Added more math operations, generalized and simplified existing math operations, added some list operations for the lisp lists

lib/ast.ml

@@ -25,6 +25,40 @@ type lisp_val =
  recursive with lisp_val *)
 and environment = (string, lisp_val) Hashtbl.t list
 
+(* It is clear that we need some primitives for working with the lisp
+   data structures.
+
+   For example, the LCons and LNil values, together, form a linked list.
+   This is the intended form of all source code in lisp, yet because
+   we are using our own implementation of a linked list instead of
+   ocaml's List, we can not use its many functions.
+
+   It may be tempting to switch to a different implementation.
+   Remember however, that classic lisp semantics allow for the
+   CDR component of a cons cell (the part that would point to the
+   next member) to be of a type other than the list itself.
+ *)
+
+let reverse vs =
+  let rec aux prev = function
+    | LNil -> prev
+    | LCons (v, next) -> aux (LCons (v, prev)) next
+    | _ -> invalid_arg "cannot reverse non-list!"
+  in aux LNil vs
+
+let map f =
+  let rec aux accum = function
+    | LNil -> reverse accum
+    | LCons (v, next) -> aux (LCons (f v, accum)) next
+    | _ -> invalid_arg "cannot map over non-list!"
+  in aux LNil
+
+let reduce init f =
+  let rec aux accum = function
+    | LNil -> accum
+    | LCons (v, next) -> aux (f accum v) next
+    | _ -> invalid_arg "cannot reduce over non-list!"
+  in aux init
 
 let rec dbg_print_one v =
   let pf = Printf.sprintf in