A.J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus (extended summary). In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 2--11. IEEE Computer Society Press, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We use the name fl in accordance with Kfoury and Wells [18] See Barendregt [2] for a definition of compatible. i) fl is strongly normalizing. ii) fl satisfies the diamond property. iii) fl nf s are unique. Our definition is identical to the definition of [12] but differs from [11]. 15 i) The proof is similar to the proof of Lemma 5.5 from Kfoury and Wells [17] Let appl(M) be the set of subterms of M that are applications, and let ffi(M) X (M 1 M 2 )2appl(M) max(0; jact(M 1 )j Gamma 1) If M fl N , then ffi (M) ffi (N) 1. Since for any M we have ffi (M) 0, ....

A.J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus (extended summary). In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 2--11. IEEE Computer Society Press, 1990.

....[2] for a definition of compatible. i) fl is strongly normalizing. ii) fl satisfies the diamond property. iii) fl nf s are unique. i) The proof is similar to the proof of Lemma 5. 5 from Kfoury and Wells [17] Our definition is identical to the definition of [12] but differs from [11]. 15 Let appl(M) be the set of subterms of M that are applications, and let ffi(M) M 1 M 2 )2appl(M) max(0; jact(M 1 )j Gamma 1) If M fl N , then ffi (M) ffi (N) 1. Since for any M we have ffi (M) 0, we can conclude that fl is strongly normalizing. In fact, ffi(M) 0 iff M ....

A.J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus (extended summary). In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 2--11. IEEE Computer Society Press, 1990.

.... [KM89,KMM91] and by acyclic semi unification [KTU90a] A characterization of Milner Mycroft typability by semi unification has independently been given by Kfoury et al. KTU89] in fact, Kfoury and Tiuryn have extended it to include the Second Order calculus limited to rank 2 derivations [KT90]. Characterizations of type inference by inequality constraints involving quantified types in the Second Order calculus have been given in [Mit88,GRDR88] We first present the reduction of Milner Mycroft typability to semi unification (Section 4.1) and then the converse reduction (Section 4.2) ....

A. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus. In Proc. 5th Annual IEEE Symp. on Logic in Computer Science (LICS), Philadelphia, Pennsylvania, pages 2--11. IEEE Computer Society Press, June 1990.

....terms carry no type information at all, and a types may be considered properties of untyped terms. This problem has been called type inference, full type inference, and type reconstruction, and has resisted complete analysis, despite intensive efforts and some partial answers (see, for example, [14, 12, 4]) We refer to (a variation of) Boehm s problem as partial type reconstruction and the other problem as full type reconstruction. We believe that partial type reconstruction is the practically more useful problem, and a number of implementations have been based on decidable subcases (see, for ....

....[ Definition 6 (Full Type Reconstruction) Given a valid Gamma and an untyped term U , determine if there exists a term M valid in Gamma such that U OE M . The decidability of full type reconstruction is still open, despite intensive efforts and a number of partial results (see, for example, [12, 4]) Unfortunately, our undecidability results seems to bear no direct relationship to the full type reconstruction problem, nor do we see how our techniques could be applied. While one might feel that full type reconstruction is a more fundamental, mathematical problem, it seems to us that partial ....

A. J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus. Information and Computation, 199? To appear.

....the name fl in accordance with Kfoury and Wells [18] See Barendregt [2] for a definition of compatible. Lemma 16 i) fl is strongly normalizing. ii) fl satisfies the diamond property. iii) fl nf s are unique. 3 Our definition is identical to the definition of [12] but differs from [11]. Proof: i) The proof is similar to the proof of Lemma 5.5 from Kfoury and Wells [17] Let appl(M) be the set of subterms of M that are applications, and let ffi(M) X (M 1 M 2 )2appl(M) max(0; jact(M 1 )j Gamma 1) If M fl N , then ffi (M) ffi (N) 1. Since for any M we have ffi ....

A.J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus (extended summary). In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science, pages 2--11. IEEE Computer Society Press, 1990.

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A.J. Kfoury and J. Tiuryn. Type reconstruction in finite-rank fragments of the polymorphic -calculus. In Fifth Annual IEEE Symposium on Logic in Computer Science, pages 2--11, Philadelphia, PA, June 1990.

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