1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/Tools/isac/Knowledge/Integrate.thy	Wed Aug 25 16:20:07 2010 +0200
     1.3 @@ -0,0 +1,54 @@
     1.4 +(* integration over the reals
     1.5 +   author: Walther Neuper
     1.6 +   050814, 08:51
     1.7 +   (c) due to copyright terms
     1.8 +
     1.9 +remove_thy"Integrate";
    1.10 +use_thy"Knowledge/Integrate";
    1.11 +use_thy_only"Knowledge/Integrate";
    1.12 +
    1.13 +remove_thy"Typefix";
    1.14 +use_thy"Knowledge/Isac";
    1.15 +*)
    1.16 +
    1.17 +Integrate = Diff +
    1.18 +
    1.19 +consts
    1.20 +
    1.21 +  Integral            :: "[real, real]=> real" ("Integral _ D _" 91)
    1.22 +(*new'_c	      :: "real => real"        ("new'_c _" 66)*)
    1.23 +  is'_f'_x            :: "real => bool"        ("_ is'_f'_x" 10)
    1.24 +
    1.25 +  (*descriptions in the related problems*)
    1.26 +  integrateBy         :: real => una
    1.27 +  antiDerivative      :: real => una
    1.28 +  antiDerivativeName  :: (real => real) => una
    1.29 +
    1.30 +  (*the CAS-command, eg. "Integrate (2*x^^^3, x)"*)
    1.31 +  Integrate           :: "[real * real] => real"
    1.32 +
    1.33 +  (*Script-names*)
    1.34 +  IntegrationScript      :: "[real,real,  real] => real"
    1.35 +                  ("((Script IntegrationScript (_ _ =))// (_))" 9)
    1.36 +  NamedIntegrationScript :: "[real,real, real=>real,  bool] => bool"
    1.37 +                  ("((Script NamedIntegrationScript (_ _ _=))// (_))" 9)
    1.38 +
    1.39 +rules 
    1.40 +(*stated as axioms, todo: prove as theorems
    1.41 +  'bdv' is a constant handled on the meta-level 
    1.42 +   specifically as a 'bound variable'            *)
    1.43 +
    1.44 +  integral_const    "Not (bdv occurs_in u) ==> Integral u D bdv = u * bdv"
    1.45 +  integral_var      "Integral bdv D bdv = bdv ^^^ 2 / 2"
    1.46 +
    1.47 +  integral_add      "Integral (u + v) D bdv = \
    1.48 +		    \(Integral u D bdv) + (Integral v D bdv)"
    1.49 +  integral_mult     "[| Not (bdv occurs_in u); bdv occurs_in v |] ==> \
    1.50 +		    \Integral (u * v) D bdv = u * (Integral v D bdv)"
    1.51 +(*WN080222: this goes into sub-terms, too ...
    1.52 +  call_for_new_c    "[| Not (matches (u + new_c v) a); Not (a is_f_x) |] ==> \
    1.53 +		    \a = a + new_c a"
    1.54 +*)
    1.55 +  integral_pow      "Integral bdv ^^^ n D bdv = bdv ^^^ (n+1) / (n + 1)"
    1.56 +
    1.57 +end
    1.58 \ No newline at end of file