Formalization of the Computational Theory of a Turing Complete Functional Language Model

This work presents a formalization in PVS of the computational theory for a computational model given as a class of partial recursive functions called PVS0. The model is built over basic operators, which, when restricted to constants, successor, projections, greater-than, and bijections from tuples...

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Bibliographic Details
Published inJournal of automated reasoning Vol. 66; no. 4; pp. 1031 - 1063
Main Authors Ramos, Thiago Mendonça Ferreira, Almeida, Ariane Alves, Ayala-Rincón, Mauricio
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.11.2022
Springer Nature B.V
Subjects
Artificial Intelligence
Automation
Computer Science
Fixed points (mathematics)
Grammar
Language
Mathematical Logic and Formal Languages
Mathematical Logic and Foundations
Recursive functions
Semantics
Symbolic and Algebraic Manipulation
Theorems
Automating termination
Computability theory
Halting Problem
Theorem proving
Functional programming models
PVS
Rice’s Theorem
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Summary:This work presents a formalization in PVS of the computational theory for a computational model given as a class of partial recursive functions called PVS0. The model is built over basic operators, which, when restricted to constants, successor, projections, greater-than, and bijections from tuples of naturals to naturals, results in a proven (formalized) Turing complete model. Complete formalizations of the Recursion theorem and Rice’s theorem are discussed in detail. Other relevant results, such as the undecidability of the Halting problem and the fixed-point theorem, were also fully formalized.
ISSN:0168-7433
1573-0670
DOI:10.1007/s10817-021-09615-x