eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-08-30
15:1
15:14
10.4230/LIPIcs.FSCD.2017.15
article
The Complexity of Principal Inhabitation
Dudenhefner, Andrej
Rehof, Jakob
It is shown that in the simply typed lambda-calculus the following decision problem of principal inhabitation is Pspace-complete: Given a simple type tau, is there a lambda-term N in beta-normal form such that tau is the principal type of N?
While a Ben-Yelles style algorithm was presented by Broda and Damas in 1999 to count normal principal inhabitants (thereby answering a question posed by Hindley), it does not induce a polynomial space upper bound for principal inhabitation. Further, the standard construction of the polynomial space lower bound for simple type inhabitation does not carry over immediately.
We present a polynomial space bounded decision procedure based on a characterization of principal inhabitation using path derivation systems over subformulae of the input type, which does not require candidate inhabitants to be constructed explicitly. The lower bound is shown by reducing a restriction of simple type inhabitation to principal inhabitation.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol084-fscd2017/LIPIcs.FSCD.2017.15/LIPIcs.FSCD.2017.15.pdf
Lambda Calculus
Type Theory
Simple Types
Inhabitation
Principal Type
Complexity