A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of s is defined by Inst H (s) foe(s) j oe : V(s) H is a substitutiong. Note that Inst H (s) Inst H (s) and that f(a b) 62 Inst H (f(x x) if a 6= b. Using models of Inst H (s) instead of Inst H (s) would make satisfiability of our constraints equivalent to semi unification and undecidable [KTU90, DR90]. 4 The Algorithm At first sight, the satisfiablity problem seems to be a not too difficult extension of rational unification. We could simply add a directed version of (Descend) Descend) x=f(u) u z OE u fresh; y=f(z) in OE: In the above application condition and in the sequel we make ....

A. Kfoury, J. Tiuryn, and P. Urzyczyn. The Undecidability of the SemiUnification Problem. In ACM Symposium on Theory of Computation, pp. 468--476, May 1990.

....) Here, a polymorphic function (op) is passed to the function f; this operation is applied to two values of unrelated type. This restriction is a result of ML s use of type inference; it has been proven that allowing polymorphic parameters makes ML style type inference an undecidable problem [23]. Ada Ada, like Cforall, allows the definition of polymorphic functions with assertion parameters. Unlike Cforall, Ada does not allow these polymorphic functions to be used as if they were monomorphic functions: the programmer must instantiate them, specifying type arguments explicitly. Cormack ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. In Proceedings of the twenty-second annual ACM symposium on Theory of computing, pages 468--476. ACM Press, 1990.

....with coordination problems. Dorre and Rounds [10] show that the satisfiability of conjunctions of feature equations and subsumption constraints is undecidable. This problem is closely related to the semi unification problem for first order terms, whose undecidability has been shown recently [27]. Yet another useful extension are roles or set valued features. Roles are symbols that are interpreted as set valued functions r : D 2 Features can be seen as special roles that map every element of the domain either to the empty set or to a singleton. Syntactically, roles can be ....

A. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Technical report, Computer Science Department, Boston University, Boston, MA, October 1989.

.... was first described in an abstract form by Henglein [Hen93] More recent papers describe concrete worklist based algorithms, which we have adopted in our work [FRD00,OCa00] The underlying problem of finding an optimal solution for a set of component and instantiation constraints is undecidable [KTU93], and we have no proof that our inference algorithm terminates. However, in practice our algorithm works well; neither we nor others working on similar algorithms have ever encountered an example that causes the algorithm to loop [Hen93,FRD00,OCa00] Our analysis is most similar to that used by ....

Assaf J. Kfoury, Jerzy Tiuryn, and Pawel Urzyczyn. The Undecidability of the Semi-Unification Problem. Information and Computation, 102(1):83--101, January 1993.

.... was first described in an abstract form by Henglein [Hen93] More recent papers describe concrete worklist based algorithms, which we have adopted in our work [FRD00,OCa00] The underlying problem of finding an optimal solution for a set of component and instantiation constraints is undecidable [KTU93], and we have no proof that our inference algorithm terminates. However, in practice our algorithm works well; neither we nor others working on similar algorithms have ever encountered an example that causes the algorithm to loop [Hen93,FRD00,OCa00] Our analysis is most similar to that used by ....

Assaf J. Kfoury, Jerzy Tiuryn, and Pawel Urzyczyn. The Undecidability of the Semi-Unification Problem. Information and Computation, 102(1):83--101, January 1993.

....However, instantiation constraints also support context sensitivity, so that constraints on one instance of a type variable do not constrain other instances of that type variable. Although solving systems of equality, component, and instantiation constraints is undecidable in the general case [KTU93], there are semi algorithms that work well in practice [Hen93,FRD00,OCa00] Previous systems have distinguished different component and instantiation constraints with an integer index representing the place where the instantiation or containment occurs, typically a method call point or an object ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Information and Computation, 102(1):83--101, Jan. 1993.

....and inferring types are both decidable, as in ML [14] but for the second idea, only type checking is decidable. With the definitional genericity principle, type inference leads to a non uniform 3 semi unification problem which has been shown to be undecidable by Kfoury, Tiuryn and Urzyczyn [10]. One reason for sticking to definitional genericity (or head condition) is that it is the most natural when predicates are seen as definitions and type schemes as abstractions of the definitions. A sound and easy modular analysis of programs also requires definitional genericity. The other ....

A.J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semiunification problem. Technical Report BUCS 89-010, Boston University, 1989.

....is shown for program boundedness. The proof is a reduction from the mortality problem for Turing machines [H66] It is a qualitatively different proof from the techniques used in [GMSV87] The mortality problem has recently been used to prove the undecidability of the semi unification problem [KTU90]. Given the decidability results of [CGKV88] for monadic programs, this tight result illustrates the power of 6= 3. We show that uniform boundedness is undecidable for arity 3 programs. This improves the arity from 5 to 3 (but leaves open arity 2) The proof, which uses nonlinear rules, is a ....

A.J. Kfoury, J. Tiuryn, P. Urzyczyn, The Undecidability of the SemiUnification Problem, Proc. 22nd ACM Symp. on Theory of Computing (1990), 468--476.

....constant are independent instances of its type scheme, whereas types of different head occurrences are renamings of the type scheme. With this principle, type inference leads to a non uniform semi unification problem which has been shown to be undecidable by Kfoury, Tiuryn and Urzyczyn [21]. In our implementation, types of constants (predicative or not) are only checked, and types of (any kind of) variables are inferred. The reason for sticking to definitional genericity is that it is the most natural when predicates are seen as definitions and type schemes as abstractions of the ....

A.J. Kfoury, J. Tiuryn, and P. Urzyczyn. The Undecidability of the Semi-Unification Problem. Technical Report BUCS 89-010, Boston University, 1989.

....for System F. 1.4 What does this article contribute The main contribution of this paper is proving the undecidability of Typ and TC for System F. 1. We first prove that the problem of semi unification can be reduced to TC using a simple encoding. Since semi unification is undecidable [KTU93], so is TC. 2. We then reduce TC to Typ using a novel method of building terms which simulate arbitrarily chosen type environments. The proof begins by showing that there exists a typable term J such that in every typing of J , its bound variable x is assigned the type ff ff: J j ....

.... M : 2.5 Semi Unification For convenience, we define semi unification using a first order signature containing the single infix binary function symbol and for the case where there are only two pairs of terms. The general definition of semi unification is reducible to this special case [Pud88, KTU93] and the proof that semi unification is undecidable is actually for this special case [KTU93] The set of algebraic terms T is defined by the grammar T : V j (T T ) This definition is chosen because it allows mapping terms onto types. In fact, T ae T. An instance Gamma of semiunification ....

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A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.

....recursive call gets one of type Trapez A (A;B) Since fstCol is polymorphic, that should be okay, but such polymorphic recursion is not allowed in Milner s type system. The reason is that type inference under polymorphic recursion is equivalent [6, 13] to semi unification, an undecidable problem [14]; see section 2. However, if the types are given by the programmer, then polymorphic recursion is allowed in Hope, Miranda TM , CAML, and one option of the Chalmers Haskell compiler (hbc fuse restr) because type checking is decidable. Polymorphic recursion can be useful. Mycroft, the ....

....unification) in Abelian groups with constants [16] in vector spaces with constants, and in a few other equational theories [10, 25] 2.3 Semi unification Semi unification is a combination of unification and matching. The applications of syntactic semi unification are surveyed by Kfoury et al. [14], but I have not found any literature on equational semi unification, apart from my own paper on Abelian groups [24] If you let E = in my definitions, you get syntactic semi unification (since =E is then syntactic equality) Definition 3 An E semi unification problem is a finite set of boxes, ....

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A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Info. and Computation, 102(1):83--101, 1993.

....papers is the demonstration of equivalence between the the reconstruction problem and the more general problem of semi unification. Their undecidability result for reconstruction is based on the undecidability of semi unification, shown recently in another paper by Kfoury, Tiuryn, and Urzyczyn [KTU93b] Note that these reconstruction problems assume we have general recursion, unlike our system. Based on stratified polymorphism discussed above [Lei91] Leivant in earlier work [Lei83] and then McCracken [McC84] present papers on type reconstruction for polymorphic systems of two levels. More ....

....framework for viewing ML style unification and the enhancements for polymorphic recursion [KTU93a] In our search for an algorithm we are walking the boundary of decidability. Huet s second order unification is only semi decidable [Hue75, Gol81] Semi unification is also undecidable in general [KTU93b] Yet unification and second order matching [HL78] are decidable. We hope to clarify the general class of matching and unification problems upon which our reconstruction depends. 4.3 Reflections, Criticisms, and Future Work This thesis establishes a new type system about which little is known, ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semiunification problem. Information and Computation, 102:83--101, 1993.

....of a predicate constant are independent instances of its type scheme, whereas types of head occurrences are renamings of the type scheme . With this principle, type inference leads to a non uniform semi unification problem which has been shown to be undecidable by Kfoury, Tiuryn and Urzyczyn [23]. In our implementation, types of constants (predicative or not) are only checked, and types of (any kind of) variables are inferred. The reason for sticking to definitional genericity is that it is the most natural when predicates are seen as definitions and type schemes as abstractions of the ....

A.J. Kfoury, J. Tiuryn, and P. Urzyczyn. The Undecidability of the Semi-Unification Problem. Technical Report BUCS 89-010, Boston University, 1989.

....is shown for program boundedness. The proof is a reduction from the mortality problem for Turing machines [H66] It is a qualitatively different proof from the techniques used in [GMSV87] The mortality problem has recently been used to prove the undecidability of the semi unification problem [KTU90]. Given the decidability results of [CGKV88] for monadic programs, this tight result illustrates the power of 6= 3. We show that uniform boundedness is undecidable for arity 3 programs. This improves the arity from 5 to 3 (but leaves open arity 2) The proof, which uses nonlinear rules, is a ....

A.J. Kfoury, J. Tiuryn, P. Urzyczyn, The Undecidability of the SemiUnification Problem, Proc. 22nd ACM Symp. on Theory of Computing (1990), 468--476.

....for ML is a consequence of the existence of most general semiunifiers. The algorithm for calculating semiunifiers differs, however, from that for calculating unifiers in the respect that when applied to an unsolvable problem, it may not terminate. This is a consequence of a result due to [ Kfoury, Tiuryn, and Urcyczyn, 1989 ] that semiunification is undecidable. This said, the proof of Kfoury et al. generates in no very direct way an input to the algorithm on which it will not terminate, and in fact no example has been found on which the algorithm does not terminate. This was one reason for creating the ....

A.Kfoury, J.Tiuryn, P.Urcyczyn. The Undecidability of the Semi-Unification Problem. Boston University, Tech. Report BUCS-89-010

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A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.

No context found.

A.J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, pages 468 -- 476, 1990. 53

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Kfoury, A.J., Tiuryn, J., and Urzyczyn, P., "The undecidability of the semi-unification problem". Information and Computation, Vol 102, no. 1, pp 83-101, 1993.

....is undecidable. 3 1. 2 Contributions of This Paper The main contributions of this paper are the following: The undecidability of the regular semi unification problem that, interestingly, calls for methods entirely di#erent from those used for the undecidability of finite semi unification [KTU93b] For the result in this paper, we use a reduction from the word problem for finitely generated monoids which we have adapted from a similar encoding of the same word problem into feature algebras in computational linguistics [DR92] For every k # 3, type inference with rank k recursive ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.

....recursive types. The latter can be reduced further to the problem of typability with rank k recursive types, for every k # 4. Interestingly, the undecidability of regular semiunification calls for methods entirely different from those used for the undecidability of finite semiunification [13]. For the result in this paper, we use a reduction from the word problem for finitely generated monoids, which we have adapted from a similar encoding of the same word problem into feature algebras in computational linguistics [2] 1.3 Future Work . Investigate the lack of a ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83-- 101, Jan. 1993.

....recursive types. The latter can be reduced further to the problem of typability with rank recursive types, for every N . Interestingly, the undecidability of regular semi unification calls for methods entirely different from those used for the undecidability of finite semi unification [KTU93b] For the result in this paper, we use a reduction from the word problem for finitely generated monoids, which we have adapted from a similar encoding of the same word problem into feature algebras in computational linguistics [DR92] 1.3 Future Work Investigate the lack of a ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.

....recursive types. The latter can be reduced further to the problem of typability with rank k recursive types, for every k # 4. Interestingly, the undecidability of regular semi unification calls for methods entirely different from those used for the undecidability of finite semi unification [KTU93b] For the result in this paper, we use a reduction from the word problem for finitely generated monoids, which we have adapted from a similar encoding of the same word problem into feature algebras in computational linguistics [DR92] 1.3 Future Work . Investigate the lack of a ....

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Inf. & Comput., 102(1):83--101, Jan. 1993.

No context found.

A. J. Kfoury, J. Tiuryn, and P. Urzyczyn. The undecidability of the semi-unification problem. Information and Computation, 102(1):83--101, Jan. 1993.

No context found.

A.J. Kfoury, J. Tiruyn, P. Urzyczyn, "The undecidability of the semi-unification problem", Technical Report BUCS-89-010, Boston Univ., Oct. 89.

No context found.

Kfoury, A., Tiuryn, J., and Urzycyzyn, P. The undecidability of the semiunification problem. In proceedings of the 22th Symposium on Theory of Computing (STOC). Baltimore, Maryland, May 1990.

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