diff -r 1714c91b8729 -r d0e16da40ea2 src/HOL/HOL.thy --- 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 ("\\ _" [40] 40) - "op &" :: [bool, bool] => bool (infixr "\\" 35) - "op |" :: [bool, bool] => bool (infixr "\\" 30) - "op -->" :: [bool, bool] => bool (infixr "\\\\" 25) - "op o" :: ['b => 'c, 'a => 'b, 'a] => 'c (infixl "\\" 55) - "op ~=" :: ['a, 'a] => bool (infixl "\\" 50) - "_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) - "@case1" :: ['a, 'b] => case_syn ("(2_ \\/ _)" 10) -(*"@case2" :: [case_syn, cases_syn] => cases_syn ("_/ \\ _")*) + Not :: "bool => bool" ("\\ _" [40] 40) + "op &" :: "[bool, bool] => bool" (infixr "\\" 35) + "op |" :: "[bool, bool] => bool" (infixr "\\" 30) + "op -->" :: "[bool, bool] => bool" (infixr "\\\\" 25) + "op o" :: "['b => 'c, 'a => 'b, 'a] => 'c" (infixl "\\" 55) + "op ~=" :: "['a, 'a] => bool" (infixl "\\" 50) + "_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) + "@case1" :: "['a, 'b] => case_syn" ("(2_ \\/ _)" 10) +(*"@case2" :: "[case_syn, cases_syn] => cases_syn" ("_/ \\ _")*) syntax (symbols output) - "op ~=" :: ['a, 'a] => bool ("(_ \\/ _)" [51, 51] 50) + "op ~=" :: "['a, 'a] => bool" ("(_ \\/ _)" [51, 51] 50) syntax (xsymbols) - "op -->" :: [bool, bool] => bool (infixr "\\" 25) + "op -->" :: "[bool, bool] => bool" (infixr "\\" 25) syntax (HTML output) - Not :: bool => bool ("\\ _" [40] 40) + Not :: "bool => bool" ("\\ _" [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