src/HOL/HOL.thy
author wenzelm
Fri Jan 24 17:12:28 1997 +0100 (1997-01-24)
changeset 2552 470bc495373e
parent 2393 651fce76c86c
child 2720 3490ef519a56
permissions -rw-r--r--
changed case symbol to \<Rightarrow>;
     1 (*  Title:      HOL/HOL.thy
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   1993  University of Cambridge
     5 
     6 Higher-Order Logic.
     7 *)
     8 
     9 HOL = CPure +
    10 
    11 
    12 (** Core syntax **)
    13 
    14 classes
    15   term < logic
    16 
    17 default
    18   term
    19 
    20 types
    21   bool
    22 
    23 arities
    24   fun :: (term, term) term
    25   bool :: term
    26 
    27 
    28 consts
    29 
    30   (* Constants *)
    31 
    32   Trueprop      :: bool => prop                     ("(_)" 5)
    33   not           :: bool => bool                     ("~ _" [40] 40)
    34   True, False   :: bool
    35   If            :: [bool, 'a, 'a] => 'a   ("(if (_)/ then (_)/ else (_))" 10)
    36   Inv           :: ('a => 'b) => ('b => 'a)
    37 
    38   (* Binders *)
    39 
    40   Eps           :: ('a => bool) => 'a
    41   All           :: ('a => bool) => bool             (binder "! " 10)
    42   Ex            :: ('a => bool) => bool             (binder "? " 10)
    43   Ex1           :: ('a => bool) => bool             (binder "?! " 10)
    44   Let           :: ['a, 'a => 'b] => 'b
    45 
    46   (* Infixes *)
    47 
    48   o             :: ['b => 'c, 'a => 'b, 'a] => 'c   (infixl 55)
    49   "="           :: ['a, 'a] => bool                 (infixl 50)
    50   "&"           :: [bool, bool] => bool             (infixr 35)
    51   "|"           :: [bool, bool] => bool             (infixr 30)
    52   "-->"         :: [bool, bool] => bool             (infixr 25)
    53 
    54 
    55 (* Overloaded Constants *)
    56 
    57 axclass
    58   plus < term
    59 
    60 axclass
    61   minus < term
    62 
    63 axclass
    64   times < term
    65 
    66 consts
    67   "+"           :: ['a::plus, 'a] => 'a             (infixl 65)
    68   "-"           :: ['a::minus, 'a] => 'a            (infixl 65)
    69   "*"           :: ['a::times, 'a] => 'a            (infixl 70)
    70 
    71 
    72 
    73 (** Additional concrete syntax **)
    74 
    75 types
    76   letbinds  letbind
    77   case_syn  cases_syn
    78 
    79 syntax
    80 
    81   "~="          :: ['a, 'a] => bool                 (infixl 50)
    82 
    83   "@Eps"        :: [pttrn, bool] => 'a              ("(3@ _./ _)" [0, 10] 10)
    84 
    85   (* Alternative Quantifiers *)
    86 
    87   "*All"        :: [idts, bool] => bool             ("(3ALL _./ _)" [0, 10] 10)
    88   "*Ex"         :: [idts, bool] => bool             ("(3EX _./ _)" [0, 10] 10)
    89   "*Ex1"        :: [idts, bool] => bool             ("(3EX! _./ _)" [0, 10] 10)
    90 
    91   (* Let expressions *)
    92 
    93   "_bind"       :: [pttrn, 'a] => letbind           ("(2_ =/ _)" 10)
    94   ""            :: letbind => letbinds              ("_")
    95   "_binds"      :: [letbind, letbinds] => letbinds  ("_;/ _")
    96   "_Let"        :: [letbinds, 'a] => 'a             ("(let (_)/ in (_))" 10)
    97 
    98   (* Case expressions *)
    99 
   100   "@case"       :: ['a, cases_syn] => 'b            ("(case _ of/ _)" 10)
   101   "@case1"      :: ['a, 'b] => case_syn             ("(2_ =>/ _)" 10)
   102   ""            :: case_syn => cases_syn            ("_")
   103   "@case2"      :: [case_syn, cases_syn] => cases_syn   ("_/ | _")
   104 
   105 translations
   106   "x ~= y"      == "~ (x = y)"
   107   "@ x.b"       == "Eps (%x. b)"
   108   "ALL xs. P"   => "! xs. P"
   109   "EX xs. P"    => "? xs. P"
   110   "EX! xs. P"   => "?! xs. P"
   111   "_Let (_binds b bs) e"  == "_Let b (_Let bs e)"
   112   "let x = a in e"        == "Let a (%x. e)"
   113 
   114 
   115 syntax (symbols)
   116   not           :: bool => bool                     ("\\<not> _" [40] 40)
   117   "op &"        :: [bool, bool] => bool             (infixr "\\<and>" 35)
   118   "op |"        :: [bool, bool] => bool             (infixr "\\<or>" 30)
   119   "op -->"      :: [bool, bool] => bool             (infixr "\\<midarrow>\\<rightarrow>" 25)
   120   "op o"        :: ['b => 'c, 'a => 'b, 'a] => 'c   (infixl "\\<circ>" 55)
   121   "op ~="       :: ['a, 'a] => bool                 (infixl "\\<noteq>" 50)
   122   "@Eps"        :: [pttrn, bool] => 'a              ("(3\\<epsilon>_./ _)" [0, 10] 10)
   123   "! "          :: [idts, bool] => bool             ("(3\\<forall>_./ _)" [0, 10] 10)
   124   "? "          :: [idts, bool] => bool             ("(3\\<exists>_./ _)" [0, 10] 10)
   125   "?! "         :: [idts, bool] => bool             ("(3\\<exists>!_./ _)" [0, 10] 10)
   126   "@case1"      :: ['a, 'b] => case_syn             ("(2_ \\<Rightarrow>/ _)" 10)
   127 
   128 syntax (symbols output)
   129   "*All"        :: [idts, bool] => bool             ("(3\\<forall>_./ _)" [0, 10] 10)
   130   "*Ex"         :: [idts, bool] => bool             ("(3\\<exists>_./ _)" [0, 10] 10)
   131   "*Ex1"        :: [idts, bool] => bool             ("(3\\<exists>!_./ _)" [0, 10] 10)
   132 
   133 
   134 
   135 
   136 (** Rules and definitions **)
   137 
   138 rules
   139 
   140   eq_reflection "(x=y) ==> (x==y)"
   141 
   142   (* Basic Rules *)
   143 
   144   refl          "t = (t::'a)"
   145   subst         "[| s = t; P(s) |] ==> P(t::'a)"
   146   ext           "(!!x::'a. (f(x)::'b) = g(x)) ==> (%x.f(x)) = (%x.g(x))"
   147   selectI       "P(x::'a) ==> P(@x.P(x))"
   148 
   149   impI          "(P ==> Q) ==> P-->Q"
   150   mp            "[| P-->Q;  P |] ==> Q"
   151 
   152 defs
   153 
   154   True_def      "True      == ((%x::bool.x)=(%x.x))"
   155   All_def       "All(P)    == (P = (%x.True))"
   156   Ex_def        "Ex(P)     == P(@x.P(x))"
   157   False_def     "False     == (!P.P)"
   158   not_def       "~ P       == P-->False"
   159   and_def       "P & Q     == !R. (P-->Q-->R) --> R"
   160   or_def        "P | Q     == !R. (P-->R) --> (Q-->R) --> R"
   161   Ex1_def       "Ex1(P)    == ? x. P(x) & (! y. P(y) --> y=x)"
   162 
   163 rules
   164   (* Axioms *)
   165 
   166   iff           "(P-->Q) --> (Q-->P) --> (P=Q)"
   167   True_or_False "(P=True) | (P=False)"
   168 
   169 defs
   170   (* Misc Definitions *)
   171 
   172   Let_def       "Let s f == f(s)"
   173   Inv_def       "Inv(f::'a=>'b)  == (% y. @x. f(x)=y)"
   174   o_def         "(f::'b=>'c) o g == (%(x::'a). f(g(x)))"
   175   if_def        "If P x y == @z::'a. (P=True --> z=x) & (P=False --> z=y)"
   176 
   177 end
   178 
   179 
   180 ML
   181 
   182 (** Choice between the HOL and Isabelle style of quantifiers **)
   183 
   184 val HOL_quantifiers = ref true;
   185 
   186 fun alt_ast_tr' (name, alt_name) =
   187   let
   188     fun ast_tr' (*name*) args =
   189       if ! HOL_quantifiers then raise Match
   190       else Syntax.mk_appl (Syntax.Constant alt_name) args;
   191   in
   192     (name, ast_tr')
   193   end;
   194 
   195 
   196 val print_ast_translation =
   197   map alt_ast_tr' [("! ", "*All"), ("? ", "*Ex"), ("?! ", "*Ex1")];