### diff agda/deltaM.agda @ 89:5411ce26d525

Defining DeltaM in Agda...
author Yasutaka Higa Mon, 19 Jan 2015 11:48:41 +0900 55d11ce7e223
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```--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/agda/deltaM.agda	Mon Jan 19 11:48:41 2015 +0900
@@ -0,0 +1,64 @@
+open import Level
+
+open import delta
+open import delta.functor
+open import nat
+open import laws
+
+module deltaM where
+
+-- DeltaM definitions
+
+data DeltaM {l : Level}
+            (M : {l' : Level} -> Set l' -> Set l')
+            {functorM : {l' : Level} -> Functor {l'} M}
+            {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+            (A : Set l)
+            : Set l where
+   deltaM : Delta (M A) -> DeltaM M {functorM} {monadM} A
+
+
+-- DeltaM utils
+
+headDeltaM : {l : Level} {A : Set l}
+             {M : {l' : Level} -> Set l' -> Set l'}
+             {functorM : {l' : Level} -> Functor {l'} M}
+             {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+             -> DeltaM M {functorM} {monadM} A -> M A
+headDeltaM (deltaM (mono x))    = x
+headDeltaM (deltaM (delta x _)) = x
+
+tailDeltaM :  {l : Level} {A : Set l}
+             {M : {l' : Level} -> Set l' -> Set l'}
+             {functorM : {l' : Level} -> Functor {l'} M}
+             {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+             -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
+tailDeltaM (deltaM (mono x))    = deltaM (mono x)
+tailDeltaM (deltaM (delta _ d)) = deltaM d
+
+appendDeltaM : {l : Level} {A : Set l}
+             {M : {l' : Level} -> Set l' -> Set l'}
+             {functorM : {l' : Level} -> Functor {l'} M}
+             {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+             -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} A
+appendDeltaM (deltaM d) (deltaM dd) = deltaM (deltaAppend d dd)
+
+
+checkOut : {l : Level} {A : Set l}
+           {M : {l' : Level} -> Set l' -> Set l'}
+           {functorM : {l' : Level} -> Functor {l'} M}
+           {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+         -> Nat -> DeltaM M {functorM} {monadM} A -> M A
+checkOut O     (deltaM (mono x))    = x
+checkOut O     (deltaM (delta x _)) = x
+checkOut (S n) (deltaM (mono x))    = x
+checkOut {l} {A} {M} {functorM} {monadM} (S n) (deltaM (delta _ d)) = checkOut {l} {A} {M} {functorM} {monadM} n (deltaM d)
+
+{-
+deltaM-fmap : {l ll : Level} {A : Set l} {B : Set ll}
+           {M : {l' : Level} -> Set l' -> Set l'}
+           {functorM : {l' : Level} -> Functor {l'} M}
+           {monadM : {l' : Level} {A : Set l'} -> Monad {l'} {A} M functorM}
+           -> (A -> B) -> DeltaM M {functorM} {monadM} A -> DeltaM M {functorM} {monadM} B
+deltaM-fmap {l} {ll} {A} {B} {M} {functorM} f (deltaM d) = deltaM (Functor.fmap delta-is-functor (Functor.fmap functorM f) d)
+-}
\ No newline at end of file```