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72
The Essence of Principal Typings
 In Proc. 29th Int’l Coll. Automata, Languages, and Programming, volume 2380 of LNCS
, 2002
"... Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A M : # meanin ..."
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Cited by 97 (15 self)
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Let S be some type system. A typing in S for a typable term M is the collection of all of the information other than M which appears in the final judgement of a proof derivation showing that M is typable. For example, suppose there is a derivation in S ending with the judgement A M : # meaning that M has result type # when assuming the types of free variables are given by A. Then (A, #) is a typing for M .
Normalization Results for Typeable Rewrite Systems
, 1997
"... In this paper we introduce Curryfied Term Rewriting Systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts and !. Three operations on types  substitution, expansion, and lifting  are used to define type assignment, and are proved to be ..."
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Cited by 30 (26 self)
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In this paper we introduce Curryfied Term Rewriting Systems, and a notion of partial type assignment on terms and rewrite rules that uses intersection types with sorts and !. Three operations on types  substitution, expansion, and lifting  are used to define type assignment, and are proved to be sound. With this result the system is proved closed for reduction. Using a more liberal approach to recursion, we define a general scheme for recursive definitions and prove that, for all systems that satisfy this scheme, every term typeable without using the typeconstant ! is strongly normalizable. We also show that, under certain restrictions, all typeable terms have a (weak) headnormal form, and that terms whose type does not contain ! are normalizable.
System E: Expansion variables for flexible typing with linear and nonlinear types and intersection types
 IN PROGRAMMING LANGUAGES & SYSTEMS, 13TH EUROPEAN SYMP. PROGRAMMING
, 2004
"... Types are often used to control and analyze computer programs. ..."
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Cited by 27 (16 self)
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Types are often used to control and analyze computer programs.
Rank 2 Intersection Type Assignment in Term Rewriting Systems
 Fundamenta Informaticae
, 1996
"... A notion of type assignment on Curryfied Term Rewriting Systems is introduced that uses Intersection Types of Rank 2, and in which all function symbols are assumed to have a type. Type assignment will consist of specifying derivation rules that describe how types can be assigned to terms, using the ..."
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Cited by 22 (14 self)
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A notion of type assignment on Curryfied Term Rewriting Systems is introduced that uses Intersection Types of Rank 2, and in which all function symbols are assumed to have a type. Type assignment will consist of specifying derivation rules that describe how types can be assigned to terms, using the types of function symbols. Using a modified unification procedure, for each term the principal pair (of basis and type) will be defined in the following sense: from these all admissible pairs can be generated by chains of operations on pairs, consisting of the operations substitution, copying, and weakening. In general, given an arbitrary typeable CuTRS, the subject reduction property does not hold. Using the principal type for the lefthand side of a rewrite rule, a sufficient and decidable condition will be formulated that typeable rewrite rules should satisfy in order to obtain this property.
Intersection types for explicit substitutions
, 2003
"... We present a new system of intersection types for a compositionfree calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical inte ..."
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Cited by 22 (8 self)
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We present a new system of intersection types for a compositionfree calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.
CutElimination in the Strict Intersection Type Assignment System is Strongly Normalising
 NOTRE DAME J. OF FORMAL LOGIC
, 2004
"... This paper defines reduction on derivations (cutelimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of term ..."
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Cited by 16 (12 self)
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This paper defines reduction on derivations (cutelimination) in the Strict Intersection Type Assignment System of [1] and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability of terms, using intersection types.
Branching Types
, 2002
"... Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type ..."
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Cited by 15 (5 self)
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Although systems with intersection types have many unique capabilities, there has never been a fully satisfactory explicitly typed system with intersection types. We introduce and prove the basic properties of # , a typed #calculus with branching types and types with quantification over type selection parameters. The new system # an explicitly typed system with the same expressiveness as a system with intersection types. Typing derivations in # use branching types to squash together what would be separate parallel derivations in earlier systems with intersection types.
Filter Models for ConjunctiveDisjunctive λcalculi
, 1996
"... The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction i ..."
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Cited by 14 (6 self)
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The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction is introduced, extending fireduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morrisstyle operational semantics and with a semantics based on a notion of capabilities.
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 ..."
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Cited by 13 (5 self)
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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.
Normalisation, Approximation, and Semantics for Combinator Systems
 Theoretical Computer Science
, 2003
"... This paper studies normalization of typeable terms and the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on type derivations; the last will be proved to be strongly normali ..."
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Cited by 13 (11 self)
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This paper studies normalization of typeable terms and the relation between approximation semantics and filter models for Combinator Systems. It presents notions of approximants for terms, intersection type assignment, and reduction on type derivations; the last will be proved to be strongly normalizable. With this result, it is shown that, for every typeable term, there exists an approximant with the same type, and a characterization of the normalization behaviour of terms using their assignable types is given. Then the two semantics are defined and compared, and it is shown that the approximants semantics is fully abstract but the filter semantics is not.