--- a/CookBook/Tactical.thy Wed Feb 25 11:28:41 2009 +0000
+++ b/CookBook/Tactical.thy Wed Feb 25 12:08:32 2009 +0000
@@ -1318,71 +1318,79 @@
section {* Conversions\label{sec:conversion} *}
text {*
-Conversions are meta-equalities depending on some input term. Their type is
-as follows:
+
+ Conversions are a ``thin'' layer on top of Isabelle's inference kernel, and
+ may be seen as a controllable, bare-bone version of Isabelle's simplifier.
+ They are meta-equalities depending on some input term. Their type is
+ as follows:
*}
-ML {*type conv = Thm.cterm -> Thm.thm*}
+ML{*type conv = Thm.cterm -> Thm.thm*}
text {*
-The simplest two conversions are @{ML "Conv.all_conv"}, which maps a term to an instance of the reflexivity theorem, and @{ML "Conv.no_conv"}, which always fails:
+ The simplest two conversions are @{ML "Conv.all_conv"}, which maps a
+ term to an instance of the reflexivity theorem, and
+ @{ML "Conv.no_conv"}, which always fails:
-@{ML_response_fake "Conv.all_conv @{cterm True}" "True \<equiv> True"}
-
-@{ML_response_fake "Conv.no_conv @{cterm True}" "*** Exception- CTERM (\"no conversion\", []) raised"}
+ @{ML_response_fake [display,gray]
+ "Conv.all_conv @{cterm True}" "True \<equiv> True"}
-A further basic conversion is, for example, @{ML "Thm.beta_conversion"}:
+ @{ML_response_fake [display,gray]
+ "Conv.no_conv @{cterm True}"
+ "*** Exception- CTERM (\"no conversion\", []) raised"}
+
+ A further basic conversion is, for example, @{ML "Thm.beta_conversion"}:
-@{ML_response_fake "Thm.beta_conversion true @{cterm \"(\<lambda>x. x \<or> False) True\"}"
-"(\<lambda>x. x \<or> False) True \<equiv> True \<or> False"}
+ @{ML_response_fake [display,gray]
+ "Thm.beta_conversion true @{cterm \"(\<lambda>x. x \<or> False) True\"}"
+ "(\<lambda>x. x \<or> False) True \<equiv> True \<or> False"}
-User-defined rewrite rules can be applied by the conversion
-@{ML "Conv.rewr_conv"}. Consider, for example, the following rule:
+ User-defined rewrite rules can be applied by the conversion
+ @{ML "Conv.rewr_conv"}. Consider, for example, the following rule:
*}
lemma true_conj1: "True \<and> P \<equiv> P" by simp
text {*
-Here is how this rule can be used for rewriting:
+ Here is how this rule can be used for rewriting:
-@{ML_response_fake "Conv.rewr_conv @{thm true_conj1} @{cterm \"True \<or> False\"}"
- "True \<and> False \<equiv> False"}
+ @{ML_response_fake [display,gray]
+ "Conv.rewr_conv @{thm true_conj1} @{cterm \"True \<or> False\"}"
+ "True \<and> False \<equiv> False"}
*}
text {*
-Basic conversions can be combined with a number of conversionals, i.e.
-conversion combinators:
+ Basic conversions can be combined with a number of conversionals, i.e.
+ conversion combinators:
-@{ML_response_fake
-"(Thm.beta_conversion true then_conv Conv.rewr_conv @{thm true_conj1})
+ @{ML_response_fake [display,gray]
+ "(Thm.beta_conversion true then_conv Conv.rewr_conv @{thm true_conj1})
@{cterm \"(\<lambda>x. x \<and> False) True\"}"
-"(\<lambda>x. x \<and> False) True \<equiv> False"}
+ "(\<lambda>x. x \<and> False) True \<equiv> False"}
-@{ML_response_fake
-"(Conv.rewr_conv @{thm true_conj1} else_conv Conv.all_conv)
+ @{ML_response_fake [display,gray]
+ "(Conv.rewr_conv @{thm true_conj1} else_conv Conv.all_conv)
@{cterm \"P \<or> (True \<and> Q)\"}"
-"P \<or> (True \<and> Q) \<equiv> P \<or> (True \<and> Q)"}
+ "P \<or> (True \<and> Q) \<equiv> P \<or> (True \<and> Q)"}
-@{ML_response_fake
-"Conv.arg_conv (Conv.rewr_conv @{thm true_conj1})
+ @{ML_response_fake [display,gray]
+ "Conv.arg_conv (Conv.rewr_conv @{thm true_conj1})
@{cterm \"P \<or> (True \<and> Q)\"}"
-"P \<or> (True \<and> Q) \<equiv> P \<or> Q"}
+ "P \<or> (True \<and> Q) \<equiv> P \<or> Q"}
-\begin{readmore}
-See @{ML_file "Pure/conv.ML"} for more conversionals. Further basic conversions
-can be found in, for example, @{ML_file "Pure/thm.ML"},
-@{ML_file "Pure/drule.ML"}, and @{ML_file "Pure/meta_simplifier.ML"}.
-\end{readmore}
+ \begin{readmore}
+ See @{ML_file "Pure/conv.ML"} for more conversionals. Further basic conversions
+ can be found in, for example, @{ML_file "Pure/thm.ML"},
+ @{ML_file "Pure/drule.ML"}, and @{ML_file "Pure/meta_simplifier.ML"}.
+ \end{readmore}
-Conversions are a thin layer on top of Isabelle's inference kernel, and may
-be seen as a controllable, bare-bone version of Isabelle's simplifier. We
-will demonstrate this feature in the following example.
+ We will demonstrate this feature in the following example.
-To begin with, let's assumes we want to simplify with the rewrite rule
-@{text true_conj1}. As a conversion, this may look as follows:
+ To begin with, let's assumes we want to simplify with the rewrite rule
+ @{text true_conj1}. As a conversion, this may look as follows:
*}
-ML {*fun all_true1_conv ctxt ct =
+ML{*fun all_true1_conv ctxt ct =
(case Thm.term_of ct of
@{term "op \<and>"} $ @{term True} $ _ =>
(Conv.arg_conv (all_true1_conv ctxt) then_conv
@@ -1393,18 +1401,18 @@
| _ => Conv.all_conv ct)*}
text {*
-Here is this conversion in action:
+ Here is this conversion in action:
-@{ML_response_fake
-"all_true1_conv @{context}
+ @{ML_response_fake [display,gray]
+ "all_true1_conv @{context}
@{cterm \"distinct [1, x] \<longrightarrow> True \<and> 1 \<noteq> x\"}"
-"distinct [1, x] \<longrightarrow> True \<and> 1 \<noteq> x \<equiv> distinct [1, x] \<longrightarrow> 1 \<noteq> x"}
+ "distinct [1, x] \<longrightarrow> True \<and> 1 \<noteq> x \<equiv> distinct [1, x] \<longrightarrow> 1 \<noteq> x"}
-Now, let's complicate the task a bit: Rewrite according to the rule
-@{text true_conj1}, but only in the first arguments of @{term If}:
+ Now, let make the task a bit more complicated by rewrite according to the rule
+ @{text true_conj1}, but only in the first arguments of @{term If}:
*}
-ML {*fun if_true1_conv ctxt ct =
+ML{*fun if_true1_conv ctxt ct =
(case Thm.term_of ct of
Const (@{const_name If}, _) $ _ =>
Conv.arg_conv (all_true1_conv ctxt) ct
@@ -1414,30 +1422,30 @@
| _ => Conv.all_conv ct)*}
text {*
-Here is an application of this conversion:
+ Here is an application of this conversion:
-@{ML_response_fake
-"if_true1_conv @{context}
+ @{ML_response_fake [display,gray]
+ "if_true1_conv @{context}
@{cterm \"if P (True \<and> 1 \<noteq> 2) then True \<and> True else True \<and> False\"}"
-"if P (True \<and> 1 \<noteq> 2) then True \<and> True else True \<and> False \<equiv> if P (1 \<noteq> 2) then True \<and> True else True \<and> False"}
+ "if P (True \<and> 1 \<noteq> 2) then True \<and> True else True \<and> False \<equiv> if P (1 \<noteq> 2) then True \<and> True else True \<and> False"}
*}
text {*
-Conversions can also be turned into a tactic with the @{ML CONVERSION}
-tactical, and there are predefined conversionals to traverse a goal state.
-Given a state @{term "\<And>x. P \<Longrightarrow> Q"}, the conversional
-@{ML Conv.params_conv} applies a conversion to @{term "P \<Longrightarrow> Q"};
-given a state @{term "\<lbrakk> P1; P2 \<rbrakk> \<Longrightarrow> Q"},
-the conversional @{ML Conv.prems_conv} applies a conversion to the premises
-@{term P1} and @{term P2}, and @{ML Conv.concl_conv} applies a conversion to
-the conclusion @{term Q}.
+ Conversions can also be turned into a tactic with the @{ML CONVERSION}
+ tactical, and there are predefined conversionals to traverse a goal state.
+ Given a state @{term "\<And>x. P \<Longrightarrow> Q"}, the conversional
+ @{ML Conv.params_conv} applies a conversion to @{term "P \<Longrightarrow> Q"};
+ given a state @{term "\<lbrakk> P1; P2 \<rbrakk> \<Longrightarrow> Q"},
+ the conversional @{ML Conv.prems_conv} applies a conversion to the premises
+ @{term P1} and @{term P2}, and @{ML Conv.concl_conv} applies a conversion to
+ the conclusion @{term Q}.
-Assume we want to apply @{ML all_true1_conv} only in the conclusion
-of the goal, and @{ML if_true1_conv} should only be applied in the premises.
-Here is a tactic doing exactly that:
+ Assume we want to apply @{ML all_true1_conv} only in the conclusion
+ of the goal, and @{ML if_true1_conv} should only be applied in the premises.
+ Here is a tactic doing exactly that:
*}
-ML {*val true1_tac = CSUBGOAL (fn (goal, i) =>
+ML{*val true1_tac = CSUBGOAL (fn (goal, i) =>
let val ctxt = ProofContext.init (Thm.theory_of_cterm goal)
in
CONVERSION (
@@ -1447,7 +1455,7 @@
end)*}
text {*
-To demonstrate this tactic, consider the following example:
+ To demonstrate this tactic, consider the following example:
*}
lemma
@@ -1460,20 +1468,18 @@
(*<*)oops(*>*)
text {*
-Conversions are not restricted to work on certified terms only, they can also
-be lifted to theorem transformers, i.e. functions mapping a theorem to a
-theorem, by the help of @{ML Conv.fconv_rule}. As an example, consider the
-conversion @{ML all_true1_conv} again:
+ Conversions are not restricted to work on certified terms only, they can also
+ be lifted to theorem transformers, i.e. functions mapping a theorem to a
+ theorem, by the help of @{ML Conv.fconv_rule}. As an example, consider the
+ conversion @{ML all_true1_conv} again:
-@{ML_response_fake
-"Conv.fconv_rule (all_true1_conv @{context})
- @{lemma \"P \<or> (True \<and> \<not>P)\" by simp}" "P \<or> \<not>P"}
+ @{ML_response_fake [display,gray]
+ "Conv.fconv_rule (all_true1_conv @{context}) @{lemma \"P \<or> (True \<and> \<not>P)\" by simp}"
+ "P \<or> \<not>P"}
*}
-
-
section {* Structured Proofs *}
text {* TBD *}