Extracting total Amb programs from proofs
It provides a foundational method for extracting provably correct concurrent programs from logical proofs, addressing a known bottleneck in program extraction for nondeterminism and concurrency.
The paper presents CFP, a logical system for extracting total and correct nondeterministic and concurrent programs from proofs, demonstrated by extracting a program translating infinite Gray code into signed digit representation.
We present a logical system CFP (Concurrent Fixed Point Logic) supporting the extraction of nondeterministic and concurrent programs that are provably total and correct. CFP is an intuitionistic first-order logic with inductive and coinductive definitions extended by two propositional operators: Restriction (binary), a strengthening of implication, and a unary operator for total concurrency. The source of the extraction is formal CFP proofs, the target is a lambda calculus with constructors and recursion extended by a constructor Amb (for McCarthy's amb) which is interpreted operationally as globally angelic choice and is used to implement nondeterminism and concurrency. The correctness of extracted programs is proven via an intermediate domain-theoretic denotational semantics. We demonstrate the usefulness of our system by extracting a nondeterministic program that translates infinite Gray code into the signed digit representation. A noteworthy feature of CFP is the fact that the proof rules for restriction and concurrency involve variants of the classical law of excluded middle that would not be interpretable computationally without Amb. This is a revised and extended version of the conference paper presented at ESOP 2022 with the same title that contains full proofs of all major results.