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Expansion: the Crucial Mechanism for Type Inference with Intersection Types: Survey and Explanation
 In: (ITRS ’04
, 2005
"... The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying ..."
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Cited by 17 (7 self)
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The operation of expansion on typings was introduced at the end of the 1970s by Coppo, Dezani, and Venneri for reasoning about the possible typings of a term when using intersection types. Until recently, it has remained somewhat mysterious and unfamiliar, even though it is essential for carrying out compositional type inference. The fundamental idea of expansion is to be able to calculate the effect on the final judgement of a typing derivation of inserting a use of the intersectionintroduction typing rule at some (possibly deeply nested) position, without actually needing to build the new derivation.
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 ..."
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Cited by 8 (1 self)
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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.
On the Safety of Nöcker’s Strictness Analysis
 FRANKFURT AM MAIN, GERMANY
"... Abstract. This paper proves correctness of Nöcker’s method of strictness analysis, implemented for Clean, which is an effective way for strictness analysis in lazy functional languages based on their operational semantics. We improve upon the work of Clark, Hankin and Hunt, which addresses correctne ..."
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Cited by 8 (7 self)
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Abstract. This paper proves correctness of Nöcker’s method of strictness analysis, implemented for Clean, which is an effective way for strictness analysis in lazy functional languages based on their operational semantics. We improve upon the work of Clark, Hankin and Hunt, which addresses correctness of the abstract reduction rules. Our method also addresses the cycle detection rules, which are the main strength of Nöcker’s strictness analysis. We reformulate Nöcker’s strictness analysis algorithm in a higherorder lambdacalculus with case, constructors, letrec, and a nondeterministic choice operator ⊕ used as a union operator. Furthermore, the calculus is expressive enough to represent abstract constants like Top or Inf. The operational semantics is a smallstep semantics and equality of expressions is defined by a contextual semantics that observes termination of expressions. The correctness of several reductions is proved using a context lemma and complete sets of forking and commuting diagrams.
Exact Intersection Typing Inference and CallbyName Evaluation
, 2004
"... It is known that inferring an exact intersection typing for a #term (i.e., a typing where the intersection operator is not idempotent) is equivalent to strong #normalisation of that term. Intersection typing derivations can provide very precise information about program behaviour, making them  ..."
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It is known that inferring an exact intersection typing for a #term (i.e., a typing where the intersection operator is not idempotent) is equivalent to strong #normalisation of that term. Intersection typing derivations can provide very precise information about program behaviour, making them  in principle  an attractive framework for program analysis. The recent innovation of expansion variables greatly simplifies the production of such typing derivations, allows their production for all #normalising terms and allows inference to be done in a truly compositional way  a big advantage for programs where components are updated frequently and separately. We present a new, truly compositional, exact intersection typing inference procedure for the recent, expansion variablebased, System E framework. Inference uses a confluent rewrite system to solve instances of a unification problem with expansion variables. Moreover, we explain precisely how the inferred typingderivation describes the evaluation of the term, showing that the typing derivation most accurately describes its callbyname evaluation via a linear transformation. For other evaluation strategies, di#erent inference algorithms will be required. 1