H. Schwichtenberg. Definierbare Funktionen im Lambda-Kalkul mit Typen. Archiv Logik Grundlagenforsch., 17:113--114, 1976. Home/Search Document Not in Database Summary Related Articles Check |
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Lectures on the Curry-Howard Isomorphism - Sørensen, Urzyczyn (1998) (2 citations) (Correct)
....: n k ; m 1 ; m l ) f(n 1 ; n k ) Delta g(m 1 ; m l ) 3.5.6. Theorem (Schwichtenberg) The definable functions are exactly the extended polynomials. The proof is omitted. One direction follows easily from what has been said already; the other direction is proved in [97]. If one does not insist that numbers be uniformly represented as terms of type int, more functions become definable see [35] Chapter 3. Simply typed calculus 3.6.1. Exercise. Show that the following terms have no type in a la Curry. 1. x:x x; 2. Omega 3. K I Omega Gamma 4. Y; 5. ....
H. Schwichtenberg. Definierbare Funktionen im Lambda-Kalkul mit Typen. Archiv Logik Grundlagenforsch., 17:113--114, 1976.
A Note on Polynomials with Non-negative Integral Coefficients - Govindarajan (Correct)
....non negative coefficients can be inferred by knowing their value at two cleverly chosen points. Our interest in this class of polynomials arises from the fact that in the simply typed calculus the class of integer functions that one can express is a small extension of this class of polynomials [5]. Rowland and Cowles [3] provided algorithms for identifying polynomials of arbitrary degree whose coefficients were bounded in magnitude by examining the value of the polynomial at small number of inputs. Note that we, on the other hand, require the coefficients to be non negative and do not ....
H. Schwichtenberg. Definierbare Funktionen im Lambda-Kalkul mit Typen. Archiv Logik Grundlagenforsch, 17:113--114, 1976.
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