Despite major steps forward, there are still many obstacles to overcome to make resource analysis technologies available to developers. 1. In OCaml programs this means using vectors or mutable fields in records. On the one hand, typed functional programs are particularly well-suited for automatic resource-bound analysis since the use of pattern matching and recursion often results in a relatively regular code structure. (3 pts) Write a function even count fr : int list -> int such that it returns the number of even in-tegers found in the input list. There are no "forward prototypes" (as seen in languages descended from C) in OCaml but there is a special syntax for defining a set of two or more mutually recursive functions, like odd and even: # let rec even n = match n with | 0 -> true | x -> odd (x-1) and odd n = match n with | 0 -> false | x -> even (x-1) ;; That can be done with tail recursion or tail call. OCaml's Hashtbl module offers two kinds of hash tables. But there is a special syntax for defining a set of two or more mutually recursive functions. Chapter 2 The Basics 2.1 Basic Types and Expressions OCaml is a strongly typed functional language. Curly braces, integer math, not whitespace sensitive, recursion, the whole nine yards. You can also use similar syntax for writing mutually recursive class definitions and modules. For this project I'll be using the OCaml language. Hi, I'm trying to build a binary tree. Pretend that OCaml does have functions of more than one argument and pretend that + is one of them. We can write mutually recursive functions by putting them togeterh with a "and" keyword. Patterns of Recursion Forward Recursion For the problems in this section, you must use forward recursion. Despite major steps forward, there are still many obstacles to overcome to make resource analysis available to developers. For this kind of use of pointers, the Pascal's instruction: x^.label := val (where x is a value of a record having a label field) corresponds to the OCaml construct x.label <- val (where x is a value of a record having a label mutable field). While implementing a recursive function, it often happens that we must resort to a separate helper function to handle the actual recursion. The first (and simpler to use) is for clients who are happy to use OCaml's built-in hash function. On the one hand, typed functional programs are particularly well-suited for automatic resource-bound analysis since the use of pattern matching and recursion often results in a relatively regular code structure. For the following exercises, consult the documentation of Hashtbl. Every node has two child nodes: root a b a1 a2 b1 b2 (a, b) are child nodes of root; (a1, a2) are child nodes of a, (b1, b2) are child nodes of b, etc. If only we could store the state, or the result of the current operation and pass it forward to the next recursion. List.map has the signature ('a -> 'b) -> 'a list -> 'b list which in English is a function that takes a function (we'll call this the mapping function) from one type (namely 'a) to another type (namely 'b) and a list of the first type. I'm having trouble converting the function into a tail-recursive one since to build the current Node in the tree I need to call the function twice for both child nodes. First note that (most) any infix operator in OCaml can also be used as a prefix operator by surrounding the operator with parens and putting it in a prefix position, like so: 2 + 3 = (+) 2 3. tail recursion ocaml, ocaml documentation: List.Map. 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