Process Types as a Descriptive Tool for Interaction

Abstract

Abstract. We demonstrate a tight relationship between linearly typed π-calculi and typed λ-calculi by giving a type-preserving translation from the call-by-value λµ-calculus into a typed π-calculus. The λµ-calculus has a particularly simple representation as typed mobile processes. The target calculus is a simple variant of the linear π-calculus. We establish full abstraction up to maximally consistent observational congruences in source and target calculi using techniques from games semantics and process calculi.

Causality in Linear Logic

“…The work [12] shows that permutation rules of Linear Logic, understood as asynchronous optimisations on processes, are included in the observational equivalence. [19] studies mutual embedding between polarised proof nets [23] and the control π-calculus [20]. In another direction, we have recently built a fully-abstract, concurrent game semantics model of the synchronous session π-calculus [8].…”

Dualized Simple Type Theory

“…There is some intuition one can use while thinking about this style of programming that is based on the encoding of classical logic -Parigot's λµ-calculus -into the π-calculus. See for example [35,17]. We can think of positive variables as input ports, and negative variables as output ports.…”

Fully abstract encodings of λ-calculus in HOcore through abstract machines

“…Related work: Since Milner's seminal work [19], other translations of the λ-calculus or one of its variants into π-calculus have been proposed, e.g., to study connections with logic [2,5,23], termination [9,4,25], sequentiality [6], control [9,12,24], or Continuation-Passing Style (CPS) transforms [21,22,10]. These works use the more expressive first-order π-calculus, except for [21,22], discussed below; full abstraction is proved w.r.t.…”

“…These works use the more expressive first-order π-calculus, except for [21,22], discussed below; full abstraction is proved w.r.t. contextual equivalence in [6,25,12], normal-form bisimilarity in [24], and normalform and applicative bisimilarities in [22]. The definitions of the encodings and the equivalences of [6,25,12] are driven by types, and therefore cannot be compared to our untyped setting.…”

“…contextual equivalence in [6,25,12], normal-form bisimilarity in [24], and normalform and applicative bisimilarities in [22]. The definitions of the encodings and the equivalences of [6,25,12] are driven by types, and therefore cannot be compared to our untyped setting. In [24], van Bakel et al establish a full abstraction result between the λµ-calculus with normal-form bisimilarity and the π-calculus.…”