Related papers: Lifting Term Rewriting Derivations in Constructor …
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…
Dropout is a widely used regularization technique in deep learning, but its effects are typically realized through stochastic masking rather than explicit optimization objectives. We propose a deterministic formulation that expresses…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…
We develop the first theory of control-flow graphs from first principles, and use it to create an algorithm for automatically synthesizing many variants of control-flow graph generators from a language's operational semantics. Our approach…
We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…
Abstract machines for the strong evaluation of lambda-terms (that is, under abstractions) are a mostly neglected topic, despite their use in the implementation of proof assistants and higher-order logic programming languages. This paper…
The rewriting method for text summarization combines extractive and abstractive approaches, improving the conciseness and readability of extractive summaries using an abstractive model. Exiting rewriting systems take each extractive…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…
This paper presents an artificial intelligence algorithm that can be used to derive formulas from various scientific disciplines called automatic derivation machine. First, the formula is abstractly expressed as a multiway tree model, and…
To refactor already working code while keeping reliability, compatibility and perhaps security, we can borrow ideas from micropass/nanopass compilers. By treating the procedure of software refactoring as composing code transformations, and…
Reduction-based interpreters are traditionally defined in terms of a one-step reduction function which systematically decomposes a term into a potential redex and context, contracts the redex, and recomposes it to construct the new term to…
Formulating an effective constraint model of a parameterised problem class is crucial to the efficiency with which instances of the class can subsequently be solved. It is difficult to know beforehand which of a set of candidate models will…