module Quox.Thin.Comp

import public Quox.Thin.Base
import public Quox.Thin.View
import Data.Singleton

%default total

||| inductive definition of OPE composition
public export
data Comp : (l : OPE n p mask1) -> (r : OPE m n mask2) ->
            (res : OPE m p mask3) -> Type where
  [search l r]
  StopZ : Comp Stop Stop Stop
  DropZ : Comp a b c -> Comp (Drop a Refl) b (Drop c Refl)
  KeepZ : Comp a b c -> Comp (Keep a Refl) (Keep b Refl) (Keep c Refl)
  KDZ   : Comp a b c -> Comp (Keep a Refl) (Drop b Refl) (Drop c Refl)

public export
record CompResult (ope1 : OPE n p mask1) (ope2 : OPE m n mask2) where
  constructor MkComp
  {mask : Nat}
  {0 ope : OPE m p mask}
  0 comp : Comp ope1 ope2 ope
%name CompResult comp

||| compose two OPEs, if the middle scope size is already known at runtime
export
comp' : {n, p, mask1, mask2 : Nat} ->
        (0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
        CompResult ope1 ope2
comp' ope1 ope2 with %syntactic (view ope1) | (view ope2)
  comp' Stop Stop | StopV | StopV =
    MkComp StopZ
  comp' (Drop ope1 Refl) ope2 | DropV _ ope1 | _ =
    MkComp $ DropZ (comp' ope1 ope2).comp
  comp' (Keep ope1 Refl) (Drop ope2 Refl) | KeepV _ ope1 | DropV _ ope2 =
    MkComp $ KDZ (comp' ope1 ope2).comp
  comp' (Keep ope1 Refl) (Keep ope2 Refl) | KeepV _ ope1 | KeepV _ ope2 =
    MkComp $ KeepZ (comp' ope1 ope2).comp

||| compose two OPEs, after recomputing the middle scope size using `appOpe`
export
comp : {p, mask1, mask2 : Nat} ->
       (0 ope1 : OPE n p mask1) -> (0 ope2 : OPE m n mask2) ->
       CompResult ope1 ope2
comp ope1 ope2 = let Val n = appOpe p ope1 in comp' ope1 ope2

-- [todo] is there a quick way to compute the mask of comp?

export
0 (.) : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
        OPE m p (comp ope1 ope2).mask
ope1 . ope2 = (comp ope1 ope2).ope

-- export
-- 0 compMask : (ope1 : OPE n p mask1) -> (ope2 : OPE m n mask2) ->
--              (ope3 : OPE m p mask3) -> Comp ope1 ope2 ope3 ->
--              mask3 = ?aaa