1 (* Title: Tools/transfer.ML |
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2 Author: Amine Chaieb, University of Cambridge, 2009 |
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3 Jeremy Avigad, Carnegie Mellon University |
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4 *) |
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5 |
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6 signature TRANSFER_DATA = |
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7 sig |
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8 type data |
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9 type entry |
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10 val get: Proof.context -> data |
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11 val del: attribute |
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12 val add: attribute |
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13 val setup: theory -> theory |
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14 end; |
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15 |
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16 structure TransferData (* : TRANSFER_DATA*) = |
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17 struct |
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18 type entry = {inj : thm list , emb : thm list , ret : thm list , cong : thm list, guess : bool, hints : string list}; |
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19 type data = simpset * (thm * entry) list; |
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20 |
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21 val eq_key = Thm.eq_thm; |
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22 fun eq_data arg = eq_fst eq_key arg; |
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23 |
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24 structure Data = GenericDataFun |
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25 ( |
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26 type T = data; |
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27 val empty = (HOL_ss, []); |
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28 val extend = I; |
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29 fun merge _ ((ss, e), (ss', e')) = |
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30 (merge_ss (ss, ss'), AList.merge eq_key (K true) (e, e')); |
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31 ); |
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32 |
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33 val get = Data.get o Context.Proof; |
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34 |
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35 fun del_data key = apsnd (remove eq_data (key, [])); |
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36 |
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37 val del = Thm.declaration_attribute (Data.map o del_data); |
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38 val add_ss = Thm.declaration_attribute |
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39 (fn th => Data.map (fn (ss,data) => (ss addsimps [th], data))); |
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40 |
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41 val del_ss = Thm.declaration_attribute |
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42 (fn th => Data.map (fn (ss,data) => (ss delsimps [th], data))); |
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43 |
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44 val transM_pat = (Thm.dest_arg1 o Thm.dest_arg o cprop_of) @{thm TransferMorphism_def}; |
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45 |
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46 fun merge_update eq m (k,v) [] = [(k,v)] |
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47 | merge_update eq m (k,v) ((k',v')::al) = |
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48 if eq (k,k') then (k',m (v,v')):: al else (k',v') :: merge_update eq m (k,v) al |
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49 |
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50 fun C f x y = f y x |
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51 |
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52 fun simpset_of_entry injonly {inj = inj, emb = emb, ret = ret, cong = cg, guess = g, hints = hints} = |
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53 HOL_ss addsimps inj addsimps (if injonly then [] else emb@ret) addcongs cg; |
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54 |
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55 fun basic_transfer_rule injonly a0 D0 e leave ctxt0 th = |
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56 let |
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57 val ([a,D], ctxt) = apfst (map Drule.dest_term o snd) (Variable.import true (map Drule.mk_term [a0, D0]) ctxt0) |
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58 val (aT,bT) = |
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59 let val T = typ_of (ctyp_of_term a) |
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60 in (Term.range_type T, Term.domain_type T) |
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61 end |
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62 val ctxt' = (Variable.declare_term (term_of a) o Variable.declare_term (term_of D) o Variable.declare_thm th) ctxt |
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63 val ns = filter (fn i => Type.could_unify (snd i, aT) andalso not (fst (fst i) mem_string leave)) (Term.add_vars (prop_of th) []) |
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64 val (ins, ctxt'') = Variable.variant_fixes (map (fst o fst) ns) ctxt' |
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65 val cns = map ((cterm_of o ProofContext.theory_of) ctxt'' o Var) ns |
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66 val cfis = map ((cterm_of o ProofContext.theory_of) ctxt'' o (fn n => Free (n, bT))) ins |
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67 val cis = map (Thm.capply a) cfis |
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68 val (hs,ctxt''') = Assumption.add_assumes (map (fn ct => Thm.capply @{cterm "Trueprop"} (Thm.capply D ct)) cfis) ctxt'' |
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69 val th1 = Drule.cterm_instantiate (cns~~ cis) th |
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70 val th2 = fold (C implies_elim) hs (fold_rev implies_intr (map cprop_of hs) th1) |
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71 val th3 = Simplifier.asm_full_simplify (Simplifier.context ctxt''' (simpset_of_entry injonly e)) |
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72 (fold_rev implies_intr (map cprop_of hs) th2) |
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73 in hd (Variable.export ctxt''' ctxt0 [th3]) end; |
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74 |
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75 local |
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76 fun transfer_ruleh a D leave ctxt th = |
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77 let val (ss,al) = get ctxt |
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78 val a0 = cterm_of (ProofContext.theory_of ctxt) a |
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79 val D0 = cterm_of (ProofContext.theory_of ctxt) D |
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80 fun h (th', e) = let val (a',D') = (Thm.dest_binop o Thm.dest_arg o cprop_of) th' |
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81 in if a0 aconvc a' andalso D0 aconvc D' then SOME e else NONE |
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82 end |
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83 in case get_first h al of |
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84 SOME e => basic_transfer_rule false a0 D0 e leave ctxt th |
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85 | NONE => error "Transfer: corresponding instance not found in context-data" |
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86 end |
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87 in fun transfer_rule (a,D) leave (gctxt,th) = |
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88 (gctxt, transfer_ruleh a D leave (Context.proof_of gctxt) th) |
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89 end; |
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90 |
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91 fun splits P [] = [] |
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92 | splits P (xxs as (x::xs)) = |
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93 let val pss = filter (P x) xxs |
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94 val qss = filter_out (P x) xxs |
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95 in if null pss then [qss] else if null qss then [pss] else pss:: splits P qss |
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96 end |
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97 |
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98 fun all_transfers leave (gctxt,th) = |
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99 let |
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100 val ctxt = Context.proof_of gctxt |
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101 val tys = map snd (Term.add_vars (prop_of th) []) |
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102 val _ = if null tys then error "transfer: Unable to guess instance" else () |
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103 val tyss = splits (curry Type.could_unify) tys |
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104 val get_ty = typ_of o ctyp_of_term o fst o Thm.dest_binop o Thm.dest_arg o cprop_of |
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105 val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_of |
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106 val insts = |
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107 map_filter (fn tys => |
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108 get_first (fn (k,ss) => if Type.could_unify (hd tys, range_type (get_ty k)) |
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109 then SOME (get_aD k, ss) |
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110 else NONE) (snd (get ctxt))) tyss |
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111 val _ = if null insts then error "Transfer guesser: there were no possible instances, use direction: in order to provide a direction" else () |
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112 val ths = map (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts |
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113 val cth = Conjunction.intr_balanced ths |
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114 in (gctxt, cth) |
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115 end; |
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116 |
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117 fun transfer_rule_by_hint ls leave (gctxt,th) = |
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118 let |
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119 val ctxt = Context.proof_of gctxt |
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120 val get_aD = Thm.dest_binop o Thm.dest_arg o cprop_of |
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121 val insts = |
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122 map_filter (fn (k,e) => if exists (fn l => l mem_string (#hints e)) ls |
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123 then SOME (get_aD k, e) else NONE) |
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124 (snd (get ctxt)) |
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125 val _ = if null insts then error "Transfer: No labels provided are stored in the context" else () |
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126 val ths = map (fn ((a,D),e) => basic_transfer_rule false a D e leave ctxt th) insts |
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127 val cth = Conjunction.intr_balanced ths |
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128 in (gctxt, cth) |
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129 end; |
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130 |
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131 |
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132 fun transferred_attribute ls NONE leave = |
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133 if null ls then all_transfers leave else transfer_rule_by_hint ls leave |
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134 | transferred_attribute _ (SOME (a,D)) leave = transfer_rule (a,D) leave |
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135 |
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136 (* Add data to the context *) |
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137 fun gen_merge_entries {inj = inj0, emb = emb0, ret = ret0, cong = cg0, guess = g0, hints = hints0} |
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138 ({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1}, |
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139 {inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2}) |
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140 = |
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141 let fun h xs0 xs ys = subtract Thm.eq_thm xs0 (merge Thm.eq_thm (xs,ys)) in |
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142 {inj = h inj0 inj1 inj2, emb = h emb0 emb1 emb2, |
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143 ret = h ret0 ret1 ret2, cong = h cg0 cg1 cg2, guess = g1 andalso g2, |
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144 hints = subtract (op = : string*string -> bool) hints0 |
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145 (hints1 union_string hints2)} |
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146 end; |
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147 |
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148 local |
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149 val h = curry (merge Thm.eq_thm) |
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150 in |
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151 fun merge_entries ({inj = inj1, emb = emb1, ret = ret1, cong = cg1, guess = g1, hints = hints1}, |
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152 {inj = inj2, emb = emb2, ret = ret2, cong = cg2, guess = g2, hints = hints2}) = |
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153 {inj = h inj1 inj2, emb = h emb1 emb2, ret = h ret1 ret2, cong = h cg1 cg2, guess = g1 andalso g2, hints = hints1 union_string hints2} |
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154 end; |
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155 |
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156 fun add ((inja,injd), (emba,embd), (reta,retd), (cga,cgd), g, (hintsa, hintsd)) = |
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157 Thm.declaration_attribute (fn key => fn context => context |> Data.map |
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158 (fn (ss, al) => |
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159 let |
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160 val _ = ((let val _ = Thm.match (transM_pat, (Thm.dest_arg o cprop_of) key) |
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161 in 0 end) |
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162 handle MATCH => error "Attribute expected Theorem of the form : TransferMorphism A a B b") |
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163 val e0 = {inj = inja, emb = emba, ret = reta, cong = cga, guess = g, hints = hintsa} |
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164 val ed = {inj = injd, emb = embd, ret = retd, cong = cgd, guess = g, hints = hintsd} |
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165 val entry = |
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166 if g then |
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167 let val (a0,D0) = (Thm.dest_binop o Thm.dest_arg o cprop_of) key |
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168 val ctxt0 = ProofContext.init (Thm.theory_of_thm key) |
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169 val inj' = if null inja then #inj (case AList.lookup eq_key al key of SOME e => e | NONE => error "Transfer: can not generate return rules on the fly, either add injectivity axiom or force manual mode with mode: manual") |
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170 else inja |
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171 val ret' = merge Thm.eq_thm (reta, map (fn th => basic_transfer_rule true a0 D0 {inj = inj', emb = [], ret = [], cong = cga, guess = g, hints = hintsa} [] ctxt0 th RS sym) emba) |
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172 in {inj = inja, emb = emba, ret = ret', cong = cga, guess = g, hints = hintsa} end |
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173 else e0 |
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174 in (ss, merge_update eq_key (gen_merge_entries ed) (key, entry) al) |
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175 end)); |
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176 |
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177 |
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178 |
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179 (* concrete syntax *) |
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180 |
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181 local |
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182 |
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183 fun keyword k = Scan.lift (Args.$$$ k) >> K () |
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184 fun keywordC k = Scan.lift (Args.$$$ k -- Args.colon) >> K () |
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185 |
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186 val congN = "cong" |
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187 val injN = "inj" |
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188 val embedN = "embed" |
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189 val returnN = "return" |
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190 val addN = "add" |
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191 val delN = "del" |
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192 val modeN = "mode" |
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193 val automaticN = "automatic" |
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194 val manualN = "manual" |
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195 val directionN = "direction" |
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196 val labelsN = "labels" |
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197 val leavingN = "leaving" |
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198 |
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199 val any_keyword = keywordC congN || keywordC injN || keywordC embedN || keywordC returnN || keywordC directionN || keywordC modeN || keywordC delN || keywordC labelsN || keywordC leavingN |
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200 |
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201 val thms = Scan.repeat (Scan.unless any_keyword Attrib.multi_thm) >> flat |
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202 val terms = thms >> map Drule.dest_term |
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203 val types = thms >> (Logic.dest_type o HOLogic.dest_Trueprop o prop_of o hd) |
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204 val name = Scan.lift Args.name |
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205 val names = Scan.repeat (Scan.unless any_keyword name) |
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206 fun optional scan = Scan.optional scan [] |
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207 fun optional2 scan = Scan.optional scan ([],[]) |
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208 |
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209 val mode = keywordC modeN |-- ((Scan.lift (Args.$$$ manualN) >> K false) || (Scan.lift (Args.$$$ automaticN) >> K true)) |
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210 val inj = (keywordC injN |-- thms) -- optional (keywordC delN |-- thms) |
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211 val embed = (keywordC embedN |-- thms) -- optional (keywordC delN |-- thms) |
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212 val return = (keywordC returnN |-- thms) -- optional (keywordC delN |-- thms) |
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213 val cong = (keywordC congN |-- thms) -- optional (keywordC delN |-- thms) |
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214 val addscan = Scan.unless any_keyword (keyword addN) |
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215 val labels = (keywordC labelsN |-- names) -- optional (keywordC delN |-- names) |
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216 val entry = Scan.optional mode true -- optional2 inj -- optional2 embed -- optional2 return -- optional2 cong -- optional2 labels |
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217 |
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218 val transf_add = addscan |-- entry |
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219 in |
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220 |
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221 val install_att_syntax = |
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222 (Scan.lift (Args.$$$ delN >> K del) || |
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223 transf_add |
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224 >> (fn (((((g, inj), embed), ret), cg), hints) => add (inj, embed, ret, cg, g, hints))) |
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225 |
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226 val transferred_att_syntax = (optional names -- Scan.option (keywordC directionN |-- (Args.term -- Args.term)) |
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227 -- optional (keywordC leavingN |-- names) >> (fn ((hints, aD),leave) => transferred_attribute hints aD leave)); |
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228 |
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229 end; |
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230 |
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231 |
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232 (* theory setup *) |
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233 |
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234 |
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235 val setup = |
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236 Attrib.setup @{binding transfer} install_att_syntax |
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237 "Installs transfer data" #> |
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238 Attrib.setup @{binding transfer_simps} (Attrib.add_del add_ss del_ss) |
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239 "simp rules for transfer" #> |
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240 Attrib.setup @{binding transferred} transferred_att_syntax |
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241 "Transfers theorems"; |
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242 |
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243 end; |
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