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12
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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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 .
Intersection Type Assignment Systems
 THEORETICAL COMPUTER SCIENCE
, 1995
"... This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essenti ..."
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Cited by 62 (34 self)
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This paper gives an overview of intersection type assignment for the Lambda Calculus, as well as compare in detail variants that have been defined in the past. It presents the essential intersection type assignment system, that will prove to be as powerful as the wellknown BCDsystem. It is essential in the following sense: it is an almost syntax directed system that satisfies all major properties of the BCDsystem, and the types used are the representatives of equivalence classes of types in the BCDsystem. The set of typeable terms can be characterized in the same way, the system is complete with respect to the simple type semantics, and it has the principal type property.
Principality and Decidable Type Inference for FiniteRank Intersection Types
 In Conf. Rec. POPL ’99: 26th ACM Symp. Princ. of Prog. Langs
, 1999
"... Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typin ..."
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Cited by 52 (17 self)
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Principality of typings is the property that for each typable term, there is a typing from which all other typings are obtained via some set of operations. Type inference is the problem of finding a typing for a given term, if possible. We define an intersection type system which has principal typings and types exactly the strongly normalizable terms. More interestingly, every finiterank restriction of this system (using Leivant's first notion of rank) has principal typings and also has decidable type inference. This is in contrast to System F where the finite rank restriction for every finite rank at 3 and above has neither principal typings nor decidable type inference. This is also in contrast to earlier presentations of intersection types where the status (decidable or undecidable) of these properties is unknown for the finiterank restrictions at 3 and above. Furthermore, the notion of principal typings for our system involves only one operation, substitution, rather than severa...
Principal type schemes for the strict type assignment system
 Logic and Computation
, 1993
"... We study the strict type assignment system, a restriction of the intersection type discipline [6], and prove that it has the principal type property. We define, for a term, the principal pair (of basis and type). We specify three operations on pairs, and prove that all pairs deducible for can be obt ..."
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Cited by 36 (20 self)
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We study the strict type assignment system, a restriction of the intersection type discipline [6], and prove that it has the principal type property. We define, for a term, the principal pair (of basis and type). We specify three operations on pairs, and prove that all pairs deducible for can be obtained from the principal one by these operations, and that these map deducible pairs to deducible pairs.
A Semantics for Static Type Inference
 Information and Computation
, 1993
"... Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show compl ..."
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Cited by 9 (0 self)
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Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show completeness for Curry's system itself, relative to an extended notion of model that validates reduction but not conversion.
OrderIncompleteness and Finite Lambda Models (Extended Abstract)
 Eleventh Annual IEEE Symposium on Logic in Computer Science
, 1996
"... Peter Selinger Department of Mathematics University of Pennsylvania 209 S. 33rd Street Philadelphia, PA 191046395 selinger@math.upenn.edu Abstract Many familiar models of the typefree lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about or ..."
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Peter Selinger Department of Mathematics University of Pennsylvania 209 S. 33rd Street Philadelphia, PA 191046395 selinger@math.upenn.edu Abstract Many familiar models of the typefree lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory of fi or fijconversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the typefree lambda calculus cannot be nontrivially partially ordered. Our second result is a syntactical characterization, in terms of socalled generalized Mal'cev operators, of those lambda theories which cannot be induced by any nontrivially partially ordered model. We also consider a notion of finite models for the typefree lambda calculus. We introduce partial syntactical lambda models, which are derived from Plotkin's syntactical models of redu...
Polymorphic Intersection Type Assignment for Rewite Systems with Intersection and betarule (Extended Abstract)
 IN TYPES’99. LNCS
, 2000
"... We define two type assignment systems for firstorder rewriting extended with application,abstraction, andreduction (TRS). The types used in these systems are a combination of (free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction t ..."
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Cited by 4 (2 self)
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We define two type assignment systems for firstorder rewriting extended with application,abstraction, andreduction (TRS). The types used in these systems are a combination of (free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction theorem and show that all typeable terms are strongly normalisable. The second is a decidable subsystem of the first, by restricting types to Rank 2. For this system we define, using an extended notion of unification, a notion of principal type, and show that type assignment is decidable.
Functionality, polymorphism, and concurrency: a mathematical investigation of programming paradigms
, 1997
"... ii COPYRIGHT ..."
Proving Properties of Typed Lambda Terms Using Realizability, Covers, and Sheaves
 Theoretical Computer Science
, 1995
"... . The main purpose of this paper is to take apart the reducibility method in order to understand how its pieces fit together, and in particular, to recast the conditions on candidates of reducibility as sheaf conditions. There has been a feeling among experts on this subject that it should be possib ..."
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. The main purpose of this paper is to take apart the reducibility method in order to understand how its pieces fit together, and in particular, to recast the conditions on candidates of reducibility as sheaf conditions. There has been a feeling among experts on this subject that it should be possible to present the reducibility method using more semantic means, and that a deeper understanding would then be gained. This paper gives mathematical substance to this feeling, by presenting a generalization of the reducibility method based on a semantic notion of realizability which uses the notion of a cover algebra (as in abstract sheaf theory). A key technical ingredient is the introduction a new class of semantic structures equipped with preorders, called preapplicative structures. These structures need not be extensional. In this framework, a general realizability theorem can be shown. Kleene's recursive realizability and a variant of Kreisel's modified realizability both fit into this...
Contents
, 2005
"... A summary of the motivation and theory behind abstract interpretation, including the accumulating semantics, Galois connections and widening. A complete demonstration of the use of abstract interpretation to define a safe and optimal sign analysis in the context of a simple imperative language is pr ..."
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A summary of the motivation and theory behind abstract interpretation, including the accumulating semantics, Galois connections and widening. A complete demonstration of the use of abstract interpretation to define a safe and optimal sign analysis in the context of a simple imperative language is presented. In addition, a example of widening is described to improve the termination properties of an interval analysis of the same language. Keywords: • Semantics • Program analysis