We present a logical system CFP (Concurrent Fixed Point Logic) from whose proofs one can extract nondeterministic and concurrent programs that are provably total and correct with respect to the proven formula. CFP is an intuitionistic first-order logic with inductive and coinductive definitions extended by two propositional operators, A || B (restriction, a strengthening of the implication B -> A) and $\ddownarrow(A)$ (total concurrency). The target of the extraction 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. The correctness of extracted programs is proven via an intermediate domain-theoretic denotational semantics. We demonstrate the usefulness of our system by extracting a concurrent program that translates infinite Gray code into the signed digit representation. A noteworthy feature of our system is 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.

翻译：我们提出了一个逻辑系统CFP(当前固定点逻辑),其证据可以从中提取非决定性和并行的程序,对于被证实的公式来说,这种程序是完全和正确的。 CFP是一种直率第一阶逻辑,由两个提议操作者A ⁇ B(限制,增强B - > A)和$\ddownrow(A) (总货币)扩展了推论和重现。提取的目标是由建造者Amb(McCarthy's amb) 扩展的建造者和循环者(对McCarthy's amb) 的羊毛微缩缩缩缩缩缩微缩缩缩缩缩缩微缩微缩微缩微缩缩微缩微缩微缩缩微缩缩缩微缩缩缩微缩缩微缩缩缩缩缩微)所扩展的逻辑,在实际操作上被解释为全球天使选择。通过中间的域论脱微缩缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩微缩音,通过。