Call-by-Value Solvability, Revisited

Abstract

Abstract. In the call-by-value lambda-calculus solvable terms have been characterised by means of call-by-name reductions, which is disappointing and requires complex reasonings. We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λCBV calculus and from Accattoli and Kesner's substitution calculus λsub. In this new setting, we characterise solvable terms as those terms having normal form with respect to a suitable restriction of the rewriting relation.

A Semantical and Operational Account of Call-by-Value Solvability

“…a variable or an abstraction. As argued in [5], a good CBV λ-calculus should enjoy an internal operational characterization (i.e. by using CBV reduction rules) of CBV-solvability.…”

“…There are many proposals of alternative CBV λ-calculi (see [9,10,11,12,5]) extending Plotkin's one by using explicit substitutions (constructors of the form let...in). In particular, Accattoli and Paolini [5] introduced recently the λ vsubcalculus where the reduction rule acts at a distance by extending the notion of β v -redex (with explicit substitutions).…”

“…In particular, Accattoli and Paolini [5] introduced recently the λ vsubcalculus where the reduction rule acts at a distance by extending the notion of β v -redex (with explicit substitutions). In this setting they give an internal operational characterization of solvability and this characterization lifts to Herbelin and Zimmermann's λ CBV -calculus, another CBV λ-calculus with explicit substitutions introduced in [9] (without rules acting at a distance but with commutation rules for explicit substitutions).…”

“…The starting points of our work are [6,5,14]. We introduce the λ σ v -calculus, a CBV λ-calculus having the same syntax as ordinary (and hence Plotkin's CBV) λ-calculus (there are no explicit substitutions) and extending the β vreduction by adding two reduction rules, σ 1 and σ 3 .…”

The Negligible and Yet Subtle Cost of Pattern Matching

“…Our proof uses a new simple formalism, the LInear Matching calculus by valuE (shortened LIME ), that is a variation over other formalisms studied by Accattoli and coauthors (the value substitution calculus [13], the GLAM abstract machine [9], and the micro-substituting abstract machine [4]). …”