author wenzelm Mon Jun 17 19:30:41 2013 +0200 (2013-06-17) changeset 52410 fb1fb867c146 parent 52409 47c62377be78 child 52411 f192c4ea5b17
more examples on proof terms;
 src/Doc/IsarImplementation/Logic.thy file | annotate | diff | revisions src/Doc/ROOT file | annotate | diff | revisions src/Doc/Ref/document/thm.tex file | annotate | diff | revisions src/HOL/Tools/reflection.ML file | annotate | diff | revisions
     1.1 --- a/src/Doc/IsarImplementation/Logic.thy	Sat Jun 15 21:07:32 2013 +0200
1.2 +++ b/src/Doc/IsarImplementation/Logic.thy	Mon Jun 17 19:30:41 2013 +0200
1.3 @@ -1314,4 +1314,107 @@
1.4    \end{description}
1.5  *}
1.6
1.7 +text %mlex {* Detailed proof information of a theorem may be retrieved
1.8 +  as follows: *}
1.9 +
1.10 +lemma ex: "A \<and> B \<longrightarrow> B \<and> A"
1.11 +proof
1.12 +  assume "A \<and> B"
1.13 +  then obtain B and A ..
1.14 +  then show "B \<and> A" ..
1.15 +qed
1.16 +
1.17 +ML_val {*
1.18 +  (*proof body with digest*)
1.19 +  val body = Proofterm.strip_thm (Thm.proof_body_of @{thm ex});
1.20 +
1.21 +  (*proof term only*)
1.22 +  val prf = Proofterm.proof_of body;
1.23 +  Pretty.writeln (Proof_Syntax.pretty_proof @{context} prf);
1.24 +
1.25 +  (*all theorems used in the graph of nested proofs*)
1.26 +  val all_thms =
1.27 +    Proofterm.fold_body_thms
1.28 +      (fn (name, _, _) => insert (op =) name) [body] [];
1.29 +*}
1.30 +
1.31 +text {* The result refers to various basic facts of Isabelle/HOL:
1.32 +  @{thm [source] HOL.impI}, @{thm [source] HOL.conjE}, @{thm [source]
1.33 +  HOL.conjI} etc.  The combinator @{ML Proofterm.fold_body_thms}
1.34 +  recursively explores the graph of the proofs of all theorems being
1.35 +  used here.
1.36 +
1.37 +  \medskip Alternatively, we may produce a proof term manually, and
1.38 +  turn it into a theorem as follows: *}
1.39 +
1.40 +ML_val {*
1.41 +  val thy = @{theory};
1.42 +  val prf =
1.43 +    Proof_Syntax.read_proof thy true false
1.44 +      "impI \<cdot> _ \<cdot> _ \<bullet> \
1.45 +      \   (Lam H: _. \
1.46 +      \     conjE \<cdot> _ \<cdot> _ \<cdot> _ \<bullet> H \<bullet> \
1.47 +      \       (Lam (H: _) Ha: _. conjI \<cdot> _ \<cdot> _ \<bullet> Ha \<bullet> H))";
1.48 +  val thm =
1.49 +    prf
1.50 +    |> Reconstruct.reconstruct_proof thy @{prop "A \<and> B \<longrightarrow> B \<and> A"}
1.51 +    |> Proof_Checker.thm_of_proof thy
1.52 +    |> Drule.export_without_context;
1.53 +*}
1.54 +
1.55 +text {* \medskip The subsequent example illustrates the use of various
1.56 +  key operations on proof terms: the proof term of an existing theorem
1.57 +  is reconstructed and turned again into a theorem using the proof
1.58 +  checker; some informative output is printed as well.  *}
1.59 +
1.60 +ML {*
1.61 +  fun recheck ctxt0 thm0 =
1.62 +    let
1.63 +      (*formal transfer and import -- avoid schematic variables*)
1.64 +      val thy = Proof_Context.theory_of ctxt0;
1.65 +      val ((_, [thm]), ctxt) =
1.66 +        Variable.import true [Thm.transfer thy thm0] ctxt0;
1.67 +
1.68 +      (*main proof information*)
1.69 +      val prop = Thm.prop_of thm;
1.70 +      val prf =
1.71 +        Proofterm.proof_of
1.72 +          (Proofterm.strip_thm (Thm.proof_body_of thm));
1.73 +      val full_prf = Reconstruct.reconstruct_proof thy prop prf;
1.74 +
1.75 +      (*informative output*)
1.76 +      fun pretty_item name prt =
1.77 +        Pretty.block [Pretty.str name, Pretty.brk 1, prt];
1.78 +      val _ =
1.79 +        [pretty_item "proposition:" (Syntax.pretty_term ctxt prop),
1.80 +         pretty_item "proof:" (Proof_Syntax.pretty_proof ctxt prf),
1.81 +         pretty_item "full proof:"
1.82 +          (Proof_Syntax.pretty_proof ctxt full_prf)]
1.83 +        |> Pretty.chunks |> Pretty.writeln;
1.84 +
1.85 +      (*rechecked theorem*)
1.86 +      val thm' =
1.87 +        Proof_Checker.thm_of_proof thy full_prf
1.88 +        |> singleton (Proof_Context.export ctxt ctxt0);
1.89 +    in thm' end;
1.90 +*}
1.91 +
1.92 +text {* As anticipated, the rechecked theorem establishes the same
1.93 +  proposition: *}
1.94 +
1.95 +ML_val {*
1.96 +  val thm = @{thm ex};
1.97 +  val thm' = recheck @{context} thm;
1.98 +  @{assert} (Thm.eq_thm_prop (thm, thm'));
1.99 +*}
1.100 +
1.101 +text {* More precise theorem equality is achieved by adjusting a few
1.102 +  accidental details of the theorems involved here: *}
1.103 +
1.104 +ML_val {*
1.105 +  val thm = Thm.map_tags (K []) @{thm ex};
1.106 +  val thm' = Thm.strip_shyps (recheck @{context} thm);
1.107 +  @{assert} (Thm.eq_thm (thm, thm'));
1.108 +*}
1.109 +
1.110  end

     2.1 --- a/src/Doc/ROOT	Sat Jun 15 21:07:32 2013 +0200
2.2 +++ b/src/Doc/ROOT	Mon Jun 17 19:30:41 2013 +0200
2.3 @@ -69,19 +69,20 @@
2.4      "document/build"
2.5      "document/root.tex"
2.6
2.7 -session IsarImplementation (doc) in "IsarImplementation" = HOL +
2.8 +session IsarImplementation (doc) in "IsarImplementation" = "HOL-Proofs" +
2.9    options [document_variants = "implementation"]
2.10    theories
2.11      Eq
2.12      Integration
2.13      Isar
2.14      Local_Theory
2.15 -    Logic
2.16      ML
2.17      Prelim
2.18      Proof
2.19      Syntax
2.20      Tactic
2.21 +  theories [proofs = 2, parallel_proofs = 0]
2.22 +    Logic
2.23    files
2.24      "../prepare_document"
2.25      "../pdfsetup.sty"

     3.1 --- a/src/Doc/Ref/document/thm.tex	Sat Jun 15 21:07:32 2013 +0200
3.2 +++ b/src/Doc/Ref/document/thm.tex	Mon Jun 17 19:30:41 2013 +0200
3.3 @@ -3,26 +3,6 @@
3.4
3.5  \section{Proof terms}\label{sec:proofObjects}
3.6
3.7 -Each theorem's derivation is stored as the {\tt der} field of its internal
3.8 -record:
3.9 -\begin{ttbox}
3.10 -#2 (#der (rep_thm conjI));
3.11 -{\out PThm (("HOL.conjI", []),}
3.12 -{\out   AbsP ("H", None, AbsP ("H", None, \dots)), \dots, None) %}
3.13 -{\out     None % None : Proofterm.proof}
3.14 -\end{ttbox}
3.15 -This proof term identifies a labelled theorem, {\tt conjI} of theory
3.16 -\texttt{HOL}, whose underlying proof is
3.17 -{\tt AbsP ("H", None, AbsP ("H", None, $\dots$))}.
3.18 -The theorem is applied to two (implicit) term arguments, which correspond
3.19 -to the two variables occurring in its proposition.
3.20 -
3.21 -Reconstruction and checking of proofs as described in \S\ref{sec:reconstruct_proofs}
3.22 -will not work for proofs constructed with {\tt proofs} set to
3.23 -{\tt 0} or {\tt 1}.
3.24 -Theorems involving oracles will be printed with a
3.25 -suffixed \verb|[!]| to point out the different quality of confidence achieved.
3.26 -
3.27  \subsection{Reconstructing and checking proof terms}\label{sec:reconstruct_proofs}
3.28  \index{proof terms!reconstructing}
3.29  \index{proof terms!checking}
3.30 @@ -115,45 +95,6 @@
3.31  argument which indicates whether the proof term should
3.32  be reconstructed before printing.
3.33
3.34 -The following example (based on Isabelle/HOL) illustrates how
3.35 -to parse and check proof terms. We start by parsing a partial
3.36 -proof term
3.37 -\begin{ttbox}
3.38 -val prf = ProofSyntax.read_proof Main.thy false
3.39 -  "impI % _ % _ %% (Lam H : _. conjE % _ % _ % _ %% H %%
3.40 -     (Lam (H1 : _) H2 : _. conjI % _ % _ %% H2 %% H1))";
3.41 -{\out val prf = PThm (("HOL.impI", []), \dots, \dots, None) % None % None %%}
3.42 -{\out   AbsP ("H", None, PThm (("HOL.conjE", []), \dots, \dots, None) %}
3.43 -{\out     None % None % None %% PBound 0 %%}
3.44 -{\out     AbsP ("H1", None, AbsP ("H2", None, \dots))) : Proofterm.proof}
3.45 -\end{ttbox}
3.46 -The statement to be established by this proof is
3.47 -\begin{ttbox}
3.48 -val t = term_of
3.49 -  (read_cterm (sign_of Main.thy) ("A & B --> B & A", propT));
3.50 -{\out val t = Const ("Trueprop", "bool => prop") $} 3.51 -{\out (Const ("op -->", "[bool, bool] => bool")$}
3.52 -{\out     \dots $\dots : Term.term} 3.53 -\end{ttbox} 3.54 -Using {\tt t} we can reconstruct the full proof 3.55 -\begin{ttbox} 3.56 -val prf' = Reconstruct.reconstruct_proof (sign_of Main.thy) t prf; 3.57 -{\out val prf' = PThm (("HOL.impI", []), \dots, \dots, Some []) %} 3.58 -{\out Some (Const ("op &", \dots)$ Free ("A", \dots) $Free ("B", \dots)) %} 3.59 -{\out Some (Const ("op &", \dots)$ Free ("B", \dots) $Free ("A", \dots)) %%} 3.60 -{\out AbsP ("H", Some (Const ("Trueprop", \dots)$ \dots), \dots)}
3.61 -{\out     : Proofterm.proof}
3.62 -\end{ttbox}
3.63 -This proof can finally be turned into a theorem
3.64 -\begin{ttbox}
3.65 -val thm = ProofChecker.thm_of_proof Main.thy prf';
3.66 -{\out val thm = "A & B --> B & A" : Thm.thm}
3.67 -\end{ttbox}
3.68 -
3.69 -\index{proof terms|)}
3.70 -\index{theorems|)}
3.71 -
3.72 -
3.73  %%% Local Variables:
3.74  %%% mode: latex
3.75  %%% TeX-master: "ref"