src/HOL/PreList.thy
author wenzelm
Fri Dec 15 17:59:30 2000 +0100 (2000-12-15)
changeset 10680 26e4aecf3207
parent 10671 ac6b3b671198
child 10733 59f82484e000
permissions -rw-r--r--
tuned comment;
     1 (*  Title:      HOL/PreList.thy
     2     ID:         $Id$
     3     Author:     Tobias Nipkow
     4     Copyright   2000 TU Muenchen
     5 
     6 A basis for building theory List on. Is defined separately to serve as a
     7 basis for theory ToyList in the documentation.
     8 *)
     9 
    10 theory PreList =
    11   Option + Wellfounded_Relations + NatSimprocs + Recdef + Record +
    12   Relation_Power + Calculation + SVC_Oracle:
    13 
    14 (*belongs to theory HOL*)
    15 declare case_split [cases type: bool]
    16 
    17 (*belongs to theory Wellfounded_Recursion*)
    18 declare wf_induct [induct set: wf]
    19 
    20 (*belongs to theory Datatype_Universe; hides popular names *)
    21 hide const Node Atom Leaf Numb Lim Funs Split Case
    22 
    23 
    24 (* generic summation indexed over nat *)
    25 
    26 (*FIXME move to Ring_and_Field, when it is made part of main HOL (!?)*)
    27 (*FIXME port theorems from Algebra/abstract/NatSum*)
    28 
    29 consts
    30   Summation :: "(nat => 'a::{zero,plus}) => nat => 'a"
    31 primrec
    32   "Summation f 0 = 0"
    33   "Summation f (Suc n) = Summation f n + f n"
    34 
    35 syntax
    36   "_Summation" :: "idt => nat => 'a => nat"    ("\<Sum>_<_. _" [0, 51, 10] 10)
    37 translations
    38   "\<Sum>i < n. b" == "Summation (\<lambda>i. b) n"
    39 
    40 theorem Summation_step:
    41     "0 < n ==> (\<Sum>i < n. f i) = (\<Sum>i < n - 1. f i) + f (n - 1)"
    42   by (induct n) simp_all
    43 
    44 end