Everything.

09-tidbit/10.rkt

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+#lang racket
+;; example of currying: turning n-ary functions into unary functions
+#;((λ (a b c) (- (string-length a) (/ b c))) "foo" 8 2)
+#;((((λ (a) (λ (b) (λ (c) (- (string-length a) (/ b c)))))
+     "foo")
+    8)
+   2)
+
+;; A LExpr (Lambda expression) is one of:
+;; - Symbol <- identifier
+;; - (list 'λ (list Symbol) LExpr) <- function
+;; - (list LExpr LExpr) <- application
+
+;; An ILExpr (Index Lambda expression) is one of:
+;; - Nat
+;; - (list 'λ ILExpr)
+;; - (list ILExpr ILExpr)
+
+(define sample-lexpr
+  '((λ (x)
+      (λ (y)
+        (λ (x)
+          (y x))))
+    (λ (x) x)))
+
+(define sample-ilexpr
+  '((λ (λ (λ (1 0))))
+    (λ 0)))
+
+;; '()
+#;(;; '()
+   (λ (x) ;; '(x)
+     (λ (y) ;; '(y x)
+       (λ (x);; '(x y x)
+         (y x))))
+   ;; '()
+   (λ (x) ;; '(x)
+     x))
+
+#;((λ (λ (λ (1 0))))
+   (λ 0))
+
+;; indexify : LExpr -> ILExpr
+;; Make an index expression out of the lexpr
+(define (indexify lexpr)
+  (define (indexify/args arguments lexpr)
+    (match lexpr
+      [(? symbol? identifier)
+       (or (index-of arguments identifier)
+           (error "unbound identifier"))]
+      [(list 'λ (list (? symbol? argument)) body)
+       (list 'λ (indexify/args (cons argument arguments) body))]
+      [(list func arg)
+       (list (indexify/args arguments func)
+             (indexify/args arguments arg))]))
+  (indexify/args '() lexpr))
+
+(equal? (indexify sample-lexpr) sample-ilexpr)
+(indexify 'x)