+undef command

catprog.tex

@@ -67,15 +67,16 @@
 \providecommand{\bang}{\operatorname!}				% Initial/final map
 
 %% Various arrows
-\providecommand{\ito}{\hookrightarrow}						% Injection
-\providecommand{\pto}{\mathrel{\rightharpoonup}}	% Partial function
-\providecommand{\tto}{\mathrel{\Rightarrow}}			
-\providecommand{\dar}{\kern-1.2pt\operatorname{\downarrow}}	
-\providecommand{\uar}{\kern-1.2pt\operatorname{\uparrow}}	
+\providecommand{\ito}{\hookrightarrow}				% Injection
+\providecommand{\pto}{\mathrel{\rightharpoonup}}		% Partial function
+\providecommand{\tto}{\mathrel{\Rightarrow}}			% Double arrow
 \providecommand{\mto}{\mapsto}
 \providecommand{\xto}[1]{\,\xrightarrow{#1}\,}
 \providecommand{\xfrom}[1]{\,\xleftarrow{\;#1}\,}
 
+\providecommand{\dar}{\kern-1.2pt\operatorname{\downarrow}}	
+\providecommand{\uar}{\kern-1.2pt\operatorname{\uparrow}}	
+
 %% Logic
 \providecommand{\True}{\top}
 \providecommand{\False}{\bot}
@@ -132,12 +133,14 @@
 
 % Typographics
 \providecommand{\comma}{,\operatorname{}\linebreak[1]}		% possibly line-beaking comma
-\providecommand{\dash}{\nobreakdash-\hspace{0pt}}			    % non-line-beaking hyphen
-\providecommand{\erule}{\rule{0pt}{0pt}}		        	    % Empty object whose emptiness is not recognized by LaTeX
+\providecommand{\dash}{\nobreakdash-\hspace{0pt}}		% non-line-beaking hyphen
+\providecommand{\erule}{\rule{0pt}{0pt}}		        % Empty object whose emptiness is not recognized by LaTeX
 
 \providecommand{\by}[1]{\text{/\!\!/~#1}}			% Comments in equations
 \providecommand{\pacman}[1]{}					% Hide a piece of text
 
+\def\undef#1{\let #1\relax}
+
 \providecommand{\noqed}{\def\qed{}}				% Undefine the QED symbol
 
 % -1 superscript for the inversion operator