7,735 research outputs found
OTTER Experiments in a System of Combinatory Logic
This paper describes some experiments involving the automated theorem-proving
program OTTER in the system TRC of illative combinatory logic. We show how
OTTER can be steered to find a contradiction in an inconsistent variant of TRC,
and present some experimentally discovered identities in TRC
Using Inhabitation in Bounded Combinatory Logic with Intersection Types for Composition Synthesis
We describe ongoing work on a framework for automatic composition synthesis
from a repository of software components. This work is based on combinatory
logic with intersection types. The idea is that components are modeled as typed
combinators, and an algorithm for inhabitation {\textemdash} is there a
combinatory term e with type tau relative to an environment Gamma?
{\textemdash} can be used to synthesize compositions. Here, Gamma represents
the repository in the form of typed combinators, tau specifies the synthesis
goal, and e is the synthesized program. We illustrate our approach by examples,
including an application to synthesis from GUI-components.Comment: In Proceedings ITRS 2012, arXiv:1307.784
A herbrandized functional interpretation of classical first-order logic
We introduce a new typed combinatory calculus with a type constructor that, to each type σ, associates the star type σ^∗ of the nonempty finite subsets of elements of type σ. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements.info:eu-repo/semantics/publishedVersio
- …