NAMING CONVENTIONS FOR METAVARIABLES A,B : arity C : candidate of reducibility D,E : RTM environment F,G : global environment H : reserved: transient premise IH : reserved: inductive premise I,J : item K,L : local environment M,N : reserved: future use O,P,Q : R : generic predicate (relation) S : RTM stack T,U,V,W: term X,Y,Z : reserved: transient objet denoted by a capital letter a,b : binder polarity c : reserved: future use (lambda_delta 3) d : relocation depth e : relocation height f : g : sort degree parameter h : sort hierarchy parameter i,j : local reference position index (de Bruijn's) k : sort index l : term degree m,n : reserved: future use o : p,q : global reference position r,s : t,u : local reference position level (de Bruijn's) v,w : x,y,z : reserved: transient objet denoted by a small letter NAMING CONVENTIONS FOR CONSTRUCTORS 0: atomic 2: binary A: application to vector a: application b: binder d: abbreviation f: flat l: abstraction n: native type annotation NAMING CONVENTIONS FOR TRANSFORMATIONS AND RELATED FORMS - first letter b: bi contex-sensitive for local environments c: contex-sensitive for terms f: context-freee for closures l: sn contex-sensitive for local environments r: dx contex-sensitive for local environments t: context-free for terms - second letter i: irreducible form n: normal form p: reflexive parallel transformation q: sequential transformation r: reducible form s: strongly normalizing form - third letter b: "big tree" reduction c: conversion d: decomposed extended reduction e: decomposed extended conversion n: reduction for "big tree" normal forms q: restricted reduction r: reduction s: substitution u: supclosure x: extended reduction - forth letter (if present) c: proper single step (general) (successor) e: reflexive transitive closure to normal form (evaluation) g: proper multiple step (general) (greater) p: non-reflexive transitive closure (plus) q: reflexive closure (question) r: proper multiple step (restricted) (restricted) s: reflexive transitive closure (star) u: proper single step (restricted) (unit)