1 (* Title: HOL/ind_syntax.ML |
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2 ID: $Id$ |
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3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 Copyright 1994 University of Cambridge |
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5 |
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6 Abstract Syntax functions for Inductive Definitions |
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7 See also hologic.ML and ../Pure/section-utils.ML |
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8 *) |
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9 |
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10 (*The structure protects these items from redeclaration (somewhat!). The |
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11 datatype definitions in theory files refer to these items by name! |
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12 *) |
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13 structure Ind_Syntax = |
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14 struct |
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15 |
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16 (** Abstract syntax definitions for HOL **) |
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17 |
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18 open HOLogic; |
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19 |
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20 fun Int_const T = |
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21 let val sT = mk_setT T |
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22 in Const("op Int", [sT,sT]--->sT) end; |
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23 |
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24 fun mk_exists (Free(x,T),P) = exists_const T $ (absfree (x,T,P)); |
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25 |
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26 fun mk_all (Free(x,T),P) = all_const T $ (absfree (x,T,P)); |
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27 |
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28 (*Creates All(%v.v:A --> P(v)) rather than Ball(A,P) *) |
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29 fun mk_all_imp (A,P) = |
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30 let val T = dest_setT (fastype_of A) |
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31 in all_const T $ Abs("v", T, imp $ (mk_mem (Bound 0, A)) $ (P $ Bound 0)) |
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32 end; |
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33 |
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34 (** Cartesian product type **) |
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35 |
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36 val unitT = Type("unit",[]); |
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37 |
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38 fun mk_prod (T1,T2) = Type("*", [T1,T2]); |
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39 |
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40 (*Maps the type T1*...*Tn to [T1,...,Tn], if nested to the right*) |
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41 fun factors (Type("*", [T1,T2])) = T1 :: factors T2 |
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42 | factors T = [T]; |
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43 |
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44 (*Make a correctly typed ordered pair*) |
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45 fun mk_Pair (t1,t2) = |
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46 let val T1 = fastype_of t1 |
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47 and T2 = fastype_of t2 |
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48 in Const("Pair", [T1, T2] ---> mk_prod(T1,T2)) $ t1 $ t2 end; |
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49 |
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50 fun split_const(Ta,Tb,Tc) = |
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51 Const("split", [[Ta,Tb]--->Tc, mk_prod(Ta,Tb)] ---> Tc); |
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52 |
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53 (*Given u expecting arguments of types [T1,...,Tn], create term of |
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54 type T1*...*Tn => Tc using split. Here * associates to the LEFT*) |
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55 fun ap_split_l Tc u [ ] = Abs("null", unitT, u) |
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56 | ap_split_l Tc u [_] = u |
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57 | ap_split_l Tc u (Ta::Tb::Ts) = ap_split_l Tc (split_const(Ta,Tb,Tc) $ u) |
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58 (mk_prod(Ta,Tb) :: Ts); |
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59 |
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60 (*Given u expecting arguments of types [T1,...,Tn], create term of |
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61 type T1*...*Tn => i using split. Here * associates to the RIGHT*) |
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62 fun ap_split Tc u [ ] = Abs("null", unitT, u) |
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63 | ap_split Tc u [_] = u |
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64 | ap_split Tc u [Ta,Tb] = split_const(Ta,Tb,Tc) $ u |
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65 | ap_split Tc u (Ta::Ts) = |
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66 split_const(Ta, foldr1 mk_prod Ts, Tc) $ |
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67 (Abs("v", Ta, ap_split Tc (u $ Bound(length Ts - 2)) Ts)); |
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68 |
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69 (** Disjoint sum type **) |
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70 |
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71 fun mk_sum (T1,T2) = Type("+", [T1,T2]); |
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72 val Inl = Const("Inl", dummyT) |
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73 and Inr = Const("Inr", dummyT); (*correct types added later!*) |
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74 (*val elim = Const("case", [iT-->iT, iT-->iT, iT]--->iT)*) |
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75 |
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76 fun summands (Type("+", [T1,T2])) = summands T1 @ summands T2 |
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77 | summands T = [T]; |
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78 |
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79 (*Given the destination type, fills in correct types of an Inl/Inr nest*) |
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80 fun mend_sum_types (h,T) = |
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81 (case (h,T) of |
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82 (Const("Inl",_) $ h1, Type("+", [T1,T2])) => |
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83 Const("Inl", T1 --> T) $ (mend_sum_types (h1, T1)) |
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84 | (Const("Inr",_) $ h2, Type("+", [T1,T2])) => |
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85 Const("Inr", T2 --> T) $ (mend_sum_types (h2, T2)) |
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86 | _ => h); |
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87 |
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88 |
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89 |
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90 (*simple error-checking in the premises of an inductive definition*) |
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91 fun chk_prem rec_hd (Const("op &",_) $ _ $ _) = |
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92 error"Premises may not be conjuctive" |
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93 | chk_prem rec_hd (Const("op :",_) $ t $ X) = |
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94 deny (Logic.occs(rec_hd,t)) "Recursion term on left of member symbol" |
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95 | chk_prem rec_hd t = |
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96 deny (Logic.occs(rec_hd,t)) "Recursion term in side formula"; |
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97 |
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98 (*Return the conclusion of a rule, of the form t:X*) |
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99 fun rule_concl rl = |
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100 let val Const("Trueprop",_) $ (Const("op :",_) $ t $ X) = |
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101 Logic.strip_imp_concl rl |
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102 in (t,X) end; |
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103 |
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104 (*As above, but return error message if bad*) |
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105 fun rule_concl_msg sign rl = rule_concl rl |
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106 handle Bind => error ("Ill-formed conclusion of introduction rule: " ^ |
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107 Sign.string_of_term sign rl); |
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108 |
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109 (*For simplifying the elimination rule*) |
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110 val sumprod_free_SEs = |
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111 Pair_inject :: |
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112 map make_elim [(*Inl_neq_Inr, Inr_neq_Inl, Inl_inject, Inr_inject*)]; |
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113 |
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114 (*For deriving cases rules. |
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115 read_instantiate replaces a propositional variable by a formula variable*) |
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116 val equals_CollectD = |
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117 read_instantiate [("W","?Q")] |
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118 (make_elim (equalityD1 RS subsetD RS CollectD)); |
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119 |
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120 (*Delete needless equality assumptions*) |
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121 val refl_thin = prove_goal HOL.thy "!!P. [| a=a; P |] ==> P" |
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122 (fn _ => [assume_tac 1]); |
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123 |
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124 end; |
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