Fully Abstract Normal Form Bisimulation for Call-by-Value PCF

Pushdown Normal-Form Bisimulation: A Nominal Context-Free Approach to Program Equivalence

“…The SyTeCi tool [31] combines notions from game semantics and logical relations, and manages to overcome some of the language restrictions of game-semantics tools. Normal form bisimulation, discussed in the introduction, treats contextgenerated code symbolically, entirely removing quantification over context-generated code and leading to sound but not complete techniques, with the notable exception of the case of higher-order languages with: sequential control and state [57], state-only [6,35], and no effects [36]. It has been shown [35,43,44] that NF bisimulation relates to operational game semantics models where opponentgenerated terms are also represented by names [21,30,39].…”

“…The problem of contextual equivalence in programming languages focuses on whether two program terms exhibit the same operational behaviour within any program context [47]. Despite the problem being undecidable, recent work has advanced decidable equivalence verification in functional, higher-order languages where the behaviour of a term depends on external unknown code provided by the context as an argument [26,31,35,36,48].…”

“…The technique was originally defined for characterising Lévy-Longo tree equivalence for the lazy lambda calculus [53] and adapted to languages with call-by-name [40], call-by-value [41], nondeterminism [42], aspects [33], recursive types [43], polymorphism [44], control with state [57], state-only [6], and control-only [5]. More recently, it was used to create equivalence verification techniques for call-by-value functional languages with and without state [35,36].…”

Sharing a Perspective on the 𝜆-Calculus

“…In the literature, there are fully abstract natural models for extensions of CbV, for instance for CbV PCF by Honda and Yoshida [37], Abramsky and McCusker [2], and Koutavas et al [40], for CbV PCF with higher-order state by Abramsky, Honda, and McCusker [1], and for the CbV quantum 𝜆-calculus by Clairambault and de Visme [28]. There are however no such models for pure CbV (that is, untyped, effect-free, no arithmetic nor conditionals), and full abstraction is not preserved by restrictions nor extensions (PCF has arithmetic operations and conditionals, which can be seen as an extension, but it is typed, which is instead a restriction with respect to pure CbV).…”