Related papers: A Step-Indexing Approach to Partial Functions
Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for…
Program slicing has been mainly studied in the context of imperative languages, where it has been applied to a wide variety of software engineering tasks, like program understanding, maintenance, debugging, testing, code reuse, etc. This…
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as…
Asynchronous executions of a distributed algorithm differ from each other due to the nondeterminism in the order in which the messages exchanged are handled. In many situations of interest, the asynchronous executions induced by restricting…
The article deals with a kind of recursive function templates in C++, where the recursion is realized corresponding template parameters to achieve better computational performance. Some specialization of these template functions ends the…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's…
Clausal Language (CL) is a declarative programming and verifying system used in our teaching of computer science. CL is an implementation of, what we call, $\mathit{PR}{+}I\Sigma_1$ paradigm (primitive recursive functions with…
In-context learning (ICL) has proven highly effective across diverse large language model (LLM) tasks. However, its potential for enhancing tasks that demand step-by-step logical deduction, such as mathematical reasoning, remains…
Demonstration ordering, which is an important strategy for in-context learning (ICL), can significantly affects the performance of large language models (LLMs). However, most of the current approaches of ordering require high computational…
ACL2 was used to prove properties of two simplification procedures. The procedures differ in complexity but solve the same programming problem that arises in the context of a resolution/paramodulation theorem proving system. Term rewriting…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
We previously designed Partial Order Conflict Driven Clause Learning (PO-CDCL), a variation of the satisfiability solving CDCL algorithm with a partial order on decision levels, and showed that it can speed up the solving on problems with a…
In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed.…
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
Debugging lazy functional programs poses serious challenges. In support of the "stop, examine, and resume" debugging style of imperative languages, some debugging tools abandon lazy evaluation. Other debuggers preserve laziness but present…
Verification of algorithms and data structures utilized in modern autonomous and semi-autonomous vehicles for land, sea, air, and space presents a significant challenge. Autonomy algorithms, e.g., route planning, pattern matching, and…
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…