Program equivalence in an untyped, call-by-value functional language with uncurried functions

A Formalisation of Core Erlang, a Concurrent Actor Language

“…In this section we discuss and extend the formal syntax of the sequential sublanguage of Core Erlang as presented in our previous work [19]. For better readability, we use a syntax definition that abstracts over the concrete syntax of the language; however, any expressions written in this syntax can be simply transformed to Core Erlang.…”

“…Note that process identifiers are not patterns in Core Erlang, but with process identifiers as patterns, we can distinguish them from other values of the language; in Erlang, the is_pid function can be used instead. This distinction is needed to maintain the proof of coincidence of sequential equivalence definitions described in [19] (namely, the coincidence of behavioural and contextual equivalence).…”

“…We extend the syntax (as in [19]) with two language elements in this work, the first one is BIF (built-in function) call (denoted by call e(e 1 , . .…”

“…, v k values in the expression e. We omit further details about substitutions and static semantics since they are not in the scope of this paper. For further details we refer to our previous work [19] and to the formalisation [9]. Next, we show an example expression in the syntax presented above:…”

“…On the one hand, we are interested in using the semantics to prove particular pairs of programs equivalent, and on the other, the correctness of many local refactoring steps can be reduced to the equivalence of simple expressions. When developing precise, standard definitions of equivalence, we decided to bring our results to smaller-step semantics and developed a frame stack semantics and equivalence definitions [32] built on that for sequential Core Erlang [19]. The frame stack style for semantics is beneficial for two reasons: it is well-suited to express various standard equivalence definitions [29], and furthermore, the semantics of concurrent expressions can be defined more easily in small-step approaches [25].…”