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skio.scm
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skio.scm
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;;skio.scm
;;utc20170530
;;jpt4
;;Relational SKI combinator calculus interpreter in miniKanren
;;Chez Scheme v9.4-1
(load "miniKanren-with-symbolic-constraints/mk.scm")
;;the universe of variables
(define (varo i)
(conde
[(symbolo i)
(=/= 'I i) (=/= 'K i) (=/= 'S i)]))
;;and combinators
(define (combo i)
(conde
[(== 'I i)]
[(== 'K i)]
[(== 'S i)]))
;;terms thereof
(define (termo i)
(conde
[(varo i)]
[(combo i)]
[(fresh (a d)
(== `(,a ,d) i)
(termo a) (termo d))]))
;;coerce left association in expressions
(define (laso i o)
(conde
[(termo i) (== i o)]
[(fresh (a b resa resb)
(== `(,a ,b) i)
(laso a resa) (laso b resb) (== `(,resa ,resb) o))]
[(fresh (a b c resa resb resc)
(== `(,a ,b ,c) i)
(laso a resa) (laso b resb) (laso c resc)
(== `((,resa ,resb) ,resc) o))]
[(fresh (a b c resa resb resc)
(== `(,a ,b . ,c) i) (=/= '() c)
(laso a resa) (laso b resb) (laso `((,resa ,resb) . ,c) o)
)]
))
;;combinator reductions
(define (io i o)
(fresh (x)
(conde
[(== `(I ,x) i) (== x o)])))
(define (ko i o)
(fresh (x y)
(conde
[(== `((K ,x) ,y) i) (== x o)])))
(define (so i o)
(fresh (x y z)
(conde
[(== `(((S ,x) ,y) ,z) i) (== `((,x ,z) (,y ,z)) o)])))
;;core interpreter
(define (skio-core i t o)
(fresh (a b c t0 t1 t2 resa resb rest res diag)
(conde
[(== `(,t1 (,t1 ,t2)) t) (== i t1) (== i o)]
[(== `(,t2 (,t1 ,t0)) t) (=/= t2 t1)
(conde
[(combo i) (== i o)]
[(varo i) (== i o)]
[(io i res) (== `(,res (,t2 ,t1)) rest) (skio-core res rest o)]
[(ko i res) (== `(,res (,t2 ,t1)) rest) (skio-core res rest o)]
[(so i res) (== `(,res (,t2 ,t1)) rest) (skio-core res rest o)]
[(== `(,a ,b) i)
(skio-core a t resa) (skio-core b t resb)
(== `(,resa ,resb) res) (== `(,res (,t2 ,t1)) rest)
(skio-core res rest o)]
)])))
;;interpreter interfaces - note, contaminates mK relational logic with Scheme
;input evaluation (forward interpretation)
(define (skio exp num)
(let* ([t0 (gensym)] [t1 (gensym)] [t2 (gensym)]
[init (list t2 (list t1 t0))])
(run num (q) (fresh (i)
(laso exp i) (skio-core i init q)))))
;input synthesis (reverse interpretation) - no laso preprocessing
(define (skio-syn exp num)
(let* ([t0 (gensym)] [t1 (gensym)] [t2 (gensym)]
[init (list t2 (list t1 t0))])
(run num (q) (skio-core q init exp))))
;;Diagnostics instrumented interpreter core
(define (skio-core-diag i t o)
(fresh (a b c t0 t1 t2 resa resb rest res diag)
(conde
[(== `(,t1 (,t1 ,t2)) t) (== i t1) (== i o)
#;(== `(stop i=,i a=,a b=,b t=,t) o)]
[(== `(,t2 (,t1 ,t0)) t) (=/= t2 t1)
#;(== `(go i=,i t=,t t2=,t2 t1=,t1 t0=,t0) o)
(conde
[(combo i) (== i o)
#;(== `(combo i=,i) o)]
[(varo i) (== i o)
#;(== `(varo i=,i) o)]
[(io i res) (== `(,res (,t2 ,t1)) rest) (skio-core-diag res rest o)
#;(skio-core-diag res rest diag)
#;(== `(io i=,i res=,res t=,t rest=,rest diag=,diag) o)]
[(ko i res) (== `(,res (,t2 ,t1)) rest) (skio-core-diag res rest o)
#;(skio-core-diag res rest diag)
#;(== `(ko i=,i res=,res t=,t rest=,rest diag=,diag) o)]
[(so i res) (== `(,res (,t2 ,t1)) rest) (skio-core-diag res rest o)
#;(skio-core-diag res rest diag)
#;(== `(so i=,i res=,res t=,t rest=,rest diag=,diag) o)]
[(== `(,a ,b) i)
(skio-core-diag a t resa) (skio-core-diag b t resb)
(== `(,resa ,resb) res) (== `(,res (,t2 ,t1)) rest)
(skio-core-diag res rest o)
#;(skio-core-diag res rest diag)
#;(== `(pair i=,i a=,a b=,b t=,t resa=,resa resb=,resb res=,res
rest=,rest diag=,diag) o)]
)])))
;;;UNDER CONSTRUCTION FROM THIS POINT ONWARDS
;;record entire derivation history for a inspection
(define (skio-hist i t tls o)
(fresh (a b c t0 t1 t2 resa resb rest res diag)
(conde
[(== `(,a (,a ,b)) t) (== i a) (== i o)
#;(== `(stop i=,i a=,a b=,b t=,t t=,t) o)]
[(== `(,t2 (,t1 ,t0)) t) (=/= t2 t1)
#;(== `(go i=,i t=,t t2=,t2 t1=,t1 t0=,t0) o)
(conde
[(combo i) (== `(,i ,tls) rest) (skio-hist i rest t o)]
[(varo i) (== `(,i ,t) rest) (skio-hist i rest t o)]
[(strict-io i res) (== `(,res (,t2 ,t1)) rest) (skio-hist res rest t o)
#;(skio-hist res rest t diag)
#;(== `(so i=,i res=,res t=,t rest=,rest t=,t diag=,diag) o)]
[(strict-ko i res) (== `(,res (,t2 ,t1)) rest) #;(skio-hist res rest t o)
(skio-hist res rest t diag)
(== `(so i=,i res=,res t=,t rest=,rest t=,t diag=,diag) o)]
[(strict-so i res) (== `(,res (,t2 ,t1)) rest) (skio-hist res rest t o)
#;(skio-hist res rest t diag)
#;(== `(so i=,i res=,res t=,t rest=,rest t=,t diag=,diag) o)]
[(== `(,a ,b) i) (skio-hist a d t resa) (skio-hist b d t resb)
(== `(,resa ,resb) res) (== `(,res (,t2 ,t1)) rest) #;(skio-hist res rest t o)
#;(skio-hist res rest t diag)
(== `(pair i=,i a=,a b=,b resa=,resa resb=,resb res=,res rest=,rest t=,t t=,t diag=,diag) o)]
#; [(== `((,a ,b) ,c) i)
(skio-hist b res) (skio-hist `((,a ,res) ,c) o)]
#; [(== `(,a (,b ,c)) i)
(skio-hist b res) (skio-hist `(,a (,b ,c)) o)]
)])))
;;alternative interpreter, does better at synthesis than evaluation
(define (skio-alt i o)
(fresh (a b resa resb res)
(conde
[(irredexo i) (== i o)]
[(conde
[(io i res) (skio-alt res o)]
[(ko i res) (skio-alt res o)]
[(so i res) (skio-alt res o)]
[(== `(,a ,b) i) (skio-alt a resa) (skio-alt b resb)
(== `(,resa ,resb) res) (=/= i res) (skio-alt res o)]
[(== `(,a ,b) i) (skio-alt a resa) (skio-alt b resb)
(== `(,resa ,resb) res) (== i res) (== i o)]
)])))
;;irreducible expressions for skio-alt
(define (irredexo i)
(fresh (a b)
(conde
[(varo i)]
[(combo i)]
[(== `(K ,a) i) (irredexo a)]
[(== `(S ,a) i) (irredexo a)]
[(== `((S ,a) ,b) i) (irredexo a) (irredexo b)]
)))