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Finite Combinatory Logic with Predicates

Authors Andrej Dudenhefner , Christoph Stahl , Constantin Chaumet , Felix Laarmann , Jakob Rehof

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Author Details

Andrej Dudenhefner
  • TU Dortmund University, Germany
Christoph Stahl
  • TU Dortmund University, Germany
Constantin Chaumet
  • TU Dortmund University, Germany
Felix Laarmann
  • TU Dortmund University, Germany
Jakob Rehof
  • TU Dortmund University, Germany
  • Lamarr Institute for Machine Learning and Artificial Intelligence, Dortmund, Germany

Funding

  • Chaumet, Constantin: Deutsche Forschungsgemeinschaft (DFG, German Research Foundation – Project Number: 276879186).

Cite AsGet BibTex

Andrej Dudenhefner, Christoph Stahl, Constantin Chaumet, Felix Laarmann, and Jakob Rehof. Finite Combinatory Logic with Predicates. In 29th International Conference on Types for Proofs and Programs (TYPES 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 303, pp. 2:1-2:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.TYPES.2023.2

Abstract

Type inhabitation in extensions of Finite Combinatory Logic (FCL) is the mechanism underlying various component-oriented synthesis frameworks. In FCL inhabitant sets correspond to regular tree languages and vice versa. Therefore, it is not possible to specify non-regular properties of inhabitants, such as (dis)equality of subterms. Additionally, the monomorphic nature of FCL oftentimes hinders concise specification of components. We propose a conservative extension to FCL by quantifiers and predicates, introducing a restricted form of polymorphism. In the proposed type system (FCLP) inhabitant sets correspond to decidable term languages and vice versa. As a consequence, type inhabitation in FCLP is undecidable. Based on results in tree automata theory, we identify a fragment of FCLP with the following two properties. First, the fragment enjoys decidable type inhabitation. Second, it allows for specification of local (dis)equality constraints for subterms of inhabitants. For empirical evaluation, we implement a semi-decision procedure for type inhabitation in FCLP. We compare specification capabilities, scalability, and performance of the implementation to existing FCL-based approaches. Finally, we evaluate practical applicability via a case study, synthesizing mechanically sound robotic arms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Type theory
Keywords
  • combinatory logic
  • inhabitation
  • intersection types
  • program synthesis

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Supplementary Materials

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