A first experiment in doing temporal logic programming in miniKanren, written as an extension of Jason Hemann and Daniel P. Friedman's microKanren.
A single temporal primitive
next is implemented using delayed streams (Scheme promises), alongside immature and mature ones. Goals defined with
next are enclosed in promises, and shunted right and combined during miniKanren's interleaving. This allows goals to refer to external, time-dependent (stateful) resources, with the guaranty that goals at the same "time" increment (i.e., nested levels of
next) will be created simultaneously.
advance are defined for working with this extended definition of streams. Here is an example using the miniKanren wrappers, which also have been extended.
(define *db* 1) (define (db-now-or-latero x) (disj (== x *db*) (next (db-now-or-latero x)))) (define r (run* (q) (db-now-or-latero q))) r ;; => '(1 . #<promise>) (current r) ;; => '(1) (promised r) ;; => #<promise> (set! *db* 2) (advance r) ;; => '(2 . #<promise>)
next is indended to be used with domain-specific definitions of failure/constraint to define a more complete temporal logic framework. The file
ftl.scm uses failure as negation to implement the operators
precedes from first-order temporal logic. So the above example could be rewritten:
(define (db-now-or-later x) (always (== x *db*)))
and another example (which would of course be more interesting with constraints):
(define *db* 1) (run* (q) (fresh (a b) (== q 'success) (precedes (== 3 *db*) (== 4 *db*))))
Here is a low-level example showing the interaction between promises,
(define (==next a b) (lambda (s/c) (delay ((== a b) s/c)))) (define empty-state '(() . 0)) ((call/fresh (lambda (q) (disj (== q 4) (next (== q 5)))) ) empty-state) ;; => ((((#(0) . 4)) . 1) . #<promise>) (force (cdr ((call/fresh (lambda (q) (disj (== q 4) (next (== q 5)))) ) empty-state))) ;; => ((((#(0) . 5)) . 1)) ((call/fresh (lambda (q) (conj (== q 4) (next (== q 5)))) ) empty-state) ;; => #<promise> (force ((call/fresh (lambda (q) (conj (== q 4) (next (== q 5))))) empty-state)) ;; => ()
next is defined to facilitate the creation of delayed goals, analogous to
Zzz, and the utility functions
advance help with the dotted-lists created by these promises. The miniKanren wrappers
take-all are appropriately extended.
(define $0 (run* (q) (disj (== q 4) (next (== q 5))))) $0 ;; => (4 . #<promise>) (current $0) ;; => (4) (promised $0) ;; => #<promise> (advance $0) ;; => (5)
Disjunction is simple: in successive calls to
mplus, promises are shunted right and grouped together in a single promise.
;; equivalent (disj (next (== #(0) 6)) (disj (== #(0) 5) (next (== #(0) 7)))) (disj (== #(0) 5) (next (disj (== #(0) 6) (== #(0) 7))))
Conjunction is a little more complicated as soon as we allow for recursive promises. In
(conj g1 g2), we want the promises created by g1 and g2 to be forced at the same time, while any recursive promises created by those two groups of promises to be delayed to yet a further time. Simultaneity between two delayed predicates is defined as being nested in an equivalent number of
(define $1 (run* (q) (next (== q 4)) (disj (next (next (== q 5))) (next (== q 4))))) $1 ;; => #<promise> (advance $1) ;; => (4 . #<promise>) (advance (advance $1)) ;; => () ;; a bit impure... (define (inco x) (let r ((n 0)) (disj (== x n) (next (r (+ n 1)))))) (define $2 (run* (q) (fresh (a b) (== (list a b) q) (conj (inco a) (inco b))))) $2 ;; => ((0 0) . #<promise>) (advance $2) ;; => ((0 1) (1 0) (1 1) . #<promise>) (advance (advance $2)) ;; => ((1 2) (2 0) (2 1) (2 2) (0 2) . #<promise>) (advance (advance (advance $2))) ;; => ((0 3) (2 3) (3 0) (3 1) (3 2) (3 3) (1 3) . #<promise>)
Copyright (C) 2013 Jason Hemann and Daniel P. Friedman
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.