Task 3 done

3or4/Interpreter/Self.hs

@@ -12,10 +12,6 @@ mapExp = parse
   \ ; Cons(x,xs) -> Cons(f x, map xs)\
   \ }"
 
-substBrExp :: Exp
-substBrExp = parse
-  "rec substBr = \\x. "
-
 ifExp :: Exp
 ifExp = parse
   "\\b. \\t. \\f. case b of \
@@ -24,7 +20,27 @@ ifExp = parse
   \ }"
 
 equalExp :: Exp
-equalExp = parse ""
+equalExp = parse
+  "rec equal = \\m. \\n. case m of \
+  \ { Zero() -> case n of { Zero() -> True(); Suc(n) -> False() } \
+  \ ; Suc(m) -> case n of { Zero() -> False(); Suc(n) -> equal m n }\
+  \ }"
+
+elemExp :: Exp
+elemExp =
+  subst (Variable "equal") equalExp .
+  subst (Variable "if") ifExp $ parse
+  "\\x. rec elem = \\l. case l of \
+  \ { Nil() -> False() \
+  \ ; Cons(v,vs) -> if (equal x v) True() (elem vs)\ 
+  \ }"
+
+substBrExp :: Exp
+substBrExp =
+  subst (Variable "elem") elemExp $ parse
+  "\\subst. \\var. \\b. case b of \
+  \ { Branch(c,vs,e') -> if (elem var vs) Branch(c,vs,e') Branch(c,vs, subst e') \
+  \ }"
 
 substExp :: Exp
 substExp =
@@ -38,5 +54,5 @@ substExp =
         \ ; Var(x) -> if (equal x var) e Var(x) \
         \ ; Const(c,es) -> Const(c, map subst es) \
         \ ; Rec(x, e') -> if (equal x var) Rec(x,e') Rec(x,subst e')\
-        \ ; Case(e',bs) -> _ \
+        \ ; Case(e',bs) -> Case(subst e', map (substBr subst var) bs) \
         \ }"