Amb
From Rosetta Code
Amb is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Define and give an example of the Amb operator.
The Amb operator takes some number of expressions (or values if that's simpler in the language) and nondeterministically yields the one or fails if given no parameter, amb returns the value that doesn't lead to failure.
The example is using amb to choose four words from the following strings:
set 1: "the" "that" "a"
set 2: "frog" "elephant" "thing"
set 3: "walked" "treaded" "grows"
set 4: "slowly" "quickly"
It is a failure if the last character of word 1 is not equal to the first character of word 2, and similarly with word 2 and word 3, as well as word 3 and word 4. (the only successful sentence is "that thing grows slowly").
[edit] 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;
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. Sample output:
that thing grows slowly
[edit] ALGOL 68
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.
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 #
## (PAGE amb)VOID:
print((amb[1]+" "+amb[2]+" "+amb[3]+" "+amb[4], new line))
#OD# )
Output:
that thing grows slowly
[edit] AutoHotkey
Search autohotkey.com: [1]
Source: AMB - Ambiguous selector by infogulch
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 ""
}
[edit] 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)
)
)
that thing grows slowly
[edit] C
Note: This uses the continuations code from http://homepage.mac.com/sigfpe/Computing/continuations.html
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;
}
[edit] C#
The implementation of the Amb class
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") { }
}
Usage:
// 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();
});
}
[edit] 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"))
[edit] 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.
(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))))
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")
[edit] Macro with dynamic variables
(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"))))
(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
[edit] 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);
}
- Output:
that thing grows slowly
[edit] E
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.
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]
}
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))
[edit] 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)anddo 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 likeinstance Monoid a => Monoid (Amb a) where Amb ... `mconcat` Amb ... = ..., which would have a similar need to track decisions.
[edit] 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
Usage:
amb [
["the","that","a"]
,["frog","elephant","thing"]
,["walked","treaded","grows"]
,["slowly","quickly"]
]
[edit] Elena
The implementation
#define std'dictionary'*.
#define std'patterns'*.
#define ext'routines'*.
#subject __amb_index, __amb_available.
#symbol Joinable &former:aFirst &later:aSecond
= aFirst @ (aFirst length - 1) == aSecond @ 0.
#class AmbIndexer (BaseIndexer)
{
#field theAmbValue.
#initializer : Values
[
theAmbValue := Values.
]
#method index = theAmbValue __amb_index.
#method index'write : anIndex
[
theAmbValue __amb_index'write:anIndex.
]
#method available'is = theAmbValue __amb_available'is.
#method content = theAmbValue.
}
#class AmbValue
{
#field theValues.
#field theCurrent.
#role Unassigned
{
#method __amb_index = 0.
#method __amb_index'write : anIndex
[
theCurrent := theValues indexer.
#shift.
self __amb_index'write:anIndex.
]
}
#initializer : Values
[
theValues := Values.
theCurrent := nil.
#shift Unassigned.
]
#method indexer = AmbIndexer::$self.
#method __amb_index = theCurrent index.
#method __amb_available'is = theCurrent available'is.
#method __amb_index'write : anIndex
[
theCurrent index'write:anIndex.
]
#outer theCurrent content.
}
#class AmbOperator
{
#method seek : anExpression
[
(CombinatorWithRepetition::self)~foreach seek: anExpression.
]
}
#symbol Program =
[
#var A := AmbValue::("the","that","a").
#var B := AmbValue::("frog", "elephant", "thing").
#var C := AmbValue::("walked", "treaded", "grows").
#var D := AmbValue::("slowly", "quickly").
(A, B, C, D)~AmbOperator seek:
= (joinable &&former:A &later:B and:(joinable &&former:B &later:C) and:(joinable &&former:C &later:D)).
'program'Output << A << " " << B << " " << C << " " << D.
].
[edit] 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
Running it from the listener :
( scratchpad ) "amb" run "that thing grows slowly"
[edit] F#
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.
// 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)
[edit] Go
Solution with goroutines. See description on talk page.
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)
}
}
- Output:
[that thing grows slowly]
Alternative solution:
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")
}
}
[edit] Haskell
Haskell's List monad returns all the possible choices. Use the "head" function on the result if you just want one.
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"]
unless (joins w1 w2) (amb [])
unless (joins w2 w3) (amb [])
unless (joins w3 w4) (amb [])
return (unwords [w1, w2, w3, w4])
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"].
[edit] 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;
}
}
[edit] Icon and Unicon
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
[edit] J
amb=. ([ , ' ' , ])&>/&.>@:((({:@:[ = {.@:])&>/&> # ])@:,@:({@(,&<)))
>@(amb&.>/) ('the';'that';'a');('frog';'elephant';'thing');('walked';'treaded';'grows');(<'slowly';'quickly')
+-----------------------+
|that thing grows slowly|
+-----------------------+
amb is a dyadic verb:
('the';'that';'a') amb ('frog';'elephant';'thing') amb ('walked';'treaded';'grows') amb ('slowly';'quickly')
+-----------------------+
|that thing grows slowly|
+-----------------------+
A structured derivation of amb follows:
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...
([ , ' ' , ])&>/&.>@:((({:@:[ = {.@:])&>/&> # ])@:,@:({@(,&<)))
[edit] 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"
[edit] 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
Usage example:
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
[edit] Mathematica
Make all the tuples of all the lists, then filter out the good ones:
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]
gives back:
{{"that", "thing", "grows", "slowly"}}
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):
CheckValid2[i_List] := StringFreeQ[StringJoin[Riffle[i, ","]], a_ ~~ "," ~~ b_ /; a =!= b]
[edit] Mercury
Like Prolog, Mercury has built-in nondeterminacy; however, Mercury is explicit about it, and statically checks it.
:- 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).
The Amb defined in the Prolog solution is similar to the use of list.member/2 above. Predicates could be used instead:
:- 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").
[edit] 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.
[edit] Filtering possible combinations
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;
;;
We can take all the good results with List.filter or just take the first one with List.find.
[edit] 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
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;
;;
[edit] 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.
Output:
--------------------------- Message --------------------------- that thing grows slowly --------------------------- OK ---------------------------
[edit] 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.
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}
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.
[edit] PARI/GP
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"]])
[edit] 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).
[edit] Perl
Generates permutation of the sets with the glob function. Then, validate the combination with a regular expression.
$s1 = "the|,that|,a|";
$s2 = "frog|,elephant|,thing|";
$s3 = "walked|,treaded|,grows|";
$s4 = "slowly|,quickly|";
$sets = "{$s1}{$s2}{$s3}{$s4}";
print "$sets\n";
for( glob($sets) )
{
tr/|/ /;
print "$_\n" if(m/\w+?(\w) \1\w+?(\w) \2\w+?(\w) \3\w+/);
}
[edit] Perl 6
sub infix:<lf> ($a,$b) {
next unless try $a.substr(*-1,1) eq $b.substr(0,1);
"$a $b";
}
multi dethunk(Callable $x) { try take $x() }
multi dethunk( Any $x) { take $x }
sub amb (*@c) { gather @c».&dethunk }
say first *, do
amb(<the that a>, { die 'oops'}) Xlf
amb('frog',{'elephant'},'thing') Xlf
amb(<walked treaded grows>) Xlf
amb { die 'poison dart' },
{'slowly'},
{'quickly'},
{ die 'fire' };
- Output:
that thing grows slowly
This uses lazy lists, created by the X metaoperator applied to a user-defined function, lf, that asserts the last-first condition, and short-circuits the match so that it does not need to generate parts of the search tree that cannot match. We use the first function to pull one element from the lazy list; a subscript of [0] would have worked just as well.
The amb operator itself uses a hyper to run the dethunk calls in parallel. Results are returned asyncronously via gather/take. The dethunk call traps failures after the failure has bypassed the take.
If you consider lazy lists to be cheating on the idea of continuations, here's some admittedly grungy code that uses the continuation engine of regexes to solve it. At some point we'll wrap this up in nice syntax to let people write in a sublanguage of Perl 6 that looks more like a logic language.
sub amb($var,*@a) {
"[{
@a.pick(*).map: {"||\{ $var = '$_' }"}
}]";
}
'' ~~ m/
:my ($a,$b,$c,$d);
<{ amb '$a', <the that a> }>
<{ amb '$b', <frog elephant thing> }>
<?{ substr($a,*-1,1) eq substr($b,0,1) }>
<{ amb '$c', <walked treaded grows> }>
<?{ substr($b,*-1,1) eq substr($c,0,1) }>
<{ amb '$d', <slowly quickly> }>
<?{ substr($c,*-1,1) eq substr($d,0,1) }>
{ say "$a $b $c $d" }
<!>
/;
[edit] PicoLisp
For backtracking, Pilog (PicoLisp Prolog) is the natural choice.
(be amb (@E @Lst)
(lst @E @Lst) )
(be joins (@Left @Right)
(@T last (chop (-> @Left)))
(@R car (chop (-> @Right)))
(or
((equal @T @R))
((amb @ NIL)) ) ) # Explicitly using amb fail as required
(be ambExample ((@Word1 @Word2 @Word3 @Word4))
(amb @Word1 ("the" "that" "a"))
(amb @Word2 ("frog" "elephant" "thing"))
(amb @Word3 ("walked" "treaded" "grows"))
(amb @Word4 ("slowly" "quickly"))
(joins @Word1 @Word2)
(joins @Word2 @Word3)
(joins @Word3 @Word4) )
Output:
: (? (ambExample @Result))
@Result=("that" "thing" "grows" "slowly")
-> NIL
[edit] PureBasic
Procedure Words_Ok(String1.s, String2.s)
If Mid(String1,Len(String1),1)=Mid(String2,1,1)
ProcedureReturn #True
EndIf
ProcedureReturn #False
EndProcedure
Procedure.s Amb(Array A.s(1), Array B.s(1), Array C.s(1), Array D.s(1))
Protected a, b, c, d
For a=0 To ArraySize(A())
For b=0 To ArraySize(B())
For c=0 To ArraySize(C())
For d=0 To ArraySize(D())
If Words_Ok(A(a),B(b)) And Words_Ok(B(b),C(c)) And Words_Ok(C(c),D(d))
ProcedureReturn A(a)+" "+B(b)+" "+C(c)+" "+D(d)
EndIf
Next
Next
Next
Next
ProcedureReturn "" ; Empty string, e.g. fail
EndProcedure
If OpenConsole()
Define Text.s
Dim Set1.s(2)
Dim Set2.s(2)
Dim Set3.s(2)
Dim Set4.s(1)
Set1(0)="the": set1(1)="that": set1(2)="a"
Set2(0)="frog": set2(1)="elephant": set2(2)="thing"
Set3(0)="walked": set3(1)="treaded": set3(2)="grows"
Set4(0)="slowly": set4(1)="quickly"
text=Amb(set1(),set2(),Set3(),set4())
If Text<>""
PrintN("Correct sentence would be,"+#CRLF$+Text)
Else
PrintN("Failed to fine a correct sentence.")
EndIf
PrintN(#CRLF$+#CRLF$+"Press ENTER to exit."): Input()
CloseConsole()
EndIf
[edit] Python
(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:
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))
Sample 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
[edit] R
A brute force approach that depends on the expand.grid() function, which generates all possible paths through a list of vectors:
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)
}
Some sample output:
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"
[edit] 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")
[edit] REXX
An assumption was made that lowercase and uppercase (Latin) letters are considered a match.
/*REXX program demonstrates Amd operator (choosing 4 words from 4 sets).*/
@.='' /*default value for any # of sets*/
@.1="the that a"
@.2="frog elephant thing"
@.3="walked treaded grows"
@.4="slowly quickly"
do j=1 until @.j==''; end; @.0=j-1 /*find how many sets there are. */
/*@.0 contains number of sets. */
call Amb 1 /*find combo of words that works.*/
exit /*stick a fork in it, we're done.*/
/*─────────────────────────────────────AMB procedure────────────────────*/
Amb: procedure expose @.; parse arg # _; arg . u; if #=='' then return
if #>@.0 then do; if u=='' then return
w=word(u,1) /*(below) use upper case version.*/
do n=2 to words(_)
c=word(u,n); if left(c,1)\==right(w,1) then return; w=c
end /*n*/
say strip(_) /*_ has an extra leading blank. */
end
do j=1 for words(@.#)
call amb #+1 _ word(@.#,j) /*generate the next combination. */
end /*j*/
return
output
that thing grows slowly
[edit] Ruby
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
[edit] 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"))))
}
}
[edit] 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))
[edit] 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;
Output:
that thing grows slowly
[edit] 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;
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.
[edit] Alternate version (avoids backtracking)
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;
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.
[edit] Tcl
[edit] Brute Force
Brute force, with quick kill of failing attempts:
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]
}
}
}
}
}
[edit] 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:
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] }
[edit] 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
Output:
that thing grows slowly
[edit] TXR
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
Code:
@(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)
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:
@(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)
[edit] VBScript
[edit] Implementation
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
[edit] Invocation
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
[edit] Output
that thing grows slowly
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