Exercises

Consider the following curried function:

fun composeUnaryIntOps (f:int -> int) (g:int -> int) = fn x => f (g x);

Using this function along with anonymous functions and (possibly named) higher-order functions you devise yourself, define:

• A function negateAndInc that negates and then adds 1 to its single parameter.
• A function addThenMult with two parameters a and m, that produces a single-parameter function that first adds a and then multiplies m to its parameter.
• A function twice that takes a binary function binOp and an operand value opVal, and returns a single-parameter function that takes a value k and
  1. Applies binOp to k and opVal
  2. Applies binOp to the result and opVal
• A function that, given two unary functions, applies them to alternating elements of an integer list. In other words, it should apply f to the first element, g to the second element, f to the third element, etc.
• Rewrite the answer to the previous problem using the reduce function from lecture.