On the Implementation of Dynamic Patterns

Balabonski, Thibaut

doi:10.4204/eptcs.49.2

Cited by 1 publication

(2 citation statements)

References 7 publications

(12 reference statements)

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“…• H ∆ b (Γ, σ) τ contains all the anfs a such that b is a head subterm of a, and such that if b ∈ T(∆, σ) then a ∈ T(Γ + ∆, τ ). 1 It is worth noticing that, given Γ and σ, the set of anfs a such that there exists a derivation Π Γ a : σ is possibly infinite. However, the subset of those verifying a = A(Π) is finite; they are the minimal ones, those generated by the inhabitation algorithm (this is proved in Lemma 4.7).…”

Section: Inhabitation For System Pmentioning

confidence: 99%

“…We define a pattern calculus with explicit pattern-matching called Λ p -calculus. The use of explicit pattern-matching becomes very appropriate to implement different evaluation strategies, thus giving rise to different languages with pattern-matching [11,12,1]. In all of them, an application (λp.t)u reduces to t[p/u], where the constructor [p/u] is an explicit matching, defined by means of suitable reduction rules, which are used to decide if the argument u matches the pattern p. If the matching is possible, the evaluation proceeds by computing a substitution which is applied to the body t. Otherwise, two cases may arise: either a successful matching is not possible at all, and then the term t[p/u] reduces to a failure, denoted by the constant fail, or pattern matching could potentially become possible after the application of some pertinent substitution to the argument u, in which case the reduction is simply blocked.…”

Section: Introductionmentioning

confidence: 99%

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Solvability = Typability + Inhabitation

Bucciarelli,

Kesner,

Della Rocca

2018

Preprint

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We define an observability property for a calculus with pattern matching which is inspired by the notion of solvability for the λ-calculus. We prove that observability can be characterized by means of typability and inhabitation in an intersection type system P based on non-idempotent types. We show first that the system P characterizes the set of terms having canonical form, i.e. that a term is typable if and only if it reduces to a canonical form. But the set of observable terms is properly contained in the set of canonical form. Thus, typability alone is not sufficient to characterize observability, in contrast to the solvability case for λ-calculus. We then prove that typability, together with inhabitation, provides a full characterization of observability, in the sense that a term is observable if and only if it is typable and the types of all its arguments are inhabited. We complete the picture by providing an algorithm for the inhabitation problem of P.

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Section: Inhabitation For System Pmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%