Results 11  20
of
35
BetaReduction As Unification
, 1996
"... this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several othe ..."
Abstract

Cited by 13 (9 self)
 Add to MetaCart
this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several other benefits
Type Inference with Expansion Variables and Intersection Types in System E and an Exact Correspondence with βReduction
 In Proc. 6th Int’l Conf. Principles & Practice Declarative Programming
"... System E is a recently designed type system for the # calculus with intersection types and expansion variables. During automatic type inference, expansion variables allow postponing decisions about which nonsyntaxdriven typing rules to use until the right information is available and allow imple ..."
Abstract

Cited by 11 (4 self)
 Add to MetaCart
System E is a recently designed type system for the # calculus with intersection types and expansion variables. During automatic type inference, expansion variables allow postponing decisions about which nonsyntaxdriven typing rules to use until the right information is available and allow implementing the choices via substitution.
Modularity of Strong Normalization in the Algebraicλcube
, 1996
"... In this paper we present the algebraicλcube, an extension of Barendregt's λcube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraicλcube, provided that the firstorder rewrite rules are nonduplicating and the ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
In this paper we present the algebraicλcube, an extension of Barendregt's λcube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraicλcube, provided that the firstorder rewrite rules are nonduplicating and the higherorder rules satisfy the general schema of Jouannaud and Okada. This result is proven for the algebraic extension of the Calculus of Constructions, which contains all the systems of the algebraicλcube. We also prove that local confluence is a modular property of all the systems in the algebraicλcube, provided that the higherorder rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence.
Types, potency, and idempotency: why nonlinearity and amnesia make a type system work
 In ICFP ’04: Proceedings of the ninth ACM SIGPLAN international conference on Functional programming, 138–149, ACM
, 2004
"... Useful type inference must be faster than normalization. Otherwise, you could check safety conditions by running the program. We analyze the relationship between bounds on normalization and type inference. We show how the success of type inference is fundamentally related to the amnesia of the type ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Useful type inference must be faster than normalization. Otherwise, you could check safety conditions by running the program. We analyze the relationship between bounds on normalization and type inference. We show how the success of type inference is fundamentally related to the amnesia of the type system: the nonlinearity by which all instances of a variable are constrained to have the same type. Recent work on intersection types has advocated their usefulness for static analysis and modular compilation. We analyze SystemI (and some instances of its descendant, System E), an intersection type system with a type inference algorithm. Because SystemI lacks idempotency, each occurrence of a variable requires a distinct type. Consequently, type inference is equivalent to normalization in every single case, and time bounds on type inference and normalization are identical. Similar relationships hold for other intersection type systems without idempotency. The analysis is founded on an investigation of the relationship between linear logic and intersection types. We show a lockstep correspondence between normalization and type inference. The latter shows the promise of intersection types to facilitate static analyses of varied granularity, but also belies an immense challenge: to add amnesia to such analysis without losing all of its benefits.
Rank 2 Intersection Types for Modules
, 2003
"... We propose a rank 2 intersection type system for a language of modules built on a core MLlike language. The principal typing property of the rank 2 intersection type system for the core language plays a crucial role in the design of the type system for the module language. We first consider a "plai ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
We propose a rank 2 intersection type system for a language of modules built on a core MLlike language. The principal typing property of the rank 2 intersection type system for the core language plays a crucial role in the design of the type system for the module language. We first consider a "plain" notion of module, where a module is just a set of mutually recursive toplevel definitions, and illustrate the notions of: module intrachecking (each module is typechecked in isolation and its interface, which is the set of typings of the defined identifiers, is inferred); interface interchecking (when linking modules, typechecking is done just by looking at the interfaces); interface specialization (interface intrachecking may require to specialize the typing listed in the interfaces); principal interfaces (the principal typing property for the type system of modules); and separate typechecking (looking at the code of the modules does not provide more type information than looking at their interfaces). Then we illustrate some limitations of the "plain" framework and extend the module language and the type system in order to overcome these limitations. The decidability of the system is shown by providing algorithms for the fundamental operations involved in module intrachecking and interface interchecking.
Strictness, Totality, and NonStandard Type Inference
, 2000
"... In this paper we present two nonstandard type inference systems for conjunctive strictness and totality analyses of higherorder typed functional programs and prove completeness results for both the strictness and the totality type entailment relations. We also study the interactions between strict ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
In this paper we present two nonstandard type inference systems for conjunctive strictness and totality analyses of higherorder typed functional programs and prove completeness results for both the strictness and the totality type entailment relations. We also study the interactions between strictness and totality analyses, showing that the information obtainable by a system that combines the two analyses, even though more refined than the information given by the two separate systems, cannot be effectively used. A main feature of our approach is that all the results are proved by relying directly on the operational semantics of the programming language considered. This leads to a rather direct presentation which involves relatively little mathematical overhead.
On Type Inference in the Intersection Type Discipline
, 2004
"... We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended # calculus, where one never erases arguments that would be discarded by ordinary #reduction. We show that our notion ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We introduce a new unification procedure for the type inference problem in the intersection type discipline. We show that unification exactly corresponds to reduction in an extended # calculus, where one never erases arguments that would be discarded by ordinary #reduction. We show that our notion of unification allows us to compute a principal typing for any strongly normalizing #expression.
Strict Intersection Types for the Lambda Calculus
, 2010
"... This paper will show the usefulness and elegance of strict intersection types for the Lambda Calculus; these are strict in the sense that they are the representatives of equivalence classes of types in the BCDsystem [15]. We will focus on the essential intersection type assignment; this system is a ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
This paper will show the usefulness and elegance of strict intersection types for the Lambda Calculus; these are strict in the sense that they are the representatives of equivalence classes of types in the BCDsystem [15]. We will focus on the essential intersection type assignment; this system is almost syntax directed, and we will show that all major properties hold that are known to hold for other intersection systems, like the approximation theorem, the characterisation of (head/strong) normalisation, completeness of type assignment using filter semantics, strong normalisation for cutelimination and the principal pair property. In part, the proofs for these properties are new; we will briefly compare the essential system with other existing systems.