(* Title: HOL/Proofs/ex/Proof_Terms.thy
Author: Makarius
Basic examples involving proof terms.
*)
theory Proof_Terms
imports Main
begin
text ‹
Detailed
proof information of a
theorem may be retrieved as follows:
›
lemma ex:
"A \ B \ B \ A"
proof
assume "A \ B"
then obtain B
and A ..
then show "B \ A" ..
qed
ML_val
‹
val
thm = @{
thm ex};
(*proof body with digest*)
val body = Proofterm.strip_thm_body (
Thm.proof_body_of
thm);
(*proof term only*)
val
prf = Proofterm.proof_of body;
(*clean output*)
Pretty.writeln (Proof_Syntax.pretty_standard_proof_of
🍋 false
thm);
Pretty.writeln (Proof_Syntax.pretty_standard_proof_of
🍋 true
thm);
(*all theorems used in the graph of nested proofs*)
val all_thms =
Proofterm.fold_body_thms
(fn {thm_name, ...} => insert (op =) thm_name) [body] [];
›
text ‹
The result refers
to various basic facts of Isabelle/HOL: @{
thm [source]
HOL.impI}, @{
thm [source] HOL.conjE}, @{
thm [source] HOL.conjI} etc. The
combinator
🚫‹Proofterm.fold_body_thms
› recursively explores the graph of
the proofs of all
theorems being used here.
🚫
Alternatively, we may produce a
proof term manually,
and turn it into a
theorem as follows:
›
ML_val
‹
val thy =
🍋;
val
prf =
Proof_Syntax.read_proof thy true false
"impI \ _ \ _ \ \
\ (
🚫λH: _. java.lang.NullPointerException
\ conjE
⋅ _
⋅ _
⋅ _
∙ H
∙ java.lang.NullPointerException
\ (
🚫λ(H: _) Ha: _. conjI
⋅ _
⋅ _
∙ Ha
∙ H))
";
val
thm =
Proofterm.reconstruct_proof thy
🍋‹A
∧ B
⟶ B
∧ A
› prf
|> Proof_Checker.thm_of_proof thy
|> Drule.export_without_context;
›
end
