core.logic incomplete results - clojure

I'm struggling with this simple relation, the results are incomplete, and I don't understand why.
I'm beginning with core.logic I don't know if it is a bug or my bad understanding of it.
(require '[clojure.core.logic :as l])
(require '[clojure.core.logic.fd :as fd])
(defn zip+o [x y z]
(l/conde
[(l/== () x) (l/== () y) (l/== () z)]
[(l/fresh [fx rx fy ry fz rz]
(l/conso fx rx x)
(l/conso fy ry y)
(l/conso fz rz z)
(fd/in fx fy fz (fd/interval 10))
(fd/+ fx fy fz)
(zip+o rx ry rz))]))
; the same with defne macro
(comment
(l/defne zip+o [x y z]
([() () ()])
([[fx . rx]
[fy . ry]
[fz . rz]]
(fd/in fx fy fz (fd/interval 10))
(fd/+ fx fy fz)
(zip+o rx ry rz))))
(def expected-solutions
#{{:x [0 0] :y [1 1]}
{:x [0 1] :y [1 0]}
{:x [1 1] :y [0 0]}
{:x [1 0] :y [0 1]}})
(l/run* [q]
(l/fresh [x y]
(l/== q {:x x :y y})
(zip+o x y [1 1])))
;=> ({:x (1 0), :y (0 1)}
; {:x (0 0), :y (1 1)})

Related

Extracting finite domain lvars from a map

I want to put fresh lvars with a finite domain into a map, and establish a relationship between them in another part of my code. Consider the snippet below:
(l/run 1 [q]
(l/fresh [x y z a b c]
(fd/in x y z (fd/interval 0 100)) ; establish domain for x y z
(let [w {:a x :b y :c z}] ; store x y z in a map
(l/all
(l/featurec w {:a a :b b :c c}) ; extract x y z as a b c
(fd/+ a b c))) ; a relationship
(l/== q [a b c])))
==> Error printing return value at clojure.core.logic/verify-all-bound$verify-all-bound* (logic.clj:2136).
Constrained variable <lvar:a__5787> without domain
Is there a way to accomplish this?
Featurec isn't designed to allow deriving values (see link's example in the core.logic/featurec documentation).
In general, you can expect core.logic functions that end with a 'c' to be 'constraint functions' specialized towards filtering ('constraining') a set/domain of possible values already derived from previous logic functions. It's a useful naming convention from the library authors, and from what I've seen users of core.logic try to stick to it as well.
Normal unification works fine for this particular problem, though.
(l/run* [q]
(l/fresh [x y z a b c]
(fd/in x y z (fd/interval 0 3)) ; establish domain for x y z
(let [w {:a x :b y :c z}] ; store x y z in a map
(l/all
(l/== w {:a a :b b :c c}) ; extract x y z as a b c
(fd/+ a b c))) ; a relationship
(l/== q [a b c])))
=> ([0 0 0] [1 0 1] [0 1 1] [0 2 2] [2 0 2] [1 1 2])
Or, if you only want certain values, just extract the lvars and unify individually:
(l/run* [q]
(l/fresh [x y z a b c]
(fd/in x y z (fd/interval 0 2)) ; establish domain for x y z
(let [w {:a x :b y :c z}] ; store x y z in a map
(l/all
(l/== a (w :a)) (l/== b (w :b)) ; extract x y z as a b c
(fd/+ a b c))) ; a relationship
(l/== q [a b c]) ))
=> ([0 0 0] [1 0 1] [0 1 1] [0 2 2] [2 0 2] [1 1 2] [1 2 3] [2 1 3] [2 2 4])
(also note that we didn't unify c and z, so c can be outside the interval)
If you want, you can make a list of the lvars and corresponding keys you want, and then use everyg to add a relation for each pair:
(l/run* [q]
(l/fresh [x y z a b c]
(fd/in x y z (fd/interval 0 2)) ; establish domain for x y z
(let [w {:a x :b y :c z}
targlist [a b c]
wantedlist [:a :b :c]] ; store x y z in a map
(l/all
(everyg #(l/==
(get targlist %)
(w (get wantedlist %)))
(range (count targlist))) ; extract x y z as a b c
(apply fd/+ [a b c]))) ; a relationship
(l/== q [a b c])))
=> ([0 0 0] [1 0 1] [0 1 1] [0 2 2] [2 0 2] [1 1 2])

How to rewrite the core.logic snippet?

I'm trying to rewrite the below piece of core.logic code.
(run* [x y]
(fd/in x (fd/domain 1 2))
(fd/in y (fd/domain 1 2)))
o/p,
([1 1] [2 1] [1 2] [2 2])
I tried the below versions but none of them works,
(run* [x y]
(fresh [dom (fd/domain 1 2)])
(fd/in x dom)
(fd/in y dom)))
;; Error Unsupported binding form: (fd/domain 1 2)
(run* [x y]
(fresh [dom]
(== dom (fd/domain 1 2))
(fd/in x dom)
(fd/in y dom)))
O/P:
([1 1])
(run* [x y]
(let [dom (fd/domain 1 2)]
(fd/in x dom)
(fd/in y dom)))
O/P:
([_0 1] [_0 2])
What's the rationale for the 3 versions that I tried? Any help would be greatly appreciated.
fd/domain returns a concrete value that can be used with other goals/relations in the fd namespace — you can define it once and use it inside run* more than once:
(let [dom (fd/domain 1 2)]
(run* [x y]
(fd/in x dom)
(fd/in y dom)))
=> ([1 1] [2 1] [1 2] [2 2])
What's the rationale for the 3 versions that I tried?
The first refactoring doesn't work because fresh is being used like let, but it doesn't work like that; fresh simply allows you to give names to some fresh logic variables.
The second refactoring doesn't work because the domain value is being bound to a logic variable, and fd/in wants a concrete domain value as its second argument — not a (fresh) logic variable.
The third refactoring doesn't work (I assume) because let bindings aren't going to work like that inside the run* macro, which only wants a sequence of goals in its body.

Why does this implementation of sorto does not terminate?

I'm a beginner with logic programming.
I'm trying to implement a sorting relation like this:
(sorto [3 2 1][1 2 3]) -> #s
I'am using clojure and core.logic:
I don't understand why this can not terminate in most cases.
Any idea would be helpful, thank you.
(require '[clojure.core.logic :refer :all]
'[clojure.core.logic.fd :as fd])
First I define several little helpers:
A simple count relation: (counto [a b] 2) -> #s
(defne counto [list n]
([() 0])
([[fl . rl] _]
(fresh [nnxt]
(fd/- n 1 nnxt)
(counto rl nnxt))))
reduce and every? relational equivalents:
(defne reduceo [rel acc x y]
([_ _ () _] (== acc y))
([_ _ [fx . rx] _]
(fresh [nacc]
(rel acc fx nacc)
(reduceo rel nacc rx y))))
(defne everyo [g list]
([_ ()])
([_ [fl . rl]]
(g fl)
(everyo g rl)))
min relation: (mino 1 2 1) -> #s
(defn mino [x y z]
(conde
[(fd/<= x y) (== x z)]
[(fd/> x y) (== y z)]))
relation between a list and its minimum element: (mino* [1 2 3 0] 0) -> #s
(defne mino* [xs y]
([[fxs . rxs] _]
(reduceo mino fxs rxs y)))
The main relation: (sorto [2 3 1 4] [1 2 3 4]) -> #s
(defne sorto [x y]
([() ()])
([[fx . rx] [fy . ry]]
(fresh [x* c]
(counto rx c)
(counto ry c)
(mino* x fy)
(rembero fy x x*)
(sorto x* ry))))
The below runs doesn't terminate, I would like to understand why.
(run* [q]
(sorto q [1 2]))
; does not terminate
(run* [q]
(sorto [2 1] q))
; does not terminate
(run* [a b]
(everyo #(fd/in % (fd/interval 10)) a)
(everyo #(fd/in % (fd/interval 10)) b)
(sorto a b))
;neither
The high level answer is because conjunction are tried in order. Reordering them may sometimes make a program to terminate -- however in the general case there may not exist a "good" order.
Have a look at Chapter 5 in https://scholarworks.iu.edu/dspace/bitstream/handle/2022/8777/Byrd_indiana_0093A_10344.pdf

How to explain the &env example in book <Clojure Programming>

There's an example in the book (P252), it's about the &env in macro, I just don't understand how to get the result{x 1, y 2}
(defmacro spy-env []
(let [ks (keys &env)]
`(prn (zipmap '~ks [~#ks]))))
(let [x 1 y 2]
(spy-env)
(+ x y))
; {x 1, y 2}
;= 3
I tried in the REPL like this:
user=> (defmacro spy-env [] (let [ks (keys &env)] `(prn ~#(keys &env))))
#'user/spy-env
user=> (let [x 1 y 2] (spy-env))
2 1
It's wried.
Expanding the macro would be a great way for you to see how it works, but unfortunately macroexpand-1 doesn't convey the right bindings for &env. This example:
(let [x 1 y 2] (spy-env))
Actually expands out to:
(let [x 1 y 2] (prn (zipmap '(x y) [x y])))
Do you get it? Within the first sequence, x and y are not evaluated, but within the second, they are. So it zips the symbols to whatever they evaluate to. Within that let block, (zipmap '(x y) [x y]) evaluates to {x 1 y 2}.
a) If you try the code of the book it does output the right value
user=> (defmacro spy-env []
#_=> (let [ks (keys &env)]
#_=> `(prn (zipmap '~ks [~#ks]))))
#'user/spy-env
user=> (let [x 1 y 2] (spy-env))
{x 1, y 2}
nil
user=> (let [x 1 y 2]
#_=> (spy-env)
#_=> (+ x y))
{x 1, y 2}
3
b) now your code is different
initial code :
`(prn (zipmap '~ks [~#ks]))
vs
`(prn ~#(keys &env))
with actually #(keys &env) being equal to #ks

distincto vs. fd/distinct in core.logic

What is the advantage of using fd/distinct in cases where the elements will be in a finite domain instead of distincto?
The following all return ([0 1] [1 0]).
;;; With distincto
(run* [q]
(fresh [x y]
(fd/in x y (fd/interval 1))
(distincto [x y])
(== q [x y])))
;;; With fd/distinct
(run* [q]
(fresh [x y]
(fd/in x y (fd/interval 1))
(fd/distinct [x y])
(== q [x y])))
;;; Without fd at all.
(let [interval [0 1]]
(run* [q]
(fresh [x y]
(membero x interval)
(membero y interval)
(distincto [x y])
(== q [x y]))))
Notably, although it appears you may use distincto in any place where you may use fd/distinct (but not the other way around), the same cannot be said for membero and fd/in.
fd/distinct is much more highly optimized than distincto which must receive any kind of value. fd/distinct under the hood deals with efficient representations of constrained variables all at once using sets, distincto uses the disequality operator != in a pretty simple manner.