--- a/src/HOL/HOL.thy Wed Aug 25 20:46:40 1999 +0200
+++ b/src/HOL/HOL.thy Wed Aug 25 20:49:02 1999 +0200
@@ -6,72 +6,63 @@
Higher-Order Logic.
*)
-HOL = CPure +
+theory HOL = CPure
+files ("HOL_lemmas.ML") ("cladata.ML") ("blastdata.ML") ("simpdata.ML"):
(** Core syntax **)
global
-classes
- term < logic
+classes "term" < logic
+defaultsort "term"
-default
- term
-
-types
- bool
+typedecl bool
arities
- fun :: (term, term) term
- bool :: term
+ bool :: "term"
+ fun :: ("term", "term") "term"
consts
(* Constants *)
- Trueprop :: bool => prop ("(_)" 5)
- Not :: bool => bool ("~ _" [40] 40)
- True, False :: bool
- If :: [bool, 'a, 'a] => 'a ("(if (_)/ then (_)/ else (_))" 10)
+ Trueprop :: "bool => prop" ("(_)" 5)
+ Not :: "bool => bool" ("~ _" [40] 40)
+ True :: bool
+ False :: bool
+ If :: "[bool, 'a, 'a] => 'a" ("(if (_)/ then (_)/ else (_))" 10)
arbitrary :: 'a
(* Binders *)
- Eps :: ('a => bool) => 'a
- All :: ('a => bool) => bool (binder "ALL " 10)
- Ex :: ('a => bool) => bool (binder "EX " 10)
- Ex1 :: ('a => bool) => bool (binder "EX! " 10)
- Let :: ['a, 'a => 'b] => 'b
+ Eps :: "('a => bool) => 'a"
+ All :: "('a => bool) => bool" (binder "ALL " 10)
+ Ex :: "('a => bool) => bool" (binder "EX " 10)
+ Ex1 :: "('a => bool) => bool" (binder "EX! " 10)
+ Let :: "['a, 'a => 'b] => 'b"
(* Infixes *)
- "=" :: ['a, 'a] => bool (infixl 50)
- "&" :: [bool, bool] => bool (infixr 35)
- "|" :: [bool, bool] => bool (infixr 30)
- "-->" :: [bool, bool] => bool (infixr 25)
+ "=" :: "['a, 'a] => bool" (infixl 50)
+ & :: "[bool, bool] => bool" (infixr 35)
+ "|" :: "[bool, bool] => bool" (infixr 30)
+ --> :: "[bool, bool] => bool" (infixr 25)
(* Overloaded Constants *)
-axclass
- plus < term
-
-axclass
- minus < term
-
-axclass
- times < term
-
-axclass
- power < term
+axclass plus < "term"
+axclass minus < "term"
+axclass times < "term"
+axclass power < "term"
consts
- "+" :: ['a::plus, 'a] => 'a (infixl 65)
- "-" :: ['a::minus, 'a] => 'a (infixl 65)
- uminus :: ['a::minus] => 'a ("- _" [81] 80)
- "*" :: ['a::times, 'a] => 'a (infixl 70)
+ "+" :: "['a::plus, 'a] => 'a" (infixl 65)
+ - :: "['a::minus, 'a] => 'a" (infixl 65)
+ uminus :: "['a::minus] => 'a" ("- _" [81] 80)
+ "*" :: "['a::times, 'a] => 'a" (infixl 70)
(*See Nat.thy for "^"*)
@@ -83,22 +74,22 @@
case_syn cases_syn
syntax
- "~=" :: ['a, 'a] => bool (infixl 50)
- "_Eps" :: [pttrn, bool] => 'a ("(3SOME _./ _)" [0, 10] 10)
+ ~= :: "['a, 'a] => bool" (infixl 50)
+ "_Eps" :: "[pttrn, bool] => 'a" ("(3SOME _./ _)" [0, 10] 10)
(* Let expressions *)
- "_bind" :: [pttrn, 'a] => letbind ("(2_ =/ _)" 10)
- "" :: letbind => letbinds ("_")
- "_binds" :: [letbind, letbinds] => letbinds ("_;/ _")
- "_Let" :: [letbinds, 'a] => 'a ("(let (_)/ in (_))" 10)
+ "_bind" :: "[pttrn, 'a] => letbind" ("(2_ =/ _)" 10)
+ "" :: "letbind => letbinds" ("_")
+ "_binds" :: "[letbind, letbinds] => letbinds" ("_;/ _")
+ "_Let" :: "[letbinds, 'a] => 'a" ("(let (_)/ in (_))" 10)
(* Case expressions *)
- "@case" :: ['a, cases_syn] => 'b ("(case _ of/ _)" 10)
- "@case1" :: ['a, 'b] => case_syn ("(2_ =>/ _)" 10)
- "" :: case_syn => cases_syn ("_")
- "@case2" :: [case_syn, cases_syn] => cases_syn ("_/ | _")
+ "@case" :: "['a, cases_syn] => 'b" ("(case _ of/ _)" 10)
+ "@case1" :: "['a, 'b] => case_syn" ("(2_ =>/ _)" 10)
+ "" :: "case_syn => cases_syn" ("_")
+ "@case2" :: "[case_syn, cases_syn] => cases_syn" ("_/ | _")
translations
"x ~= y" == "~ (x = y)"
@@ -107,37 +98,37 @@
"let x = a in e" == "Let a (%x. e)"
syntax ("" output)
- "op =" :: ['a, 'a] => bool ("(_ =/ _)" [51, 51] 50)
- "op ~=" :: ['a, 'a] => bool ("(_ ~=/ _)" [51, 51] 50)
+ "op =" :: "['a, 'a] => bool" ("(_ =/ _)" [51, 51] 50)
+ "op ~=" :: "['a, 'a] => bool" ("(_ ~=/ _)" [51, 51] 50)
syntax (symbols)
- Not :: bool => bool ("\\<not> _" [40] 40)
- "op &" :: [bool, bool] => bool (infixr "\\<and>" 35)
- "op |" :: [bool, bool] => bool (infixr "\\<or>" 30)
- "op -->" :: [bool, bool] => bool (infixr "\\<midarrow>\\<rightarrow>" 25)
- "op o" :: ['b => 'c, 'a => 'b, 'a] => 'c (infixl "\\<circ>" 55)
- "op ~=" :: ['a, 'a] => bool (infixl "\\<noteq>" 50)
- "_Eps" :: [pttrn, bool] => 'a ("(3\\<epsilon>_./ _)" [0, 10] 10)
- "ALL " :: [idts, bool] => bool ("(3\\<forall>_./ _)" [0, 10] 10)
- "EX " :: [idts, bool] => bool ("(3\\<exists>_./ _)" [0, 10] 10)
- "EX! " :: [idts, bool] => bool ("(3\\<exists>!_./ _)" [0, 10] 10)
- "@case1" :: ['a, 'b] => case_syn ("(2_ \\<Rightarrow>/ _)" 10)
-(*"@case2" :: [case_syn, cases_syn] => cases_syn ("_/ \\<orelse> _")*)
+ Not :: "bool => bool" ("\\<not> _" [40] 40)
+ "op &" :: "[bool, bool] => bool" (infixr "\\<and>" 35)
+ "op |" :: "[bool, bool] => bool" (infixr "\\<or>" 30)
+ "op -->" :: "[bool, bool] => bool" (infixr "\\<midarrow>\\<rightarrow>" 25)
+ "op o" :: "['b => 'c, 'a => 'b, 'a] => 'c" (infixl "\\<circ>" 55)
+ "op ~=" :: "['a, 'a] => bool" (infixl "\\<noteq>" 50)
+ "_Eps" :: "[pttrn, bool] => 'a" ("(3\\<epsilon>_./ _)" [0, 10] 10)
+ "ALL " :: "[idts, bool] => bool" ("(3\\<forall>_./ _)" [0, 10] 10)
+ "EX " :: "[idts, bool] => bool" ("(3\\<exists>_./ _)" [0, 10] 10)
+ "EX! " :: "[idts, bool] => bool" ("(3\\<exists>!_./ _)" [0, 10] 10)
+ "@case1" :: "['a, 'b] => case_syn" ("(2_ \\<Rightarrow>/ _)" 10)
+(*"@case2" :: "[case_syn, cases_syn] => cases_syn" ("_/ \\<orelse> _")*)
syntax (symbols output)
- "op ~=" :: ['a, 'a] => bool ("(_ \\<noteq>/ _)" [51, 51] 50)
+ "op ~=" :: "['a, 'a] => bool" ("(_ \\<noteq>/ _)" [51, 51] 50)
syntax (xsymbols)
- "op -->" :: [bool, bool] => bool (infixr "\\<longrightarrow>" 25)
+ "op -->" :: "[bool, bool] => bool" (infixr "\\<longrightarrow>" 25)
syntax (HTML output)
- Not :: bool => bool ("\\<not> _" [40] 40)
+ Not :: "bool => bool" ("\\<not> _" [40] 40)
syntax (HOL)
- "_Eps" :: [pttrn, bool] => 'a ("(3@ _./ _)" [0, 10] 10)
- "ALL " :: [idts, bool] => bool ("(3! _./ _)" [0, 10] 10)
- "EX " :: [idts, bool] => bool ("(3? _./ _)" [0, 10] 10)
- "EX! " :: [idts, bool] => bool ("(3?! _./ _)" [0, 10] 10)
+ "_Eps" :: "[pttrn, bool] => 'a" ("(3@ _./ _)" [0, 10] 10)
+ "ALL " :: "[idts, bool] => bool" ("(3! _./ _)" [0, 10] 10)
+ "EX " :: "[idts, bool] => bool" ("(3? _./ _)" [0, 10] 10)
+ "EX! " :: "[idts, bool] => bool" ("(3?! _./ _)" [0, 10] 10)
@@ -145,57 +136,59 @@
local
-rules
+axioms
- eq_reflection "(x=y) ==> (x==y)"
+ eq_reflection: "(x=y) ==> (x==y)"
(* Basic Rules *)
- refl "t = (t::'a)"
- subst "[| s = t; P(s) |] ==> P(t::'a)"
+ refl: "t = (t::'a)"
+ subst: "[| s = t; P(s) |] ==> P(t::'a)"
(*Extensionality is built into the meta-logic, and this rule expresses
a related property. It is an eta-expanded version of the traditional
rule, and similar to the ABS rule of HOL.*)
- ext "(!!x::'a. (f x ::'b) = g x) ==> (%x. f x) = (%x. g x)"
+ ext: "(!!x::'a. (f x ::'b) = g x) ==> (%x. f x) = (%x. g x)"
- selectI "P (x::'a) ==> P (@x. P x)"
+ selectI: "P (x::'a) ==> P (@x. P x)"
- impI "(P ==> Q) ==> P-->Q"
- mp "[| P-->Q; P |] ==> Q"
+ impI: "(P ==> Q) ==> P-->Q"
+ mp: "[| P-->Q; P |] ==> Q"
defs
- True_def "True == ((%x::bool. x) = (%x. x))"
- All_def "All(P) == (P = (%x. True))"
- Ex_def "Ex(P) == P(@x. P(x))"
- False_def "False == (!P. P)"
- not_def "~ P == P-->False"
- and_def "P & Q == !R. (P-->Q-->R) --> R"
- or_def "P | Q == !R. (P-->R) --> (Q-->R) --> R"
- Ex1_def "Ex1(P) == ? x. P(x) & (! y. P(y) --> y=x)"
+ True_def: "True == ((%x::bool. x) = (%x. x))"
+ All_def: "All(P) == (P = (%x. True))"
+ Ex_def: "Ex(P) == P(@x. P(x))"
+ False_def: "False == (!P. P)"
+ not_def: "~ P == P-->False"
+ and_def: "P & Q == !R. (P-->Q-->R) --> R"
+ or_def: "P | Q == !R. (P-->R) --> (Q-->R) --> R"
+ Ex1_def: "Ex1(P) == ? x. P(x) & (! y. P(y) --> y=x)"
-rules
+axioms
(* Axioms *)
- iff "(P-->Q) --> (Q-->P) --> (P=Q)"
- True_or_False "(P=True) | (P=False)"
+ iff: "(P-->Q) --> (Q-->P) --> (P=Q)"
+ True_or_False: "(P=True) | (P=False)"
defs
(*misc definitions*)
- Let_def "Let s f == f(s)"
- if_def "If P x y == @z::'a. (P=True --> z=x) & (P=False --> z=y)"
+ Let_def: "Let s f == f(s)"
+ if_def: "If P x y == @z::'a. (P=True --> z=x) & (P=False --> z=y)"
(*arbitrary is completely unspecified, but is made to appear as a
definition syntactically*)
- arbitrary_def "False ==> arbitrary == (@x. False)"
+ arbitrary_def: "False ==> arbitrary == (@x. False)"
-(** initial HOL theory setup **)
+(* theory and package setup *)
-setup Simplifier.setup
-setup ClasetThyData.setup
+use "HOL_lemmas.ML" setup attrib_setup
+use "cladata.ML" setup Classical.setup setup clasetup
+use "blastdata.ML" setup Blast.setup
+use "simpdata.ML" setup Simplifier.setup setup simpsetup setup Clasimp.setup
end