# HG changeset patch # User wenzelm # Date 862919369 -7200 # Node ID 943f25285a3eac6078094cebf7e2d450ca54572a # Parent a02abeafca6767ef928cce668fdd3067d4df27ba fixed simplifier ex; diff -r a02abeafca67 -r 943f25285a3e doc-src/Intro/advanced.tex --- a/doc-src/Intro/advanced.tex Tue May 06 13:43:54 1997 +0200 +++ b/doc-src/Intro/advanced.tex Tue May 06 13:49:29 1997 +0200 @@ -1024,14 +1024,14 @@ \index{simplification}\index{examples!of simplification} -Isabelle's simplification tactics repeatedly apply equations to a subgoal, -perhaps proving it. For efficiency, the rewrite rules must be -packaged into a {\bf simplification set},\index{simplification sets} -or {\bf simpset}. We take the standard simpset for first-order logic and -insert the equations proved in the previous section, namely -$0+n=n$ and ${\tt Suc}(m)+n={\tt Suc}(m+n)$: +Isabelle's simplification tactics repeatedly apply equations to a +subgoal, perhaps proving it. For efficiency, the rewrite rules must +be packaged into a {\bf simplification set},\index{simplification + sets} or {\bf simpset}. We augment the implicit simpset of {\FOL} +with the equations proved in the previous section, namely $0+n=n$ and +${\tt Suc}(m)+n={\tt Suc}(m+n)$: \begin{ttbox} -val add_ss = FOL_ss addsimps [add_0, add_Suc]; +Addsimps [add_0, add_Suc]; \end{ttbox} We state the goal for associativity of addition, and use \ttindex{res_inst_tac} to invoke induction on~$k$: @@ -1049,10 +1049,10 @@ {\out Suc(x) + m + n = Suc(x) + (m + n)} \end{ttbox} The base case holds easily; both sides reduce to $m+n$. The -tactic~\ttindex{simp_tac} rewrites with respect to the given simplification -set, applying the rewrite rules for addition: +tactic~\ttindex{Simp_tac} rewrites with respect to the current +simplification set, applying the rewrite rules for addition: \begin{ttbox} -by (simp_tac add_ss 1); +by (Simp_tac 1); {\out Level 2} {\out k + m + n = k + (m + n)} {\out 1. !!x. x + m + n = x + (m + n) ==>} @@ -1060,10 +1060,10 @@ \end{ttbox} The inductive step requires rewriting by the equations for addition together the induction hypothesis, which is also an equation. The -tactic~\ttindex{asm_simp_tac} rewrites using a simplification set and any -useful assumptions: +tactic~\ttindex{Asm_simp_tac} rewrites using the implicit +simplification set and any useful assumptions: \begin{ttbox} -by (asm_simp_tac add_ss 1); +by (Asm_simp_tac 1); {\out Level 3} {\out k + m + n = k + (m + n)} {\out No subgoals!} diff -r a02abeafca67 -r 943f25285a3e doc-src/Intro/intro.ind --- a/doc-src/Intro/intro.ind Tue May 06 13:43:54 1997 +0200 +++ b/doc-src/Intro/intro.ind Tue May 06 13:49:29 1997 +0200 @@ -20,7 +20,7 @@ \item {\tt allI} theorem, 37 \item arities \subitem declaring, 4, \bold{49} - \item {\tt asm_simp_tac}, 60 + \item {\tt Asm_simp_tac}, 60 \item {\tt assume_tac}, 30, 32, 37, 47 \item assumptions \subitem deleting, 20 @@ -207,7 +207,7 @@ \item search \subitem depth-first, 63 \item signatures, \bold{9} - \item {\tt simp_tac}, 60 + \item {\tt Simp_tac}, 60 \item simplification, 59 \item simplification sets, 59 \item sort constraints, 25