Didier R'emy. Syntactic theories and the algebra of record terms. Technical Report 1869, INRIA-Rocquencourt, BP 105, F-78 153 Le Chesnay Cedex, 1992. File record-algebras.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....countable collection of term variables, and range over an in nitely countable collection of type variables, and range over an in nitely countable collection of row variables and b ranges over a given set of base types. The de nitions of elds and rows are just as in R emy s calculus [16] except for the fact that a eld is tagged with a variable instead of a label. We omit superscripts in rows whenever we can complete them. We sometimes regard a as a set of pairs of variables and monotypes, that is, x : 2 if and only if = 0 ; x : We use I for a set of ....

....j= v : S( 4 Type Inference In this section, we develop a type inference algorithm. The type system of our system contains rows which are essentially equivalent to ones in R emy s [14] If we exclude the monomorphic polytypes [ from the system, types would be an instance of the record algebra [16] which is well developed and we would be able to utilize that technique. However, our system contains another component of monomorphic polytypes which requires another kind of treatment. We must carefully mix the above constituents to obtain an appropriate type inference algorithm. We follow the ....

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Didier Remy. Syntactic theories and the algebra of record terms. Research Report 1869, Institut National de Recherche en Informatique et Automatisme, Rocquencourt, BP 105, 78 153 Le Chesnay Cedex, France, 1992.

....0 ] 1 g is the type of pairs composed of a value of type 0 and a record whose fields are functions of domains 0 and of codomains described by 1 , i.e. the type of objects with exposed state 0 . Projective types are described in more details in the appendix B. They are fully formalized in [R em93a] and also introduced more intuitively in [R em92b] In [R em92b] projective types are used to type more powerful primitives. In ML ART they essentially define more precise types such as the type of objects. 2.4 Recursive types Recursive types are only provided through data type declarations in ....

Didier R'emy. Syntactic theories and the algebra of record terms. Research Report 1869, Institut National de Recherche en Informatique, BP 105, F-78 153 Le Chesnay Cedex, 1993.

.... p: a W, which is clearly less general by than the result of unification. 2.5 Further issues and Related work Tagged types were compared to row types in the introductory section. In the general allowing higher order sorts (not discussed here) tagged Types and the generalized record types in [14] have different expressiveness since record types do nor admit higher order expansion patterns while tagged types do not allow type 9 variables to be shared between expansion patterns as in the record type a b a b . However, when neither of these features are used, one can ....

D. Rémy, "Syntactic Theories and the Algebra of Record Terms", Research Report 1869, INRIA, March 93.

....Extending a free algebra with a record algebra The intuitions of previous sections are formalized by the algebra of record terms. The algebra of record terms is introduced for an arbitrary free algebra; record types are an instance. The record algebra was introduced in [R em90] and revisited in [R em92b] We summarize it below but we recommend [R em92b] for a more thorough presentation. We are given a set of variables V and a set of symbols C with their arities (C n ) n2IN . Raw terms We call unsorted record terms the terms of the free unsorted algebra T 0 (D 0 ; V) where D 0 is the set ....

....intuitions of previous sections are formalized by the algebra of record terms. The algebra of record terms is introduced for an arbitrary free algebra; record types are an instance. The record algebra was introduced in [R em90] and revisited in [R em92b] We summarize it below but we recommend [R em92b] for a more thorough presentation. We are given a set of variables V and a set of symbols C with their arities (C n ) n2IN . Raw terms We call unsorted record terms the terms of the free unsorted algebra T 0 (D 0 ; V) where D 0 is the set of symbols composed of C plus a unary symbol Pi ....

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Didier R'emy. Syntactic theories and the algebra of record terms. Technical report, BP 105, F-78 153 Le Chesnay Cedex, BP 105, F-78 153 Le Chesnay Cedex, 1992. To appear. Also in [R'em90], chapter 2.

....between types, rows, row elements, and presence annotations such that for all i, i wf and 0 i wf, and for all j, there exists a kind j such that j : j and 0 j : j . The existence of principal uni ers follows from the fact that our equational theory is syntactic and regular [21]. The algorithm mgu is given in appendix A. Theorem 6 (Principal types) There exists a type inference algorithm W satisfying the following conditions: ffl (Correctness) If E is well kinded and ( W (E; a) is de ned, then (E) a : ffl (Completeness) If E is well kinded and there ....

Didier R#my. Syntactic theories and the algebra of record terms. Research report 1869, INRIA, 1993.

....left implicit in an ellipsis hm i : i i2I ; i (abbreviations explained in section 8 can even be used to share ellipsis) In the formal presentation, we keep both ; and row variables explicit. A label can only appear once in an object type. This is easily ensured by sorting type expressions [30]. The distinction between and can also be guaranteed by sorts. Thus, we omit the distinction and simply write below. Type equality is defined by the following family of leftcommutativity axioms: m 1 : 1 ; m 2 : 2 ; m 2 : 2 ; m 1 : 1 ; plus standard rules for recursive types ....

....solutions, even in the presence of recursion [31] The unification algorithm is a simplification of the one used in ML ART [31] It is described in figure 5 as a rewriting process over unification problems. This formalism was introduced in [15] and has already been used for record types in [30]. A unification problem also called a unificand, is a multi set of multi equations preceded by a list of existentially quantified variables. It is written 9 ff 1 ; ff p : e 1 : e q . A multi equation e is a multi set of types written 1 = n . The algorithm assumes that recursive ....

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Didier R emy. Syntactic theories and the algebra of record terms. Research Report 1869, Institut National de Recherche en Informatique et Automatisme, BP 105, F-78 153 Le Chesnay Cedex, 1993.

....of types, that is, f i : i i2I g. This type says that fields i s are defined with values of type i s. However, it does not imply anything about other fields. Another richer, more symmetric structure has also been used for record types, originally to allow type inference for records in ML [23, 24]. There, record types are treated as total functions mapping labels to field types, with the restriction that all but a finite number of labels have isomorphic images (i.e. are equal modulo renaming) Thus, record types can still be represented finitely by listing all significant labels with their ....

....not be overriden, nor accessed, and thus it could be just given type U. Our use of variances also eliminate the ability to specify the type of a field without specifying its variance, which may cause problem with type inference [22] An essential imported tool is the structure of record types of [23], which was originally designed for type inference in ML [24] The use of a richer structure of record types has previously been proposed for type checking records [15, 16, 13, 12] To our knowledge, the benefits of symmetric information were first transfered from record types to object types in ....

Didier R'emy. Syntactic theories and the algebra of record terms. Research Report 1869, Institut National de Recherche en Informatique et Automatisme, Rocquencourt, BP 105, 78 153 Le Chesnay Cedex, France, 1993.

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Didier R'emy. Syntactic theories and the algebra of record terms. Technical Report 1869, INRIA-Rocquencourt, BP 105, F-78 153 Le Chesnay Cedex, 1992. File record-algebras.

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Didier R'emy. Syntactic theories and the algebra of record terms. Technical report, BP 105, F-78 153 Le Chesnay Cedex, BP 105, F-78 153 Le Chesnay Cedex, 1992. To appear. Also in [R'em90], chapter 2.

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