--- a/src/HOL/IsaMakefile Tue Feb 26 00:21:31 2002 +0100
+++ b/src/HOL/IsaMakefile Tue Feb 26 00:24:37 2002 +0100
@@ -432,9 +432,7 @@
HOL-W0: HOL $(LOG)/HOL-W0.gz
-$(LOG)/HOL-W0.gz: $(OUT)/HOL W0/I.ML W0/I.thy W0/Maybe.ML W0/Maybe.thy \
- W0/MiniML.ML W0/MiniML.thy W0/ROOT.ML W0/Type.ML W0/Type.thy W0/W.ML \
- W0/W.thy
+$(LOG)/HOL-W0.gz: $(OUT)/HOL W0/ROOT.ML W0/W0.thy W0/document/root.tex
@$(ISATOOL) usedir $(OUT)/HOL W0
@@ -568,9 +566,9 @@
Isar_examples/KnasterTarski.thy Isar_examples/MutilatedCheckerboard.thy \
Isar_examples/NestedDatatype.thy Isar_examples/Peirce.thy \
Isar_examples/Puzzle.thy Isar_examples/Summation.thy \
- Isar_examples/ROOT.ML Isar_examples/W_correct.thy \
- Isar_examples/document/proof.sty Isar_examples/document/root.bib \
- Isar_examples/document/root.tex Isar_examples/document/style.tex
+ Isar_examples/ROOT.ML Isar_examples/document/proof.sty \
+ Isar_examples/document/root.bib Isar_examples/document/root.tex \
+ Isar_examples/document/style.tex
@$(ISATOOL) usedir $(OUT)/HOL Isar_examples
--- a/src/HOL/Isar_examples/ROOT.ML Tue Feb 26 00:21:31 2002 +0100
+++ b/src/HOL/Isar_examples/ROOT.ML Tue Feb 26 00:24:37 2002 +0100
@@ -13,8 +13,6 @@
time_use_thy "Summation";
time_use_thy "KnasterTarski";
time_use_thy "MutilatedCheckerboard";
-with_path "../W0" (no_document time_use_thy) "Type";
-with_path "../W0" time_use_thy "W_correct";
with_path "../NumberTheory" (no_document time_use_thy) "Primes";
with_path "../NumberTheory" time_use_thy "Fibonacci";
time_use_thy "Puzzle";
--- a/src/HOL/Isar_examples/W_correct.thy Tue Feb 26 00:21:31 2002 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,142 +0,0 @@
-(* Title: HOL/Isar_examples/W_correct.thy
- ID: $Id$
- Author: Markus Wenzel, TU Muenchen
-
-Correctness of Milner's type inference algorithm W (let-free version).
-*)
-
-header {* Milner's type inference algorithm~W (let-free version) *}
-
-theory W_correct = Main + Type:
-
-text_raw {*
- \footnote{Based upon \url{http://isabelle.in.tum.de/library/HOL/W0/}
- by Dieter Nazareth and Tobias Nipkow.}
-*}
-
-
-subsection "Mini ML with type inference rules"
-
-datatype
- expr = Var nat | Abs expr | App expr expr
-
-
-text {* Type inference rules. *}
-
-consts
- has_type :: "(typ list * expr * typ) set"
-
-syntax
- "_has_type" :: "typ list => expr => typ => bool"
- ("((_) |-/ (_) :: (_))" [60, 0, 60] 60)
-translations
- "a |- e :: t" == "(a, e, t) : has_type"
-
-inductive has_type
- intros
- Var: "n < length a ==> a |- Var n :: a ! n"
- Abs: "t1#a |- e :: t2 ==> a |- Abs e :: t1 -> t2"
- App: "a |- e1 :: t2 -> t1 ==> a |- e2 :: t2
- ==> a |- App e1 e2 :: t1"
-
-
-text {* Type assigment is closed wrt.\ substitution. *}
-
-lemma has_type_subst_closed: "a |- e :: t ==> $s a |- e :: $s t"
-proof -
- assume "a |- e :: t"
- thus ?thesis (is "?P a e t")
- proof induct
- case (Var a n)
- hence "n < length (map ($ s) a)" by simp
- hence "map ($ s) a |- Var n :: map ($ s) a ! n"
- by (rule has_type.Var)
- also have "map ($ s) a ! n = $ s (a ! n)"
- by (rule nth_map)
- also have "map ($ s) a = $ s a"
- by (simp only: app_subst_list)
- finally show "?P a (Var n) (a ! n)" .
- next
- case (Abs a e t1 t2)
- hence "$ s t1 # map ($ s) a |- e :: $ s t2"
- by (simp add: app_subst_list)
- hence "map ($ s) a |- Abs e :: $ s t1 -> $ s t2"
- by (rule has_type.Abs)
- thus "?P a (Abs e) (t1 -> t2)"
- by (simp add: app_subst_list)
- next
- case App
- thus ?case by (simp add: has_type.App)
- qed
-qed
-
-
-subsection {* Type inference algorithm W *}
-
-consts
- W :: "expr => typ list => nat => (subst * typ * nat) maybe"
-
-primrec
- "W (Var i) a n =
- (if i < length a then Ok (id_subst, a ! i, n) else Fail)"
- "W (Abs e) a n =
- ((s, t, m) := W e (TVar n # a) (Suc n);
- Ok (s, (s n) -> t, m))"
- "W (App e1 e2) a n =
- ((s1, t1, m1) := W e1 a n;
- (s2, t2, m2) := W e2 ($s1 a) m1;
- u := mgu ($ s2 t1) (t2 -> TVar m2);
- Ok ($u o $s2 o s1, $u (TVar m2), Suc m2))"
-
-
-subsection {* Correctness theorem *}
-
-theorem W_correct: "!!a s t m n. Ok (s, t, m) = W e a n ==> $ s a |- e :: t"
- (is "PROP ?P e")
-proof (induct e)
- fix a s t m n
- {
- fix i
- assume "Ok (s, t, m) = W (Var i) a n"
- thus "$ s a |- Var i :: t" by (simp add: has_type.Var split: if_splits)
- next
- fix e assume hyp: "PROP ?P e"
- assume "Ok (s, t, m) = W (Abs e) a n"
- then obtain t' where "t = s n -> t'"
- and "Ok (s, t', m) = W e (TVar n # a) (Suc n)"
- by (auto split: bind_splits)
- with hyp show "$ s a |- Abs e :: t"
- by (force intro: has_type.Abs)
- next
- fix e1 e2 assume hyp1: "PROP ?P e1" and hyp2: "PROP ?P e2"
- assume "Ok (s, t, m) = W (App e1 e2) a n"
- then obtain s1 t1 n1 s2 t2 n2 u where
- s: "s = $ u o $ s2 o s1"
- and t: "t = u n2"
- and mgu_ok: "mgu ($ s2 t1) (t2 -> TVar n2) = Ok u"
- and W1_ok: "Ok (s1, t1, n1) = W e1 a n"
- and W2_ok: "Ok (s2, t2, n2) = W e2 ($ s1 a) n1"
- by (auto split: bind_splits simp: that)
- show "$ s a |- App e1 e2 :: t"
- proof (rule has_type.App)
- from s have s': "$ u ($ s2 ($ s1 a)) = $s a"
- by (simp add: subst_comp_tel o_def)
- show "$s a |- e1 :: $ u t2 -> t"
- proof -
- from W1_ok have "$ s1 a |- e1 :: t1" by (rule hyp1)
- hence "$ u ($ s2 ($ s1 a)) |- e1 :: $ u ($ s2 t1)"
- by (intro has_type_subst_closed)
- with s' t mgu_ok show ?thesis by simp
- qed
- show "$ s a |- e2 :: $ u t2"
- proof -
- from W2_ok have "$ s2 ($ s1 a) |- e2 :: t2" by (rule hyp2)
- hence "$ u ($ s2 ($ s1 a)) |- e2 :: $ u t2"
- by (rule has_type_subst_closed)
- with s' show ?thesis by simp
- qed
- qed
- }
-qed
-
-end