21. However, all primitive recursive functions halt. 22. A total recursive function is a partial recursive function that is defined for every input. 23. A total recursive function is a partial recursive function that is defined for every input. 24. For non-recursive function calls, this is usually an ML family among others. 25. Rice's theorem says " any nontrivial property of partial recursive functions is undecidable" 26. It allows a more natural style of expressing computation than simply using primitive recursive functions . 27. Effectively, this, in combination with the order, allows the definition of recursive functions . 28. Here is a complete program defining and using the traditional recursive function to calculate a factorial. 29. Later in 1943 and 1952 Stephen Kleene defined an equivalent concept in terms of recursive functions . 30. Recursive function theory / lambda calculus?
