From: Charles Wells <cfw2@po.cwru.edu>
Topos theorists and people in denotational semantics use the notation [[t]] to denote a mathematical object that is the meaning of t in some semantics. In particular, in the case of a formula f, [[f]] is the truth value. APL and Donald Knuth use [f] for the truth value of a formula (or so I have been told). Does anyone know who used the double square bracket notation first (topos theorists, denotational semantics people, or whoever), and whether it was suggested by the APL usage?
The first occurrence I know of is in the Scott-Solovay treatment of Boolean-Valued models. I've always called them "Scott-open and Scott-close". Mike Prof. Michael P. Fourman email mikef@dcs.ed.ac.uk Dept. of Computer Science 'PHONE (+44) (0)31-650 5198 (sec) JCMB, King's Buildings, Mayfield Road, (+44) (0)31-650 5197 Edinburgh EH9 3JZ, Scotland, UK FAX (+44) (0)31 667 7209 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++