Types in lambda calculi and programming languages

We present a polyvariant closure, safety, and binding time analysis for the untyped lambda calculus. The innovation is to analyze each abstraction afresh at all syntactic application points. This is achieved by a semantics-preserving program transformation followed by a novel monovariant analysis, expressed using type constraints. The constraints are solved in cubic time by a single fixed-point computation.Safety analysis is aimed at determining if a term will cause an error during evaluation. We have recently proved that the monovariant safety analysis accepts strictly more terms than simple type inference. This paper demonstrates that the polyvariant transformation makes even more terms acceptable, even some without higher-order polymorphic types. Furthermore, polyvariant binding time analysis can improve the partial evaluators that base a polyvariant specialization on only monovariant binding time analysis.

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“…This is still true if we allow recursive types, as in the λµ-calculus [2]. Proo: This is also proved in [21].…”

Section: Comparison With Type Inference Resultmentioning

confidence: 67%

Polyvariant Analysis of the Untyped Lambda Calculus

Palsberg

Schwartzbach

1992

DPB

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“…The results are still valid if we allow recursive types, as in the λµ-calculus [1]. Here the TI constraints are exactly the same, but the type schemes are changed from finite to regular trees.…”

Section: Theorem 59mentioning

confidence: 80%

Safety Analysis versus Type Inference

Palsberg¹,

Schwartzbach²

1992

DPB

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Safety analysis is an algorithm for determining if a term in the untyped lambda calculus with constants is safe, i.e., if it does not cause an error during evaluation. This ambition is also shared by algorithms for type inference. Safety analysis and type inference are based on rather different perspectives, however. Safety analysis is based on closure analysis, whereas type inference attempts to assign a type to all subterms.In this paper we prove that safety analysis is sound, relative to both a strict and a lazy operational semantics, and superior to type inference, in the sense that it accepts strictly more safe lambda terms.The latter result may indicate the relative potentials of static program analyses based on respectively closure analysis and type inference.

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“…In our proofs we also use the (generation) Lemma 5.2.13 described in [2]. The (cut) rule is obtained taking ∆ ≡ in Sbs:…”

Section: Lemma 2 (Elementary Properties)mentioning

confidence: 99%

“…Pure Type Systems (PTS) [1,2] provide a flexible and general framework to study dependent type system properties. Moreover, PTS also include many interesting systems.…”

Section: Introductionmentioning

confidence: 99%

A Cut-Free Sequent Calculus for Pure Type Systems Verifying the Structural Rules of Gentzen/Kleene

Gutiérrez

Ruiz

2003

Logic Based Program Synthesis and Transformation

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Abstract. In this paper, a new notion for sequent calculus (à la Gentzen) for Pure Type Systems (PTS) is introduced. This new calculus, K, is equivalent to the standard PTS, and it has a cut-free subsystem, K cf , that will be proved to hold non-trivial properties such as the structural rules of Gentzen/Kleene: thinning, contraction, and interchange. An interpretation of completeness of the K cf system yields the concept of Cut Elimination, (CE), and it is an essential technique in proof theory; thus we think that it will have a deep impact on PTS and in logical frameworks based on PTS.

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Types in lambda calculi and programming languages

Cited by 34 publications

References 20 publications

Polyvariant Analysis of the Untyped Lambda Calculus

Polyvariant Analysis of the Untyped Lambda Calculus

Safety Analysis versus Type Inference

A Cut-Free Sequent Calculus for Pure Type Systems Verifying the Structural Rules of Gentzen/Kleene

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