Reinhard Kahle and Thomas Studer. Formalizing non-termination of recursive programs. To appear in Journal of Logic and Algebraic Programming. Home/Search Document Details and Download
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Axioms for Strict and Lazy Functional Programs - Stärk (Correct)
....candidate has similar properties as our auxiliary relations . It is not clear how the least fixed point properties that we need in this paper can be obtained using the general method. Howe s method is extended by Gordon to typed functional languages in [6] Kahle and Studer write in [10] that in typed functional programming languages, like ML, fixed point operators are built in, but there is no way to guarantee on the syntactical level that the solution produced by these operators will be the least fixed point. They claim that the least fixed point property is only given by the ....
....directly in terms of call by value and call byname evaluation. Note also that in our basic logic of partial terms we can derive (rec fx.f x) v for any syntactical value v (see proof of Lemma 3. 2) Hence, there are provably non terminating programs in our theory as they are in the theory LFP of [10]. In [14] Moran and Sands develop an operational theory for the call by need # calculus with recursive lets, constructors, and case expressions. Their theory is cost sensitive and reflects the computational distinctions between call by need and call by name. It would be interesting to extend ....
R. Kahle and T. Studer. Formalizing non-termination of recursive programs. J. of Logic and Algebraic Programming, 49(1&2):1--14, 2001.
Constructive Foundations for Featherweight Java - Studer (2001) (1 citation) Self-citation (Studer) (Correct)
....languages. In particular, they have been shown to provide a unitary axiomatic framework for representing programs, stating properties of programs and proving properties of programs. Important references for the use of explicit mathematics in this context are Feferman [16 18] Kahle and Studer [30], Stark [35, 36] Studer [37, 39] as well as Turner [43, 44] Beeson [6] and Tatsuta [41] make use of realizability interpretations for systems of explicit mathematics to prove theorems about program extraction. Feferman [16] claims that impredicative comprehension principles are not needed for ....
....N ) with axioms about computability (Comp) and the statement that everything is a natural number. The resulting system allows to define a least fixed point operator and therefore it will be possible to show that recursively defined methods belong to a certain function space, cf. Kahle and Studer [30]. Computability. These axioms are intended to capture the idea that convergent computations should converge in finitely many steps. In the formal statement of the axioms the expression c(f, x, n) 0 can be read as the computation fx converges in n steps. The idea of these axioms is due to ....
[Article contains additional citation context not shown here]
Reinhard Kahle and Thomas Studer. Formalizing non-termination of recursive programs. To appear in Journal of Logic and Algebraic Programming.
Truth in Applicative Theories - Kahle (2001) Self-citation (Kahle) (Correct)
....ID # 1 ) FON (T I N ) N ; 3. c ID 1 ) FON (L F I N ) N : Please note that the recursion theorem in applicative theories does not help to de ne least xed points (for a discussion of possibilities of least xed point operators in the applicative framework, we refer to [KS0x]) For this reason, there is no possibility to de ne a truth theory based on applicative theories which allows an embedding of ID 1 in the same manner. However, later, we will de ne a truth theory based on supervaluation which allows a syntactical embedding of ID 1 . 11 5 Universes over Frege ....
Reinhard Kahle and Thomas Studer. Formalizing non-termination of recursive programs. 200x. Submitted.
Constructive Foundations for Featherweight Java - Studer (2000) (1 citation) Self-citation (Studer) (Correct)
....In particular, they have been shown to provide a unitary axiomatic framework for representing programs, stating properties of programs and proving properties of programs. Important references for the use of explicit mathematics in this context are Feferman [15, 16, 17] Kahle 2 and Studer [29], Stark [34, 35] Studer [37, 36] as well as Turner [41, 42] Beeson [5] and Tatsuta [39] make use of realizability interpretations for systems of explicit mathematics to prove theorems about program extraction. Feferman [15] claims that impredicative comprehension principles are not needed for ....
....N ) with axioms about computability (Comp) and the statement that everything is a natural number. The resulting system allows to define a least fixed point operator and therefore it will be possible to show that recursively defined methods belong to a certain function space, cf. Kahle and Studer [29]. Computability. These axioms are intended to capture the idea that convergent computations should converge in finitely many steps. In the formal statement 10 of the axioms the expression c t (x, n) 0 can be read as the computation tx converges in n steps. The idea of these axioms is due ....
[Article contains additional citation context not shown here]
Reinhard Kahle and Thomas Studer. Formalizing non-termination of recursive programs. Submitted.
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