--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/stack-subtype.agda.replaced	Tue Sep 08 18:38:08 2020 +0900
@@ -0,0 +1,123 @@
+open import Level hiding (lift)
+open import Data.Maybe
+open import Data.Product
+open import Data.Nat hiding (suc)
+open import Function
+
+module stack-subtype (A : Set) where
+
+-- data definitions
+
+data Element (a : Set) : Set where
+  cons : a @$\rightarrow$@ Maybe (Element a) @$\rightarrow$@ Element a
+
+datum : {a : Set} @$\rightarrow$@ Element a @$\rightarrow$@ a
+datum (cons a _) = a
+
+next : {a : Set} @$\rightarrow$@ Element a @$\rightarrow$@ Maybe (Element a)
+next (cons _ n) = n
+
+record SingleLinkedStack (a : Set) : Set where
+  field
+    top : Maybe (Element a)
+open SingleLinkedStack
+
+record Context : Set where
+  field
+    -- fields for concrete data segments
+    n       : @$\mathbb{N}$@ 
+    -- fields for stack
+    element : Maybe A
+
+
+
+
+
+open import subtype Context as N
+
+instance
+  ContextIsDataSegment : N.DataSegment Context
+  ContextIsDataSegment = record {get = (\c @$\rightarrow$@ c) ; set = (\_ c @$\rightarrow$@ c)}
+
+
+record Meta  : Set@$\_{1}$@ where
+  field
+    -- context as set of data segments
+    context : Context
+    stack   : SingleLinkedStack A  
+    nextCS  : N.CodeSegment Context Context
+    
+
+    
+
+open import subtype Meta as M
+
+instance
+  MetaIncludeContext : M.DataSegment Context
+  MetaIncludeContext = record { get = Meta.context
+                              ; set = (\m c @$\rightarrow$@ record m {context = c}) }
+
+  MetaIsMetaDataSegment : M.DataSegment Meta
+  MetaIsMetaDataSegment  = record { get = (\m @$\rightarrow$@ m) ; set = (\_ m @$\rightarrow$@ m) }
+
+
+liftMeta : {X Y : Set} {{_ : M.DataSegment X}} {{_ : M.DataSegment Y}} @$\rightarrow$@ N.CodeSegment X Y @$\rightarrow$@ M.CodeSegment X Y
+liftMeta (N.cs f) = M.cs f
+
+liftContext : {X Y : Set} {{_ : N.DataSegment X}} {{_ : N.DataSegment Y}} @$\rightarrow$@ N.CodeSegment X Y @$\rightarrow$@ N.CodeSegment Context Context
+liftContext {{x}} {{y}} (N.cs f) = N.cs (\c @$\rightarrow$@ N.DataSegment.set y c (f (N.DataSegment.get x c)))
+ 
+-- definition based from Gears(209:5708390a9d88) src/parallel_execution
+
+emptySingleLinkedStack : SingleLinkedStack A
+emptySingleLinkedStack = record {top = nothing}
+
+
+pushSingleLinkedStack : Meta @$\rightarrow$@ Meta
+pushSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (push s e) })
+  where
+    n = Meta.nextCS m
+    s = Meta.stack  m
+    e = Context.element (Meta.context m)
+    push : SingleLinkedStack A @$\rightarrow$@ Maybe A @$\rightarrow$@ SingleLinkedStack A
+    push s nothing  = s
+    push s (just x) = record {top = just (cons x (top s))}
+
+
+
+popSingleLinkedStack : Meta @$\rightarrow$@ Meta
+popSingleLinkedStack m = M.exec (liftMeta n) (record m {stack = (st m) ; context = record con {element = (elem m)}})
+  where
+    n = Meta.nextCS m
+    con  = Meta.context m
+    elem : Meta @$\rightarrow$@ Maybe A
+    elem record {stack = record { top = (just (cons x _)) }} = just x
+    elem record {stack = record { top = nothing           }} = nothing
+    st : Meta @$\rightarrow$@ SingleLinkedStack A
+    st record {stack = record { top = (just (cons _ s)) }} = record {top = s}
+    st record {stack = record { top = nothing           }} = record {top = nothing}
+   
+
+
+
+pushSingleLinkedStackCS : M.CodeSegment Meta Meta
+pushSingleLinkedStackCS = M.cs pushSingleLinkedStack
+
+popSingleLinkedStackCS : M.CodeSegment Meta Meta
+popSingleLinkedStackCS = M.cs popSingleLinkedStack
+
+
+-- for sample
+
+firstContext : Context
+firstContext = record {element = nothing ; n = 0}
+
+
+firstMeta : Meta 
+firstMeta = record { context = firstContext
+                   ; stack = emptySingleLinkedStack
+                   ; nextCS = (N.cs (\m @$\rightarrow$@ m))
+                   }
+
+
+