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UNARY PRIMITIVE RECURSIVE FUNCTIONS
, 2006
"... Abstract. In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parame ..."
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Abstract. In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without
The Primitive Recursive Functions are Recursively Enumerable
"... Metaoperations on primitive recursive functions sit at the brink of what is computationally possible: the semantic equality of primitive recursive programs is undecidable, and yet this paper shows that the whole class of p.r. functions can be enumerated without semantic duplicates. More generally, ..."
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Metaoperations on primitive recursive functions sit at the brink of what is computationally possible: the semantic equality of primitive recursive programs is undecidable, and yet this paper shows that the whole class of p.r. functions can be enumerated without semantic duplicates. More generally
Primitive Recursive Functions
"... .51> zero(x) j 0 2. successor: defined by succ(x) j x + 1 3. projection: defined by proj n k (x 1 ; : : : ; xn ) j x k and two basic operators for constructing new functions: 1. composition: denoted by h k = comp( f n ; g k 1 ; g k 2 ; : : : ; g k n ) 2. primitive recursion: deno ..."
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.51> zero(x) j 0 2. successor: defined by succ(x) j x + 1 3. projection: defined by proj n k (x 1 ; : : : ; xn ) j x k and two basic operators for constructing new functions: 1. composition: denoted by h k = comp( f n ; g k 1 ; g k 2 ; : : : ; g k n ) 2. primitive recursion
Nonprimitive Recursive Function Definitions
 Proceedings of the 8th International Workshop on Higher Order Logic Theorem Proving and Its Applications (LNCS 971
, 1995
"... This paper presents an approach to the problem of introducing nonprimitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially nonterminating. Once we have proved termin ..."
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Cited by 2 (0 self)
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This paper presents an approach to the problem of introducing nonprimitive recursive function definitions in higher order logic. A recursive specification is translated into a domain theory version, where the recursive calls are treated as potentially nonterminating. Once we have proved
An Exactification of the Monoid of Primitive Recursive Functions
"... Abstract. We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual ..."
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Abstract. We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable
The Set of Primitive Recursive Functions 1
"... Summary. We follow [31] in defining the set of primitive recursive functions. The important helper notion is the homogeneous function from finite sequences of natural numbers into natural numbers where homogeneous means that all the sequences in the domain are of the same length. The set of all such ..."
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Summary. We follow [31] in defining the set of primitive recursive functions. The important helper notion is the homogeneous function from finite sequences of natural numbers into natural numbers where homogeneous means that all the sequences in the domain are of the same length. The set of all
Models of Computation Primitive Recursive Functions
"... 1.1 Intuitive syntax and semantics In informal mathematical notation we often define the addition function in the following way: 0 + n = n m ′ + n = (m + n) ′ We have used the notation m ′ for the successor of the number m. In a functional language we can use a similar definition: add 0 n = n add (s ..."
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(s m) n = s (add m n) We know that this is a meaningful definition since the addition function for the argument s n is defined using the value of the function for the argument n. This kind of recursion is well defined since n is smaller than s n. The recursion scheme is called primitive recursion
Invariance of Function Complexity Under Primitive Recursive Functions
"... Abstract. Genetic Programming (GP) [1] often uses a tree form of a graph to represent solutions. An extension to this representation, Automatically Defined Functions (ADFs) [1] is to allow the ability to express modules. In [2] we proved that the complexity of a function is independent of the primit ..."
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Cited by 1 (1 self)
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recursion into their representations. These representations are then capable of expressing a wider classes of functions, for example the primitive recursive functions (PRFs). We prove that given two representations which express the PRFs (and only the PRFs), the complexity of a function with respect
Symbolic test case generation for primitive recursive functions
 Formal Approaches to Testing of Software, number 3395 in Lecture Notes in Computer Science
, 2004
"... Abstract We present a method for the automatic generation of test cases for HOL formulae containing primitive recursive predicates. These test cases can be used for the animation of specifications as well as for blackbox testing of external programs. Our method is twostaged: first, the original fo ..."
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Cited by 27 (15 self)
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Abstract We present a method for the automatic generation of test cases for HOL formulae containing primitive recursive predicates. These test cases can be used for the animation of specifications as well as for blackbox testing of external programs. Our method is twostaged: first, the original
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