Download PDFOpen PDF in browserA Prolog-based Proof Tool for Type-Theory TA-lambda and Implicational Intuitionistic-Logic9 pages•Published: May 15, 2012AbstractStudies on type theory have brought numerous important contributions to computer science. In this paper we present a GUI-based proof tool that provides assistance in constructing deductions in type theory and validating implicational intuitionistic logic formulas. As such, this proof tool is a testbed for learning type theory and implicational intuitionistic logic. This proof tool focuses on an important variant of type theory named TA<sub>λ</sub>, especially on its two core algorithms: the principal-type algorithm and the type inhabitant search algorithm. The former algorithm finds a most general type assignable to a given λ-term, while the latter finds inhabitants (closed λ-terms in β-normal form) to which a given type can be assigned. By the Curry-Howard correspondence, the latter algorithm provides provability for implicational formulas in intuitionistic logic. We elaborate on how to implement those two algorithms declaratively in Prolog and the overall GUI-based program architecture. In our implementation, we make some modification to improve the performance of the principal-type algorithm. We have also built a web-based version of the proof tool called λ-Guru.Keyphrases: definite clause grammar, implicational intuitionistic logic, lambda calculus, proof tool, type inhabitant search algorithm, type theory In: Geoff Sutcliffe, Stephan Schulz and Eugenia Ternovska (editors). IWIL 2010. The 8th International Workshop on the Implementation of Logics, vol 2, pages 33-41.
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