scala - Composing type-level functions with implicit witnesses -

i experimenting rather complex type-level calculations. there, have type tags (say, a, b, , c), , functions working on them, represented implicit witnesses path-dependent result types:

class class b class c  trait f1[t] { type result } trait f2[t] { type result }  implicit object f1ofa extends f1[a] { type result = b } implicit object f2ofb extends f2[b] { type result = c }  trait composed[t] { type result } 

in course of calculations, when "implementing" composed, need make use of fact can, given above code, in principle transform a c (in example, need composition, there's more things involved).

however, don't know how express composition, limited restriction implicits not transitively applied; following code fails "implicit not found":

implicit def composed1[x](implicit f2dotf1ofx: f2[f1[x]]): composed[x] =     new composed[x] { type result = f2dotf1ofx.result }  implicitly[composed[c]] 

what tried write following:

implicit def composed2[x](implicit f1ofx: f1[x], f2oflast: f2[f1ofx.result]): composed[x] =   new composed[x] { type result = f2oflast.result } 

this of course failed because there used f1oflast in same parameter list defined. if not implicit parameter, write

implicit def composed3a[x](f1ofx: f1[x])(f2oflast: f2[f1ofx.result]): composed[x] =    new composed[x] { type result = f2oflast.result } 

but not possible using 2 implicit parameter lists, since disallowed language.

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in short: how can witness f2[f1[x]] in above examples? if necessary, change way of writing type-level functions, have not yet found way express them.

you use type parameter , require f1ofx.result that:

implicit def composed4[x, y](implicit f1ofx: f1[x] { type result = y },   f2oflast: f2[y]): composed[x] =     new composed[x] { type result = f2oflast.result }