No more if

3or4/Interpreter/Self.hs

@@ -14,13 +14,6 @@ mapExp = parse
   \ ; Cons(x,xs) -> Cons(f x, map xs)\
   \ }"
 
-ifExp :: Exp
-ifExp = parse
-  "\\b. \\t. \\f. case b of \
-  \ { True() -> t \
-  \ ; False() -> f \
-  \ }"
-
 equalExp :: Exp
 equalExp = parse
   "rec equal = \\m. \\n. case m of \
@@ -30,33 +23,36 @@ equalExp = parse
 
 elemExp :: Exp
 elemExp =
-  subst (Variable "equal") equalExp .
-  subst (Variable "if") ifExp $ parse
+  subst (Variable "equal") equalExp $ parse
   "\\x. rec elem = \\l. case l of \
   \ { Nil() -> False() \
-  \ ; Cons(v,vs) -> if (equal x v) True() (elem vs)\ 
+  \ ; Cons(v,vs) -> case (equal x v) of { True() -> True(); False() -> (elem vs) } \
   \ }"
 
 substBrExp :: Exp
 substBrExp =
-  subst (Variable "if") ifExp .
   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') \
+  \ { Branch(c,vs,e') -> case (elem var vs) of \
+  \   { True() -> Branch(c,vs,e') \
+  \   ; False() -> Branch(c,vs, subst e') \
+  \   } \
   \ }"
 
 substExp :: Exp
 substExp =
-  subst (Variable "if") ifExp .
   subst (Variable "equal") equalExp .
   subst (Variable "substBr") substBrExp .
   subst (Variable "map") mapExp $ parse
         "\\var. \\e. rec subst = \\x. case x of\
         \ { Apply(e1,e2) -> Apply(subst e1, subst e2) \
-        \ ; Lambda(x,y) -> if (equal x var) Lambda(x,y) Lambda(x,subst y) \
-        \ ; Var(x) -> if (equal x var) e Var(x) \
+        \ ; Lambda(x,y) -> case (equal x var) of \
+        \     { True() -> Lambda(x,y) \
+        \     ; False() -> Lambda(x,subst y) \
+        \     } \
+        \ ; Var(x) -> case (equal x var) of {True() -> e; False() -> Var(x)} \
         \ ; Const(c,es) -> Const(c, map subst es) \
-        \ ; Rec(x, e') -> if (equal x var) Rec(x,e') Rec(x,subst e')\
+        \ ; Rec(x, e') -> case (equal x var) of {True() -> Rec(x,e'); False() -> Rec(x,subst e')}\
         \ ; Case(e',bs) -> Case(subst e', map (substBr subst var) bs) \
         \ }"
 
@@ -64,7 +60,6 @@ substExp =
 
 lookupExp :: Exp
 lookupExp =
-  subst (Variable "if") ifExp .
   subst (Variable "equal") equalExp $ parse
   "\\c. rec lookup = \\xs. case xs of \
   \ { Cons(b,bs) -> \