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1 (* use"tests/calculate.sml"; |
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2 use"calculate.sml"; |
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3 *) |
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4 (*contents |
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5 " ================= calculate.sml: calculate_ ======================== "; |
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6 " ================= calculate.sml: aus script ======================== "; |
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7 " ================= calculate.sml: from test-root-equ.sml ================== "; |
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8 " ================= calculate.sml: 2.8.02 check test-root-equ ======== "; |
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9 " ================= calculate.sml:10.8.02 2002:///->/ ======== "; |
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10 " ================= calculate.sml: calculate_ 2002 =================== "; |
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11 " ================= eval_binop Float =================== "; |
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12 *) |
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13 |
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14 (* [("Var",("Tools.Var",fn)),("Length",("Tools.Length",fn)), |
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15 ("Nth",("Tools.Nth",fn)), |
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16 ("power_",("Atools.pow",fn)),("plus",("op +",fn)),("times",("op *",fn)), |
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17 ("is_const",("Atools.is'_const",fn)), |
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18 ("le",("op <",fn)),("leq",("op <=",fn)), |
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19 ("ident",("Atools.ident",fn))] *) |
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20 |
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21 " ================= calculate.sml: calculate_ ======================== "; |
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22 " ================= calculate.sml: calculate_ ======================== "; |
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23 " ================= calculate.sml: calculate_ ======================== "; |
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24 |
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25 |
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26 val thy = Test.thy; |
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27 val t = (term_of o the o (parse thy)) "1+2"; |
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28 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t; |
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29 |
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30 val t = (term_of o the o (parse thy)) "((1+2)*4/3)^^^2"; |
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31 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t; |
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32 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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33 Sign.string_of_term (sign_of thy) t; |
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34 (*val it = "(#3 * #4 // #3) ^^^ #2" : string*) |
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35 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"times"))) t; |
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36 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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37 Sign.string_of_term (sign_of thy) t; |
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38 (*val it = "(#12 // #3) ^^^ #2" : string*) |
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39 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"divide_")))t; |
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40 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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41 Sign.string_of_term (sign_of thy) t; |
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42 (*it = "#4 ^^^ #2" : string*) |
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43 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_")))t; |
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44 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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45 Sign.string_of_term (sign_of thy) t; |
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46 (*val it = "#16" : string*) |
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47 if it <> "16" then raise error "calculate.sml: new behaviour in calculate_" |
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48 else (); |
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49 |
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50 " ================= calculate.sml: aus script ======================== "; |
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51 " ================= calculate.sml: aus script ======================== "; |
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52 " ================= calculate.sml: aus script ======================== "; |
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53 |
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54 store_pbt |
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55 (prep_pbt Test.thy |
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56 (["test"], |
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57 [], |
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58 e_rls, None, [])); |
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59 store_pbt |
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60 (prep_pbt Test.thy |
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61 (["calculate","test"], |
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62 [("#Given" ,["realTestGiven t_"]), |
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63 ("#Find" ,["realTestFind s_"]) |
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64 ], |
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65 e_rls, None, [("Test.thy","test_calculate")])); |
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66 |
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67 methods:= overwritel (!methods, |
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68 [ |
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69 prep_met |
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70 (("Test.thy","test_calculate"):metID, |
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71 [("#Given" ,["realTestGiven t_"]), |
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72 ("#Find" ,["realTestFind s_"]) |
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73 ], |
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74 {rew_ord'="sqrt_right",rls'=tval_rls,srls=e_rls,prls=e_rls, |
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75 calc=[("plus" ,("op +" ,eval_binop "#add_")), |
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76 ("times" ,("op *" ,eval_binop "#mult_")), |
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77 ("divide_" ,("HOL.divide" ,eval_cancel "#divide_")), |
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78 ("power_" ,("Atools.pow" ,eval_binop "#power_"))], |
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79 asm_rls=[],asm_thm=[]}, |
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80 "Script STest_simplify (t_::real) = \ |
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81 \(Repeat \ |
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82 \ ((Try (Repeat (Calculate plus))) @@ \ |
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83 \ (Try (Repeat (Calculate times))) @@ \ |
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84 \ (Try (Repeat (Calculate divide_))) @@ \ |
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85 \ (Try (Repeat (Calculate power_))))) t_" |
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86 ) |
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87 ]); |
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88 |
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89 val fmz = ["realTestGiven (((1+2)*4/3)^^^2)","realTestFind s"]; |
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90 val (dI',pI',mI') = |
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91 ("Test.thy",["calculate","test"],("Test.thy","test_calculate")); |
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92 val p = e_pos'; val c = []; |
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93 val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI'))); |
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94 val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree; |
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95 (*nxt =("Add_Given",Add_Given "realTestGiven (((#1 + #2) * #4 // #3) ^^^#2)")*) |
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96 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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97 (*nxt = ("Add_Find",Add_Find "realTestFind s") : string * mstep*) |
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98 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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99 (*nxt = ("Specify_Domain",Specify_Domain "Test.thy") : string * mstep*) |
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100 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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101 (*nxt = ("Specify_Problem",Specify_Problem ["calculate","test"])*) |
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102 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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103 (*nxt = ("Specify_Method",Specify_Method ("Test.thy","test_calculate"))*) |
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104 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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105 (*nxt = ("Apply_Method",Apply_Method ("Test.thy","test_calculate"))*) |
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106 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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107 (*nxt = ("Calculate",Calculate "plus")*) |
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108 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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109 (*nxt = ("Calculate",Calculate "times")*) |
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110 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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111 (*nxt = ("Calculate",Calculate "divide_")*) |
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112 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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113 (*nxt = ("Calculate",Calculate "power_")*) |
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114 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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115 (*nxt = ("Check_Postcond",Check_Postcond ["calculate","test"])*) |
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116 val (p,_,f,nxt,_,pt) = me nxt p [1] pt; |
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117 (*nxt = ("End_Proof'",End_Proof')*) |
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118 if f = Form' (FormKF (~1,EdUndef,0,Nundef,"16")) then () |
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119 else raise error "calculate.sml: script test_calculate changed behaviour"; |
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120 |
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121 |
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122 |
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123 |
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124 " ================= calculate.sml: from test-root-equ.sml ================== "; |
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125 " ================= calculate.sml: from test-root-equ.sml ================== "; |
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126 " ================= calculate.sml: from test-root-equ.sml ================== "; |
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127 val thy' = "Test.thy"; |
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128 val ct = "1 + 2"; |
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129 val (ct,thm') = the (calculate thy' (the(assoc(calclist,"plus"))) ct); |
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130 (*val ct = "#3" : string |
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131 val thm' = ("#add_#1_#2","\"#1 + #2 = #3\"") : thm'*) |
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132 |
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133 "----- me -----"; |
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134 val (dI',pI',mI') = ("Test.thy",e_pblID, |
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135 ("Test.thy","sqrt-equ-test")); |
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136 val p = e_pos'; val c = []; |
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137 val (mI,m) = ("Init_Proof",Init_Proof ([], (dI',pI',mI'))); |
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138 val (p,_,_,_,_,pt) = me (mI,m) p c EmptyPtree; |
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139 val nxt = ("Specify_Domain",Specify_Domain "Test.thy"); |
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140 val (p,_,_,_,_,pt) = me nxt p c pt; |
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141 val (pt,_) = cappend_atomic pt [1] e_istate "1 + 2" |
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142 (Calculate "test") ct Complete; |
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143 val p = ([1],Frm):pos'; |
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144 val nxt = ("Calculate",Calculate "plus"); |
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145 val (p,_,f,nxt,_,pt)=me nxt p c pt; |
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146 Compiler.Control.Print.printDepth:=9; (*4 default*) |
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147 (* Nd (PblObj... |
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148 [Nd (PrfObj |
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149 {branch=NoBranch,cell=[],form="#1 + #2",loc=(([],None),([],None)), |
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150 mstep=Calculate "plus",ostate=Complete,result="#3"},[])]) : squ*) |
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151 Compiler.Control.Print.printDepth:=4; (*4 default*) |
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152 |
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153 val (pt,_) = cappend_atomic pt [1] e_istate "6/4" |
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154 (Calculate "test") ct Complete; |
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155 val p = ([1],Frm):pos'; |
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156 val nxt = ("Calculate",Calculate "divide_"); |
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157 val (p,_,f,nxt,_,pt)=me nxt p c pt; |
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158 (*{branch=NoBranch,cell=[],form="#6 // #4",loc=(([],None),([],None)), |
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159 mstep=Calculate "divide_",ostate=Complete,result="#3 // #2"},[])]) *) |
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160 |
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161 (*5.7.00: interne ops in calclist*) |
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162 |
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163 |
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164 " ================= calculate.sml: 2.8.02 check test-root-equ ======== "; |
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165 " ================= calculate.sml: 2.8.02 check test-root-equ ======== "; |
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166 " ================= calculate.sml: 2.8.02 check test-root-equ ======== "; |
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167 (*(1): 2nd Test_simplify didn't work: |
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168 val ct = |
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169 "sqrt (x ^^^ 2 + -3 * x) = (-3 + 2 * x + -1 * (9 + 4 * x)) / (-1 * 2)" |
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170 > val rls = ("Test_simplify"); |
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171 > val (ct,_) = the (rewrite_set thy' ("tval_rls") false rls ct); |
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172 val ct = "sqrt (x ^^^ 2 + -3 * x) = |
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173 (-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2))))"; |
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174 ie. cancel does not work properly |
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175 *) |
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176 val thy = "Test.thy"; |
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177 val op_ = "divide_"; |
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178 val ct = "sqrt (x ^^^ 2 + -3 * x) =\ |
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179 \(-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2))))"; |
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180 val Some (ct,_) = calculate thy (the(assoc(calclist,op_))) ct; |
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181 writeln ct; |
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182 (* |
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183 sqrt (x ^^^ 2 + -3 * x) =\ |
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184 \(-9) / (-2) + (-3 / (-2) + (x * ((-4) / (-2)) + x * (2 / (-2)))) |
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185 ............... does not work *) |
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186 |
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187 (*--------------(2): does divide work in Test_simplify ?: ------*) |
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188 val thy = Test.thy; |
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189 val t = (term_of o the o (parse thy)) "6 / 2"; |
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190 val rls = Test_simplify; |
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191 val (t,_) = the (rewrite_set_ thy false rls t); |
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192 (*val t = Free ("3","RealDef.real") : term*) |
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193 |
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194 val thy = "Test.thy"; |
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195 val t = "6 / 2"; |
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196 val rls = "Test_simplify"; |
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197 val (t,_) = the (rewrite_set thy false rls t); |
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198 (*val t = "3" : string |
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199 ....... works, thus: which rule in SqRoot_simplify works differently ?*) |
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200 |
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201 |
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202 (*--------------(3): is_const works ?: -------------------------------------*) |
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203 val t = (term_of o the o (parse Test.thy)) "2 is_const"; |
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204 atomty Test.thy t; |
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205 rewrite_set_ Test.thy false tval_rls t; |
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206 (*val it = Some (Const ("True","bool"),[]) ... works*) |
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207 |
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208 |
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209 (*--------------(4): check bottom up: ---------------------------*) |
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210 (*-------------- eval_cancel works: *) |
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211 trace_rewrite:=true; |
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212 val thy = Test.thy; |
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213 val t = (term_of o the o (parse thy)) "(-4) / 2"; |
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214 val Some (_,t) = eval_cancel "xxx" 111 t thy; |
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215 term2str t; |
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216 "-4 / 2 = (-2)"; |
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217 (*-------------- but ... *) |
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218 val ct = "x + (-4) / 2"; |
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219 val (ct,_) = the (rewrite_set thy' false rls ct); |
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220 "(-2) + x"; |
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221 (*-------------- while ... *) |
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222 val ct = "(-4) / 2"; |
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223 val (ct,_) = the (rewrite_set thy' false rls ct); |
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224 "(-2)"; |
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225 |
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226 (*--------------(5): reproduce (1) with simpler term: ------------*) |
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227 val thy = "Test.thy"; |
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228 val t = "(3+5)/2"; |
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229 val (t,_) = the (rewrite_set thy false rls t); |
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230 (*val t = "4" ... works*) |
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231 |
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232 val t = "(3+1+2*x)/2"; |
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233 val (t,_) = the (rewrite_set thy false rls t); |
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234 (*val t = "2 + x" ... works*) |
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235 |
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236 val t = "(3+(1+2*x))/2"; |
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237 val (t,_) = the (rewrite_set thy false rls t); |
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238 (*val t = "2 + x" ... works: give up----------------------------------------*) |
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239 |
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240 |
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241 |
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242 (*--- trace_rewrite before correction of ... -------------------- |
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243 val ct = "(-3 + 2 * x + -1) / 2"; |
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244 val (ct,_) = the (rewrite_set thy' false rls ct); |
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245 : |
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246 ### trying thm 'root_ge0_2' |
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247 ### rewrite_set_: x + (-1 + -3) / 2 |
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248 ### trying thm 'radd_real_const_eq' |
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249 ### trying thm 'radd_real_const' |
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250 ### rewrite_set_: x + (-4) / 2 |
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251 ### trying thm 'rcollect_right' |
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252 : |
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253 "x + (-4) / 2" |
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254 -------------------------------------while before Isabelle20002: |
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255 val ct = "(#-3 + #2 * x + #-1) // #2"; |
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256 val (ct,_) = the (rewrite_set thy' false rls ct); |
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257 : |
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258 ### trying thm 'root_ge0_2' |
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259 ### rewrite_set_: x + (#-1 + #-3) // #2 |
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260 ### trying thm 'radd_real_const_eq' |
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261 ### trying thm 'radd_real_const' |
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262 ### rewrite_set_: x + #-4 // #2 |
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263 ### rewrite_set_: x + #-2 |
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264 ### trying thm 'rcollect_right' |
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265 : |
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266 "#-2 + x" |
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267 -----------------------------------------------------------------*) |
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268 |
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269 |
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270 toggle trace_rewrite; |
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271 (*===================*) |
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272 trace_rewrite:=true; |
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273 val thy' = "Test.thy"; |
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274 val rls = "Test_simplify"; |
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275 val ct = "x + (-1 + -3) / 2"; |
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276 val (ct,_) = the (rewrite_set thy' false rls ct); |
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277 "x + (-4) / 2"; |
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278 (* |
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279 ### trying calc. 'cancel' |
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280 @@@ get_pair: binop, t = x + (-4) / 2 |
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281 @@@ get_pair: t else |
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282 @@@ get_pair: t else -> None |
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283 @@@ get_pair: binop, t = (-4) / 2 |
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284 @@@ get_pair: then 1 |
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285 @@@ get_pair: t -> None |
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286 @@@ get_pair: t1 -> None |
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287 @@@ get_calculation: None |
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288 ### trying calc. 'pow' |
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289 *) |
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290 |
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291 trace_rewrite:=true; |
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292 val thy' = "Test.thy"; |
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293 val rls = "Test_simplify"; |
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294 val ct = "x + (-4) / 2"; |
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295 val (ct,_) = the (rewrite_set thy' false rls ct); |
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296 "(-2) + x"; |
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297 (* |
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298 ### trying calc. 'cancel' |
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299 @@@ get_pair: binop, t = x + -4 / 2 |
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300 @@@ get_pair: t else |
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301 @@@ get_pair: t else -> None |
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302 @@@ get_pair: binop, t = -4 / 2 |
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303 @@@ get_pair: then 1 |
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304 @@@ get_calculation: Some #cancel_-4_2 |
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305 ### calc. to: x + (-2) |
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306 ### trying calc. 'cancel' |
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307 *) |
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308 trace_rewrite:=false; |
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309 |
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310 " ================= calculate.sml:10.8.02 2002:///->/ ======== "; |
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311 " ================= calculate.sml:10.8.02 2002:///->/ ======== "; |
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312 " ================= calculate.sml:10.8.02 2002:///->/ ======== "; |
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313 " ----------------- rewriting works ? -----------------------"; |
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314 val thy = Isac.thy; |
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315 val prop = (#prop o rep_thm) real_divide_1; |
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316 atomty thy prop; |
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317 (*** ------------- |
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318 *** Const ( Trueprop, bool => prop) |
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319 *** . Const ( op =, [real, real] => bool) |
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320 *** . . Const ( HOL.divide, [real, real] => real) |
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321 *** . . . Var ((x, 0), real) |
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322 *** . . . Const ( 1, real) |
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323 *** . . Var ((x, 0), real) *) |
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324 val prop' = (#prop o rep_thm o num_str) real_divide_1; |
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325 atomty thy prop'; |
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326 (*** ------------- |
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327 *** Const ( Trueprop, bool => prop) |
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328 *** . Const ( op =, [real, real] => bool) |
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329 *** . . Const ( HOL.divide, [real, real] => real) |
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330 *** . . . Var ((x, 0), real) |
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331 *** . . . Free ( 1, real) (*app_num_tr'*) |
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332 *** . . Var ((x, 0), real)*) |
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333 val t = (term_of o the o (parseold thy)) "aaa/1"; |
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334 atomty thy t; |
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335 (*** ------------- |
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336 *** Const ( HOL.divide, ['a, 'a] => 'a) |
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337 *** . Free ( aaa, 'a) |
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338 *** . Free ( 1, 'a) *) |
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339 val t = (term_of o the o (parse thy)) "aaa/1"; |
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340 atomty thy t; |
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341 (*** ------------- |
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342 *** Const ( HOL.divide, [real, real] => real) |
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343 *** . Free ( aaa, real) |
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344 *** . Free ( 1, real) *) |
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345 val thm = num_str real_divide_1; |
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346 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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347 (*val t = Free ("aaa","RealDef.real") : term*) |
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348 |
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349 |
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350 val prop = (#prop o rep_thm) realpow_eq_one; |
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351 atomty thy prop; |
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352 (*** ------------- |
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353 *** Const ( Trueprop, bool => prop) |
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354 *** . Const ( op =, [real, real] => bool) |
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355 *** . . Const ( Nat.power, [real, nat] => real) |
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356 *** . . . Const ( 1, real) |
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357 *** . . . Var ((n, 0), nat) |
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358 *** . . Const ( 1, real) *) |
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359 val prop' = (#prop o rep_thm o num_str) realpow_eq_one; |
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360 atomty thy prop'; |
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361 (*** ------------- |
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362 *** Const ( Trueprop, bool => prop) |
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363 *** . Const ( op =, [real, real] => bool) |
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364 *** . . Const ( Nat.power, [real, nat] => real) |
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365 *** . . . Free ( 1, real) |
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366 *** . . . Var ((n, 0), nat) |
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367 *** . . Free ( 1, real)*) |
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368 val t = (term_of o the o (parseold thy)) "1 ^ aaa"; |
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369 atomty thy t; |
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370 (*** ------------- |
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371 *** Const ( Nat.power, ['a, nat] => 'a) |
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372 *** . Free ( 1, 'a) |
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373 *** . Free ( aaa, nat) *) |
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374 val t = (term_of o the o (parse thy)) "1 ^ aaa"; |
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375 atomty thy t; |
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376 (*** ------------- |
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377 *** Const ( Nat.power, [real, nat] => real) |
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378 *** . Free ( 1, real) |
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379 *** . Free ( aaa, nat) .......................... nat !!! *) |
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380 val thm = num_str realpow_eq_one; |
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381 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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382 (*val t = Free ("1","RealDef.real") : term*) |
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383 |
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384 " ================= calculate.sml: calculate_ 2002 =================== "; |
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385 " ================= calculate.sml: calculate_ 2002 =================== "; |
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386 " ================= calculate.sml: calculate_ 2002 =================== "; |
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387 |
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388 val thy = Test.thy; |
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389 val t = (term_of o the o (parse thy)) "12 / 3"; |
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390 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"divide_")))t; |
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391 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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392 "12 / 3 = 4"; |
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393 val thy = Test.thy; |
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394 val t = (term_of o the o (parse thy)) "4 ^^^ 2"; |
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395 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_"))) t; |
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396 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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397 "4 ^ 2 = 16"; |
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398 |
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399 val t = (term_of o the o (parse thy)) "((1 + 2) * 4 / 3) ^^^ 2"; |
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400 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"plus"))) t; |
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401 "1 + 2 = 3"; |
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402 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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403 Sign.string_of_term (sign_of thy) t; |
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404 "(3 * 4 / 3) ^^^ 2"; |
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405 val Some (thmID,thm) = get_calculation_ thy (the(assoc(calclist,"times")))t; |
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406 "3 * 4 = 12"; |
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407 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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408 Sign.string_of_term (sign_of thy) t; |
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409 "(12 / 3) ^^^ 2"; |
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410 val Some (thmID,thm) =get_calculation_ thy(the(assoc(calclist,"divide_")))t; |
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411 "12 / 3 = 4"; |
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412 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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413 Sign.string_of_term (sign_of thy) t; |
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414 "4 ^^^ 2"; |
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415 val Some (thmID,thm) = get_calculation_ thy(the(assoc(calclist,"power_")))t; |
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416 "4 ^^^ 2 = 16"; |
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417 val Some (t,_) = rewrite_ thy tless_true tval_rls true thm t; |
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418 Sign.string_of_term (sign_of thy) t; |
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419 "16"; |
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420 if it <> "16" then raise error "calculate.sml: new behaviour in calculate_" |
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421 else (); |
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422 |
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423 (*13.9.02 *** calc: operator = pow not defined*) |
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424 val t = (term_of o the o (parse thy)) "3^^^2"; |
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425 val Some (thmID,thm) = |
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426 get_calculation_ thy (the(assoc(calclist,"power_"))) t; |
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427 (*** calc: operator = pow not defined*) |
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428 |
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429 val (op_, eval_fn) = the (assoc(calclist,"power_")); |
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430 (* |
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431 val op_ = "Atools.pow" : string |
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432 val eval_fn = fn : string -> term -> theory -> (string * term) option*) |
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433 |
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434 val Some (thmid,t') = get_pair thy op_ eval_fn t; |
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435 (*** calc: operator = pow not defined*) |
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436 |
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437 val Some (id,t') = eval_fn op_ t thy; |
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438 (*** calc: operator = pow not defined*) |
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439 |
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440 val (thmid, (Const (op0,t0) $ Free (n1,t1) $ Free(n2,t2))) = (op_, t); |
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441 val Some (id,t') = eval_binop thmid op_ t thy; |
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442 (*** calc: operator = pow not defined*) |
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443 |
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444 |
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445 |
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446 " ================= eval_binop Float =================== "; |
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447 val t = str2term "Float ((1,2),(0,0))"; |
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448 atomty thy t; |
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449 val Const ("Float.Float",_) $ |
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450 (Const ("Pair",_) $ |
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451 (Const ("Pair",_) $ Free (i1,_) $ Free (i2,_)) $ _) = t; |
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452 |
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453 val t = str2term "Float ((1,2),(0,0)) * Float ((3,4),(0,0))"; |
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454 atomty thy t; |
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455 (*GOON.10.4.03*) |