Move for next

2025-12-08 15:21:42 +01:00
parent 11f5ef158c
commit a8c41dfd7d
15 changed files with 30 additions and 0 deletions
--- a/3or4or6/Interpreter/Self.hs
+++ b/3or4or6/Interpreter/Self.hs
@ -0,0 +1,99 @@
+{-# Language LambdaCase, Strict #-}
+
+module Interpreter.Self where
+
+import Chi
+import Interpreter.Haskell
+
+-- Task 3
+
+mapExp :: Exp
+mapExp = parse
+  "\\f. rec map = \\xs. case xs of \
+  \ { Nil() -> Nil() \
+  \ ; Cons(x,xs) -> Cons(f x, map xs)\
+  \ }"
+
+equalExp :: Exp
+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 $ parse
+  "\\x. rec elem = \\l. case l of \
+  \ { Nil() -> False() \
+  \ ; Cons(v,vs) -> case (equal x v) of { True() -> True(); False() -> (elem vs) } \
+  \ }"
+
+substBrExp :: Exp
+substBrExp =
+  subst (Variable "elem") elemExp $ parse
+  "\\subst. \\var. \\b. case b of \
+  \ { 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 "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) -> 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') -> 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) \
+        \ }"
+
+-- Task 4
+
+lookupExp :: Exp
+lookupExp =
+  subst (Variable "equal") equalExp $ parse
+  "\\c. rec lookup = \\xs. case xs of \
+  \ { Cons(b,bs) -> \
+  \     case b of \
+  \       { Branch(c', xs, e') -> case (equal c c') of \
+  \         { True() -> Pair(xs,e') \
+  \         ; False() -> lookup bs \
+  \         } \
+  \       } \
+  \ }"
+
+substsExp :: Exp
+substsExp =
+  subst (Variable "subst") substExp $ parse
+  "rec substs = \\xs. \\vs. \\e'. case xs of \
+  \ { Nil() -> case vs of { Nil() -> e' } \
+  \ ; Cons(x,xs) -> case vs of { Cons(v,vs) -> subst x v (substs xs vs e') }\
+  \ }"
+
+evalExp :: Exp
+evalExp =
+  subst (Variable "map") mapExp .
+  subst (Variable "lookup") lookupExp .
+  subst (Variable "substs") substsExp .
+  subst (Variable "subst") substExp $ parse
+  "rec eval = \\e. case e of \
+  \ { Lambda(x,e) -> Lambda(x,e) \
+  \ ; Apply(e1,e2) -> case eval e1 of \
+  \    { Lambda(x,e) -> eval (subst x (eval e2) e) } \
+  \ ; Rec(x,e) -> eval (subst x Rec(x,e) e) \
+  \ ; Const(c,es) -> Const(c, map eval es) \
+  \ ; Case(e,bs) -> case eval e of \
+  \     { Const(c,vs) -> case lookup c bs of \
+  \        { Pair(xs,e') -> eval (substs xs vs e') } \
+  \     } \
+  \ ; Var(x) -> Var(x) \
+  \ }"