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The Essence of Principal Typings - Wells (2002) (51 citations) (Correct)
....the discussion here gives only the highlights. The first system of intersection types for which principal typings was proved was presented by Coppo, Dezani, and Venneri [3] a later version is [4] The same general approach has been followed by Ronchi Della Rocca and Venneri [30] and van Bakel [34] for other systems of intersection types. In this approach, finding a principal typing algorithm for a term M involves finding a normal form (or approximate normal form) M # for M , assigning a typing t to M # , proving that any typing for the normal form M # is also a typing for the ....
....to understand. The first potentially practical approaches to principal typing with intersection types were subsequent unification based methods which focused on the rank 2 restriction of intersection types. Van Bakel presented a unification algorithm for principal typing for a rank 2 system [34]. Later independent work by Jim also attacks the same problem, but with more emphasis on handling practical programming language issues such as recursive definitions, separate compilation, and accurate error messages [15] Successors to Jim s method include Banerjee s [1] which integrates flow ....
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Intersection Types and the Linear Lambda-Calculus - Ario Florido And (2001) (Correct)
....type system in a derivation in the Coppo Dezani type system (which types all strongly normalizable terms) This can be done by induction in the length of the derivation tree. The only if part is similar to proofs of the same property of other intersection type systems (see, for example, Pot80] or [vB93]) The technique used is to show that the intersection type system types terms in normal form. Then we show that if A C[M [N=x] and N is typable then A C[ x:M)N ] C[ is the usual notation for a context) Finally the result follows by induction on the inside out reduction path of ....
S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Department of Computer Science, University of Nijmegen, 1993.
Rank 2 Type Systems and Recursive Definitions - Jim (1995) (15 citations) (Correct)
....that ranks 3 and higher in System F are undecidable. Leivant s original paper is almost the only work on rank 2 of the intersection type discipline, which we call I 2 . Leivant sketched a type inference algorithm for I 2 , but the algorithm was not formalized and proved correct until recently [33]. Leivant also conjectured the undecidability of ranks 3 and higher in the intersection system; to our knowledge the details of his proof idea have never been verified. I 2 has a significant advantage over 2 : it has principal typings. This means that for any term M , if M is typable in I 2 , ....
....1 [ S 2 ) t) t otherwise. Note that we have made a severe restriction on substitutions: they map type variables only to simple types, and not types in general. 2. 2 The rank 2 intersection type system There are many different formulations of intersection type systems; see van Bakel [33] for a survey. We will present a very restricted intersection type system here, the system of rank 2 intersection types. Our system is a slight generalization of van Bakel s version (see x4.1) The terms of the intersection type system are just the terms of the lambda calculus. The sets T 1 and T ....
[Article contains additional citation context not shown here]
Steffen van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Mathematisch Centrum, Amsterdam, February 1993.
Rank 2 Type Systems and Recursive Definitions - Jim (1995) (15 citations) (Correct)
....that ranks 3 and higher in System F are undecidable. Leivant s original paper is almost the only work on rank 2 of the intersection type discipline, which we call I 2 . Leivant sketched a type inference algorithm for I 2 , but the algorithm was not formalized and proved correct until recently [33]. Leivant also conjectured the undecidability of ranks 3 and higher in the intersection system; to our knowledge the details of his proof idea have never been verified. I 2 has a significant advantage over 2 : it has principal typings. This means that for any term M , if M is typable in I 2 , ....
....(S 1 [ S 2 ) t) t otherwise. Note that we have made a severe restriction on substitutions: they map type variables only to simple types, and not types in general. 2. 2 The rank 2 intersection type system There are many different formulations of intersection type systems; see van Bakel [33] for a survey. We will present a very restricted intersection type system here, the system of rank 2 intersection types. Our system is a slight generalization of van Bakel s version (see x4.1) The terms of the intersection type system are just the terms of the lambda calculus. The sets T 1 and T ....
[Article contains additional citation context not shown here]
Steffen van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Mathematisch Centrum, Amsterdam, February 1993.
A Typed Intermediate Language for Flow-Directed Compilation - Wells, Dimock, Muller.. (1997) (14 citations) (Correct)
....information [6] While it is clearly possible to compute, record, and use the flow and type information separately, we believe that a single representation is more natural for compilation. General research into intersection types that has influenced our thinking includes the work of Van Bakel [29] and Jim [15] Research on both intersection and union types that we have consulted includes the work by Pierce [22] Aiken, Wimmers, and Lakshman [3, 4] Barbanera and Dezani Ciancaglini [7] and Trifonov and Smith [28] Of the above, only Pierce considers intersection and union types in an ....
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Catholic University of Nijmegen, 1993.
Strongly Typed Flow-Directed Representation.. - Dimock, Muller.. (1997) (15 citations) (Correct)
....R ST ) then [A # ] R,M # # # CIL [M # ] R,E start ,M # : # # ] R,M # . We have not yet proved that applying the RT algorithm preserves the meaning of the program. 4 Related Work General research into the use of intersection types which has influenced us includes the work of Van Bakel [27] and Jim [14, 15] Relevant research on both intersection and union types includes the work by Pierce [21] Aiken, Wimmers, and Lakshman [3] Trifonov, Smith, and Eifrig [26, 9] and Barbanera, Dezani Ciancaglini, and de Liguoro [7] Of the above, only Pierce considers intersection and union types ....
Ste#en J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Relating Typability and Expressiveness in Finite-Rank.. - Kfoury, Mairson (1999) (Correct)
....on generic containers such as lists, trees, etc. It is well known that it is undecidable whether a # term M is typable with intersection and function types, because this holds exactly when M is strongly normalizable. However, the rank 2 restriction of intersection types, studied by van Bakel [vB93] and Jim [Jim96] has computable type inference, and recognizes strictly more typable terms than the Hindley Milner system at the core of ML and Haskell type inference. The finite rank restriction on intersection types bounds how deeply the # can appear in type expressions, counting nesting in ....
....of # types only occurs at # term variables, and so is absorbed into the VAR rule. The restricted placement of # introduction and # elimination simplifies type inference, but types the same set of (untyped) terms as other intersection type systems, the set of strongly # normalizing terms [CDCV80, CDCV81, RDRV84, vB93]. The APP rule requires each of the alternatives in the argument of an application to be a typed version of the same untyped # term. This is similar to the formulation of # CIL , the flow typed intermediate language being used in the Church Project [WDMT0X] 6 . Key di#erences are that (1) # ....
[Article contains additional citation context not shown here]
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Catholic University of Nijmegen, 1993.
On Type Inference - In The Intersection (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, PhD Thesis, Mathematisch Centrum, Amsterdam (####).
Expansion: the Crucial Mechanism for Type Inference with.. - Carlier, Wells (2004) (1 citation) (Correct)
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Ste#en J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
On Type Inference in the - Intersection Type Discipline (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, PhD Thesis, Mathematisch Centrum, Amsterdam (1993).
Strongly Typed Flow-Directed Representation Transformations - Dimock, Muller, Turbak.. (1997) (15 citations) (Correct)
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Steffen van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, University of Nijmegen, 1993.
Expansion: the Crucial Mechanism for Type Inference with.. - Carlier, Wells (2004) (1 citation) (Correct)
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Ste#en J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Rank-2 Intersection and Polymorphic Recursion - Damiani (2005) (2 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (1996) (Correct)
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van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993. 34
Type Inference with Expansion Variables and Intersection.. - Carlier, Wells (5 citations) (Correct)
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S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Intersection Types, λ-models, and Böhm Trees - Dezani-Ciancaglini.. (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Ph.D. Thesis, Mathematisch Centrum, Amsterdam, 1993.
Expansion: the Crucial Mechanism for Type Inference with.. - Carlier, Wells (2005) (1 citation) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
The Essence of Principal Typings - Wells (2002) (51 citations) (Correct)
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S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Restricted intersection type assignment systems and object.. - de'Liguoro (2002) (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, PhD Thesis, University of Nijmegen, 1993.
Rank 2 Intersection Types for Modules (Version with conclusions.. - Damiani (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993.
A Typed Intermediate Language for Flow-Directed Compilation - Wells, Dimock, Muller.. (1997) (14 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, University of Nijmegen, 1993.
Rank 2 Intersection Types for Local Definitions and Conditional.. - Damiani (2003) (15 citations) (Correct)
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VAN BAKEL, S. 1993. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Katholieke Universiteit Nijmegen.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (2000) (Correct)
No context found.
van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993.
Type Inference with Expansion Variables and Intersection.. - Carlier, Wells (2004) (5 citations) (Correct)
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S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Types, Potency, and Idempotency: Why Nonlinearity and.. - Neergaard, Mairson (2004) (Correct)
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S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Principality and Decidable Type Inference for Finite-Rank.. - Kfoury, Wells (1998) (19 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Principality and Decidable Type Inference for Finite-Rank.. - Kfoury, Wells (1998) (19 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (1996) (Correct)
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van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993. 34
Beta-Reduction As Unification - Kfoury (1996) (8 citations) (Correct)
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van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993. 32
On Type Inference in the Intersection Type Discipline - Boudol, Zimmer (2004) (3 citations) (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, PhD Thesis, Mathematisch Centrum, Amsterdam (####).
Type Inference with Expansion Variables and Intersection.. - Carlier, Wells (5 citations) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
Principality and Type Inference for Intersection Types Using.. - Kfoury, Wells (2003) (4 citations) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Catholic University of Nijmegen, 1993.
Rank 2 Intersection Types for Modules - Damiani (2003) (12 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993.
Characterizing Convergent Terms in Object Calculi via.. - de'Liguoro (Correct)
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S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting, Ph.D. Thesis, Mathematisch Centrum, Amsterdam 1993.
Strictness, Totality, and Non-Standard Type - Inference Mario Coppo (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993. 52
A Type System Equivalent to Model Checking - Naik (2003) (Correct)
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Stefan van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1991.
Principal Typings and True Rank 2 Intersection Typable Recursive.. - Damiani (2003) (3 citations) (Correct)
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S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993.
Principality and Type Inference for Intersection Types Using.. - Kfoury, Wells (2003) (4 citations) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Catholic University of Nijmegen, 1993.
Restricted intersection type assignment systems and object.. - de'Liguoro (2002) (Correct)
No context found.
S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, PhD Thesis, University of Nijmegen, 1993.
Rank 2 Intersection Types for Modules (Version with conclusions.. - Damiani (Correct)
No context found.
S. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Katholieke Universiteit Nijmegen, 1993.
Type Inference with Expansion Variables and Intersection.. - Carlier, Wells (5 citations) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (2000) (Correct)
No context found.
van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993.
A Linearization of the Lambda-Calculus and Consequences - Kfoury (1996) (Correct)
No context found.
van Bakel, S., Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems, Doctoral dissertation, Catholic University of Nijmegen, also issued by the Mathematisch Centrum, Amsterdam, 1993. 34
Relating Typability and Expressiveness in Finite-Rank .. - Kfoury, Mairson.. (1999) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. Ph.D. thesis, Catholic University of Nijmegen, 1993.
The Essence of Principal Typings - Wells (2002) (51 citations) (Correct)
No context found.
S. J. van Bakel. Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting Systems. PhD thesis, Catholic University of Nijmegen, 1993.
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