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.
The accessors current, promised, and 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 always, eventually, until, and 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, conj and disj.
(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))
;; => ()
The macro next is defined to facilitate the creation of delayed goals, analogous to Zzz, and the utility functions promised, current and advance help with the dotted-lists created by these promises. The miniKanren wrappers run, run*, pull, take and 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 disj or 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 delays.
(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
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