Non-linear Pattern Matching with Backtracking for Non-free Data Types
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26,098 papers · page 408 of 1,305
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We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explici…
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We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution. We then refine to a machine with closure…
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The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical study. We show that the first-order theo…
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Program synthesis is the mechanised construction of software. One of the main difficulties is the efficient exploration of the very large solution space, and tools often require a user-provided syntactic restriction of the search space. We propose a new approach to program synthe…
Given a relational specification between Boolean inputs and outputs, the goal of Boolean functional synthesis is to synthesize each output as a function of the inputs such that the specification is met. In this paper, we first show that unless some hard conjectures in complexity …
Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for probabilistic programs. First, we present…
The cornerstone of dynamic partial order reduction (DPOR) is the notion of independence that is used to decide whether each pair of concurrent events p and t are in a race and thus both $$p \cdot t$$ and $$t \cdot p$$ must be explored. We present constrained dynamic partial order…
Symbolic automata (s-FAs) allow transitions to carry predicates over rich alphabet theories, such as linear arithmetic, and therefore extend classic automata to operate over infinite alphabets, such as the set of rational numbers. In this paper, we study the problem of the learna…