Formalization of the Undecidability of the Halting Problem for a Functional Language [chapter]

Thiago Mendonça Ferreira Ramos, César Muñoz, Mauricio Ayala-Rincón, Mariano Moscato, Aaron Dutle, Anthony Narkawicz
2018 Lecture Notes in Computer Science  
This paper presents a formalization of the proof of the undecidability of the halting problem for a functional programming language. The computational model consists of a simple first-order functional language called PVS0 whose operational semantics is specified in the Prototype Verification System (PVS). The formalization is part of a termination analysis library in PVS that includes the specification and equivalence proofs of several notions of termination. The proof of the undecidability of
more » ... he halting problem required classical constructions such as mappings between naturals and PVS0 programs and inputs. These constructs are used to disprove the existence of a PVS0 program that decides termination of other programs, which gives rise to a contradiction.
doi:10.1007/978-3-662-57669-4_11 fatcat:lj2acounojd5fabkdwera4vlpa