Add more homework solutions.

HomeworkTwelve.idr

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+module HomeworkTwelve
+%default total
+
+data Op = Push Nat | Pop | Add
+
+Stack : Type 
+Stack = List Nat
+
+data Step : Stack -> Op -> Stack -> Type where
+  SPush : Step xs (Push n) (n::xs)
+  SPop : Step (n::xs) Pop xs
+  SAdd : Step (n1::n2::xs) Add ((n1+n2)::xs)
+
+Ops : Type
+Ops = List Op
+
+data Steps : Stack -> Ops -> Stack -> Type where
+  SEmpty : Steps xs [] xs
+  SSeq : Step xs o ys -> Steps ys os zs -> Steps xs (o::os) zs
+
+stepsEx : Steps [] [Push 3, Push 5, Add] [8]
+stepsEx = SSeq SPush (SSeq SPush (SSeq SAdd SEmpty))