1
An assumption was made that equivalent lowercase and uppercase (Latin) letters are considered a match,
although that isn't case here for these words (required by this task). <lang rexx>/*REXX program demonstrates the Amd operator, choosing a word from each set. */
@.1 = "the that a" @.2 = "frog elephant thing" @.3 = "walked treaded grows" @.4 = "slowly quickly" @.0 = 4 /*define the number of sets being ised.*/
call Amb 1 /*find all word combinations that works*/ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Amb: procedure expose @.; parse arg # x; arg . u /*ARG uppercases U value. */
if #>@.0 then do; y= word(u, 1) /*Y: is a uppercased U. */ do n=2 to words(u); ?= word(u, n) if left(?, 1) \== right(y, 1) then return; y= ? end /*n*/ say strip(x) /*¬show superfluous blanks.*/ end do j=1 for words(@.#); call Amb #+1 x word(@.#, j) /*gen all combos recursively*/ end /*j*/; return</lang>

output when using the default internal inputs:
that thing grows slowly
version 2
<lang rexx> /* REXX **************************************************************
* 25.08.2013 Walter Pachl derived from PL/I *********************************************************************/ mm=0 w.= l.=0 Call mkset 1,'the that a if' Call mkset 2,'frog elephant thing' Call mkset 3,'walked treaded grows trots' Call mkset 4,'slowly quickly'
Call show Do i=1 to 3 /* loop over sets */ Call showm k=i+1 /* the following set */ Do ii=1 To 10 /* loop over elements in set k*/ If words(w.i.ii)=i Then Do /* a sentence part found */ Do jj=1 To 10 /* loop over following words */ If right(w.i.ii,1)=left(w.k.jj,1) Then Do /* fitting */ ns=w.i.ii' 'w.k.jj /* build new sentence (part) */ If words(ns)=k Then /* 'complete' part */ Call add k,ns /* add to set k */ End End End End End
Do jj=1 To 10 /* show the results */ If words(w.4.jj)=4 Then Say '-->' w.4.jj End Return
add: Procedure Expose w. /********************************************************************* * add a sentence (part) to set ni *********************************************************************/ Parse Arg ni,s Do i=1 To 10 While w.ni.i> /* look for an empty slot */ End w.ni.i=s /* add the sentence (part) */ Return
mkset: Procedure Expose w. mm l. /********************************************************************* * initialize the sets *********************************************************************/ Parse Arg i,wl Do j=1 By 1 While wl<> Parse Var wl w.i.j wl l.i=max(l.i,length(w.i.j)) End mm=max(mm,j-1) Return
show: Procedure Expose w. mm l.
/********************************************************************* * show the input *********************************************************************/ Say 'Input:' Do j=1 To mm /* output lines */ ol= Do i=1 To 4 ol=ol left(w.i.j,l.i) End Say strip(ol) End; say Return
showm: Procedure Expose w.
/********************************************************************* * show the sets' contents *********************************************************************/ dbg=0 If dbg Then Do Do i=1 To 4 Do j=1 To 10 If w.i.j> Then Say i j w.i.j End End End Return</lang>
Output: identical to PL/I's
Ring
<lang ring>
Project : Amb
set1 = ["the","that","a"] set2 = ["frog","elephant","thing"] set3 = ["walked","treaded","grows"] set4 = ["slowly","quickly"] text = amb(set1,set2,set3,set4) if text != ""
see "Correct sentence would be: " + nl + text + nl
else
see "Failed to fine a correct sentence."
ok
func wordsok(string1, string2)
if substr(string1,len(string1),1) = substr(string2,1,1) return true ok return false
func amb(a,b,c,d)
for a2 = 1 to len(a) for b2 =1 to len(b) for c2 = 1 to len(c) for d2 = 1 to len(d) if wordsok(a[a2],b[b2]) and wordsok(b[b2],c[c2]) and wordsok(c[c2],d[d2]) return a[a2]+" "+b[b2]+" "+c[c2]+" "+d[d2] ok next next next next return ""
</lang> Output:
Correct sentence would be: that thing grows slowly
Ruby
<lang ruby>require "continuation"
class Amb
class ExhaustedError < RuntimeError; end
def initialize @fail = proc { fail ExhaustedError, "amb tree exhausted" } end
def choose(*choices) prev_fail = @fail callcc { |sk| choices.each { |choice|
callcc { |fk| @fail = proc { @fail = prev_fail fk.call(:fail) } if choice.respond_to? :call sk.call(choice.call) else sk.call(choice) end }
} @fail.call } end
def failure choose end
def assert(cond) failure unless cond end
end
A = Amb.new w1 = A.choose("the", "that", "a") w2 = A.choose("frog", "elephant", "thing") w3 = A.choose("walked", "treaded", "grows") w4 = A.choose("slowly", "quickly")
A.choose() unless w1[-1] == w2[0] A.choose() unless w2[-1] == w3[0] A.choose() unless w3[-1] == w4[0]
puts w1, w2, w3, w4</lang>
Rust
<lang rust>use std::ops::Add; struct Amb<'a> {
list: Vec<Vec<&'a str>>,
} fn main() {
let amb = Amb { list: vec![ vec!["the", "that", "a"], vec!["frog", "elephant", "thing"], vec!["walked", "treaded", "grows"], vec!["slowly", "quickly"], ], }; match amb.do_amb(0, 0 as char) { Some(text) => println!("{}", text), None => println!("Nothing found"), }
} impl<'a> Amb<'a> {
fn do_amb(&self, level: usize, last_char: char) -> Option<String> { if self.list.is_empty() { panic!("No word list"); } if self.list.len() <= level { return Some(String::new()); } let mut res = String::new(); let word_list = &self.list[level]; for word in word_list { if word.chars().next().unwrap() == last_char || last_char == 0 as char { res = res.add(word).add(" "); let answ = self.do_amb(level + 1, word.chars().last().unwrap()); match answ { Some(x) => { res = res.add(&x); return Some(res); } None => res.clear(), } } } None }
}</lang>
Monadic
<lang rust>// ==== main ==== //
fn main() {
let results = amb(&["the", "that", "a"]) >> move |a| amb(&["frog", "elephant", "thing"]) >> move |b| amb(&["walked", "treaded", "grows"]) >> move |c| amb(&["slowly", "quickly"]) >> move |d| assert(joins(a, b)) >> move |_| assert(joins(b, c)) >> move |_| assert(joins(c, d)) >> move |_|
ret((a, b, c, d)); for (a, b, c, d) in results { println!("{} {} {} {}", a, b, c, d); }
}
fn joins(x: &str, y: &str) -> bool {
x.chars().last() == y.chars().next()
}
// ==== Amb ==== //
struct Amb<T: Iterator>(T);
impl<T: Iterator> IntoIterator for Amb<T> {
type IntoIter = T; type Item = T::Item; fn into_iter(self) -> Self::IntoIter { self.0 }
}
impl<T, U, F> std::ops::Shr<F> for Amb<T> where
T: Iterator, U: Iterator, F: FnMut(T::Item) -> Amb,
{
type Output = Amb<std::iter::FlatMap<T, Amb, F>>; fn shr(self, f: F) -> Self::Output { Self(self.0.flat_map(f)) }
}
fn amb<I: IntoIterator>(i: I) -> Amb<I::IntoIter> {
Amb(i.into_iter())
}
fn assert(x: bool) -> Amb<impl Iterator<Item = ()>> {
Amb(std::iter::once(()).filter(move |_| x))
}
fn ret<T>(x: T) -> Amb<impl Iterator<Item = T>> {
Amb(std::iter::once(x))
}</lang>
Scala
<lang Scala>object Amb {
def amb(wss: List[List[String]]): Option[String] = { def _amb(ws: List[String], wss: List[List[String]]): Option[String] = wss match { case Nil => ((Some(ws.head): Option[String]) /: ws.tail)((a, w) => a match { case Some(x) => if (x.last == w.head) Some(x + " " + w) else None case None => None }) case ws1 :: wss1 => ws1.flatMap(w => _amb(w :: ws, wss1)).headOption } _amb(Nil, wss.reverse) }
def main(args: Array[String]) { println(amb(List(List("the", "that", "a"), List("frog", "elephant", "thing"), List("walked", "treaded", "grows"), List("slowly", "quickly")))) }
}</lang>
Scheme
<lang scheme>(define fail
(lambda () (error "Amb tree exhausted")))
(define-syntax amb
(syntax-rules () ((AMB) (FAIL)) ; Two shortcuts. ((AMB expression) expression) ((AMB expression ...) (LET ((FAIL-SAVE FAIL)) ((CALL-WITH-CURRENT-CONTINUATION ; Capture a continuation to (LAMBDA (K-SUCCESS) ; which we return possibles. (CALL-WITH-CURRENT-CONTINUATION (LAMBDA (K-FAILURE) ; K-FAILURE will try the next (SET! FAIL K-FAILURE) ; possible expression. (K-SUCCESS ; Note that the expression is (LAMBDA () ; evaluated in tail position expression)))) ; with respect to AMB. ... (SET! FAIL FAIL-SAVE) ; Finally, if this is reached, FAIL-SAVE))))))) ; we restore the saved FAIL.

(let ((w-1 (amb "the" "that" "a"))
(w-2 (amb "frog" "elephant" "thing")) (w-3 (amb "walked" "treaded" "grows")) (w-4 (amb "slowly" "quickly"))) (define (joins? left right) (equal? (string-ref left (- (string-length left) 1)) (string-ref right 0))) (if (joins? w-1 w-2) '() (amb)) (if (joins? w-2 w-3) '() (amb)) (if (joins? w-3 w-4) '() (amb)) (list w-1 w-2 w-3 w-4))</lang>
Seed7
<lang seed7>$ include "seed7_05.s7i";
const type: setListType is array array string;
const func array string: amb (in string: word1, in setListType: listOfSets) is func
result var array string: ambResult is 0 times ""; local var string: word2 is ""; begin for word2 range listOfSets[1] do if length(ambResult) = 0 and word1[length(word1) len 1] = word2[1 len 1] then if length(listOfSets) = 1 then ambResult := [] (word1) & [] (word2); else ambResult := amb(word2, listOfSets[2 ..]); if length(ambResult) <> 0 then ambResult := [] (word1) & ambResult; end if; end if; end if; end for; end func;
const func array string: amb (in setListType: listOfSets) is func
result var array string: ambResult is 0 times ""; local var string: word1 is ""; begin for word1 range listOfSets[1] do if length(ambResult) = 0 then ambResult := amb(word1, listOfSets[2 ..]); end if; end for; end func;
const proc: main is func
local var array string: ambResult is 0 times ""; var string: word is ""; begin ambResult := amb([] ([] ("the", "that", "a"), [] ("frog", "elephant", "thing"), [] ("walked", "treaded", "grows"), [] ("slowly", "quickly"))); for word range ambResult do write(word <& " "); end for; writeln; end func;</lang>

Output:
that thing grows slowly
SETL
<lang SETL>program amb;
sets := unstr('[{the that a} {frog elephant thing} {walked treaded grows} {slowly quickly}]');
words := [amb(words): words in sets]; if exists lWord = words(i), rWord in {words(i+1)} |
lWord(#lWord) /= rWord(1) then fail;
end if;
proc amb(words);
return arb {word in words | ok};
end proc;
end program;</lang> Sadly ok and fail were only ever implemented in CIMS SETL, and are not in any compiler or interpreter that is available today, so this is not very useful as it stands.
Alternate version (avoids backtracking)
<lang SETL>program amb;
sets := unstr('[{the that a} {frog elephant thing} {walked treaded grows} {slowly quickly}]');
print(amb(sets));
proc amb(sets);
return amb1([], {}, sets);
end proc;
proc amb1(prev, mbLast, sets);
if sets = [] then return prev; else words fromb sets; if exists word in words | (forall last in mbLast | last(#last) = word(1)) and (exists sentence in {amb1(prev with word, {word}, sets)} | true) then return sentence; end if; end if;
end proc;
end program;</lang> We cheat a bit here - this version of amb must be given the whole list of word sets, and that list is consumed recursively. It can't pick a word from an individual list.
Tcl
Brute Force
Brute force, with quick kill of failing attempts: <lang Tcl>set amb {
{the that a} {frog elephant thing} {walked treaded grows} {slowly quickly}
}
proc joins {a b} {
expr {[string index $a end] eq [string index $b 0]}
}
foreach i [lindex $amb 0] {
foreach j [lindex $amb 1] { if ![joins $i $j] continue foreach k [lindex $amb 2] { if ![joins $j $k] continue foreach l [lindex $amb 3] { if [joins $k $l] { puts [list $i $j $k $l] } } } }
}</lang>
With Coroutines
A more sophisticated using Tcl 8.6's coroutine facility that avoids the assumption of what the problem is in the code structure: <lang Tcl>package require Tcl 8.6 proc cp {args} {
coroutine cp.[incr ::cps] apply {{list args} {
yield [info coroutine] foreach item $list { if {[llength $args]} { set c [cp {*}$args] while 1 { yield [list $item {*}[$c]] } } else { yield $item } } return -code break
}} {*}$args
} proc amb {name filter args} {
coroutine $name apply {{filter args} {
set c [cp {*}$args] yield [info coroutine] while 1 { set value [$c] if {[{*}$filter $value]} { yield $value } } return -code break
}} $filter {*}$args
}
proc joins {a b} {
expr {[string index $a end] eq [string index $b 0]}
} proc joins* list {
foreach a [lrange $list 0 end-1] b [lrange $list 1 end] {
if {![joins $a $b]} {return 0}
} return 1
}
amb words joins* \
{the that a} \ {frog elephant thing} \ {walked treaded grows} \ {slowly quickly}
while 1 { puts [words] }</lang>
TUSCRIPT
<lang tuscript>$$ MODE TUSCRIPT set1="the'that'a" set2="frog'elephant'thing" set3="walked'treaded'grows" set4="slowly'quickly" LOOP w1=set1
lastw1=EXTRACT (w1,-1,0) LOOP w2=set2 IF (w2.sw.$lastw1) THEN lastw2=EXTRACT (w2,-1,0) LOOP w3=set3 IF (w3.sw.$lastw2) THEN lastw3=EXTRACT (w3,-1,0) LOOP w4=set4 IF (w4.sw.$lastw3) sentence=JOIN (w1," ",w2,w3,w4) ENDLOOP ENDIF ENDLOOP ENDIF ENDLOOP
ENDLOOP PRINT sentence</lang>

Output:
that thing grows slowly
TXR
Delimited Continuations
Because we are using delimited continuations, we are able to confine the amb computation into a scope. To express this, we define an amb-scope operator which is just a syntactic sugar for using block to create a delimiting prompt whose name is amb-scope. Everything outside of an instance of this operator knows nothing about amb and is not involved in the backtracking flow at all. As far as the outside is concerned, the amb-scope block calculates something, terminates and returns a value, like any other ordinary Lisp form:
<lang txrlisp>(defmacro amb-scope (. forms)
^(block amb-scope ,*forms))</lang>
Next, we define amb as a function.
But first, a note about a convention: we are using the Lisp object nil not only to represent Boolean false, but also a failure. Thus (amb nil) fails. A nil return out of the entire amb-scope denotes overall failure.
The function is very simple. It captures a single continuation and binds it to the cont variable, using the suspend macro. Then, it iterates over all of its arguments. Each argument which is nil is ignored. For any other value, the function effectively asks the question, "if, with this argument, I run my future computation to completion (i.e. back up to the delimiting contour defined by amb-scope) will the answer be a Boolean true?". It asks the question simply by invoking the continuation on the argument. If the answer is affirmative, then it breaks out of the loop and returns that argument value immediately. Otherwise the iteration continues with the next argument, to try a different alternative future. If the loop runs through to completion, then the function returns nil, indicating failure.

<lang txrlisp>(defun amb (. args)
(suspend amb-scope cont (each ((a args)) (when (and a (call cont a)) (return-from amb a)))))</lang>
And some test code:

Output:
$ txr -i amb.tl 1> (amb-scope (let ((w1 (amb "the" "that" "a")) (w2 (amb "frog" "elephant" "thing")) (w3 (amb "walked" "treaded" "grows")) (w4 (amb "slowly" "quickly"))) (amb (and (eql [w1 -1] [w2 0]) (eql [w2 -1] [w3 0]) (eql [w3 -1] [w4 0]))) (list w1 w2 w3 w4))) ("that" "thing" "grows" "slowly") 2>
Pattern Language
This is not exactly the implementation of an operator, but a solution worth presenting. The language has the built in pattern matching and backtracking behavior suited for this type of text mining task.
For convenience, we prepare the data in four files:
$ cat amb/set1 the that a $ cat amb/set2 frog elephant thing $ cat amb/set3 walked treaded grows $ cat amb/set4 slowly quickly
Then code is:
<lang txr>@(define first_last (first last whole)) @ (all) @(skip :greedy)@{last 1} @ (and) @{first 1}@(skip) @ (and) @whole @ (end) @(end) @(next "amb/set1") @(skip) @(first_last fi1 la1 w1) @(next "amb/set2") @(skip) @(first_last la1 la2 w2) @(next "amb/set3") @(skip) @(first_last la2 la3 w3) @(next "amb/set4") @(skip) @(first_last la3 la4 w4) @(output) @w1 @w2 @w3 @w4 @(end)</lang>

Run:
$ ./txr amb.txr that thing grows slowly
As you can see, this has the "nondeterministic flavor" of Amb. The @(skip) directives"magically" skip over the lines of input that do not succeed.
This example naturally handles empty strings, since the first_last function simply does not match such inputs.
Here is how to embed the task's specific data in the code:
<lang txr>@(define first_last (first last whole)) @ (all) @(skip :greedy)@{last 1} @ (and) @{first 1}@(skip) @ (and) @whole @ (end) @(end) @(next :list ("the" "that" "a")) @(skip) @(first_last fi1 la1 w1) @(next :list ("frog" "elephant" "thing")) @(skip) @(first_last la1 la2 w2) @(next :list ("walked" "treaded" "grows")) @(skip) @(first_last la2 la3 w3) @(next :list ("slowly" "quickly")) @(skip) @(first_last la3 la4 w4) @(output) @w1 @w2 @w3 @w4 @(end)</lang>
VBScript
Implementation
<lang vb>class ambiguous dim sRule
public property let rule( x ) sRule = x end property
public default function amb(p1, p2) amb = eval(sRule) end function end class</lang>
Invocation
<lang vb>dim amb set amb = new ambiguous
amb.rule = "right(p1,1)=left(p2,1)"
dim w1, w2, w3, w4 for each w1 in split("the that a", " ") for each w2 in split("frog elephant thing", " ") for each w3 in split("walked treaded grows", " ") for each w4 in split("slowly quickly", " ") if amb(w1, w2) and amb(w2, w3) and amb(w3, w4) then wscript.echo w1, w2, w3, w4 end if next next next next</lang>

Output:
that thing grows slowly
zkl
zkl doesn't support dynamic scoping so no variable update (without using reflection, which is not a good thing).
These solutions assume that the solution space is ordered: the possibilities in a always precede those in b, etc.
Some constraints on the constraint to make the task easier: it is a function of two strings rather than n items. All solutions are returned, empty list otherwise. <lang zkl>fcn joins(a,b){ a[-1]==b[0] } // the constraint</lang> The do-it-in-one-wack solution: <lang zkl>amb(joins,
T("the","that","a"), T("frog","elephant","thing"), T("walked","treaded","grows"), T("slowly","quickly")
).println();</lang>

Output:
L("that thing grows slowly")
Or, we can defer the computations (the future method starts a worker thread, the result is not forced until it is used). <lang zkl>a:=amb.future(joins,T("the","that","a"),T("frog","elephant","thing")); b:=amb.future(joins,T("walked","treaded","grows"),T("slowly","squacking")); c:=amb.future(joins,a,b); // a future of futures println(a,b,c); c=c.noop(); // trigger the landslide, referencing c forces a result for a,b,c println(a.noop(),b.noop(),c); // even though a has a result, it doesn't know it until we force it</lang>

Output:
DeferredDeferredDeferred L("the elephant","that thing")L("grows slowly","grows squacking")L("that thing grows slowly","that thing grows squacking")
Your basic Cartesian product recursive decent tree traversal, making extensive use of varargs: <lang zkl>fcn amb(f,a,b,etc){
fcn(sink,f,a,b,etc){ abc:=vm.arglist[2,*]; // ((the,that),(frog,elephant)) if(abc.len()<2) return(sink.write(abc[0][0])); // back out of recursion foreach a,b in (abc[0],abc[1]){ // Cartesian product
if(f(a,b)) self.fcn(sink,f,T(String(a," ",b)),abc[2,*].xplode());
} }(s:=List(),vm.pasteArgs()); s
}</lang> A more general solution, where each possible solution is a list, which is passed to the constraining function and the first solution found is returned: <lang zkl>fcn amb(f,a,b,c,etc){ Walker.cproduct(vm.pasteArgs(1)).filter1(f) }</lang> <lang zkl> // [()] notation unpacks parameter list: f((1,2,3))-->a=1,b=2,c=3 fcn f([(a,b,c,d)]){ joins(a,b) and joins(b,c) and joins(c,d) } amb(f, T("the","that","a"), T("frog","elephant","thing"),
T("walked","treaded","grows"), T("slowly","quickly")
).println();</lang>

Output:
L("that","thing","grows","slowly")
Here is an example using an infinite list as the first possibility space: <lang zkl>amb(fcn([(x,y,z)]){ x*x + y*y == z*z },[1..],[1..10],[1..10]).println();</lang>

Output:
L(3,4,5)