Programming Languages – Math Theory Behind Language Design

To elaborate DeadMG's answer, it sounds like they mean:

1. Static array: an array whose size is known, and whose storage is allocated, at compile time. In C, you might write at global (file) scope:

   int static_array[7];
   

2. Fixed stack-dynamic array: you know the size of your array at compile time, but allow it to be allocated automatically on the stack (the size is fixed at compile time but the storage is allocated when you enter its scope, and released when you leave it)

   void foo()
   {
     int fixed_stack_dynamic_array[7];
     /* ... */
   }
   

3. Stack dynamic array: you don't know the size until runtime, eg. C99 allows this:

   void foo(int n)
   {
     int stack_dynamic_array[n];
     /* ... */
   }
   

4. Fixed heap dynamic array: same as the 2 except using explicit heap allocation

   int * fixed_heap_dynamic_array = malloc(7 * sizeof(int));
   

5. Heap dynamic array: you can probably guess this:

   void foo(int n)
   {
     int * heap_dynamic_array = malloc(n * sizeof(int));
   }
   

Is this the same book as Concepts of Programming Languages? Because again, these aren't a useful classification of types, they only address the allocation mechanism. Once you pass any of these "different" things into a function, their classification under this scheme is irrelevant.

What experience with other programming languages do you have which make you feel the idea of TM and the ideas of Computer Science in general? Can you specify how you think?

There is the structured program theorem, which ties pretty much any procedural programming language directly to Turing Machines. As you hinted, functional languages are tied to TMs via lambda calculus. And there rather few languages that are Turing-complete and can't be trivially translated into either procedural or functional programming (hi there, Prolog).

For me, the main implication is that independently of technology and programming language, there are very few problems that can't be solved. This makes me hate people who say that something is impossible :)