1(* Author: Florian Haftmann, TU Muenchen *) 2 3section \<open>Reflecting Pure types into HOL\<close> 4 5theory Typerep 6imports String 7begin 8 9datatype typerep = Typerep String.literal "typerep list" 10 11class typerep = 12 fixes typerep :: "'a itself \<Rightarrow> typerep" 13begin 14 15definition typerep_of :: "'a \<Rightarrow> typerep" where 16 [simp]: "typerep_of x = typerep TYPE('a)" 17 18end 19 20syntax 21 "_TYPEREP" :: "type => logic" ("(1TYPEREP/(1'(_')))") 22 23parse_translation \<open> 24 let 25 fun typerep_tr (*"_TYPEREP"*) [ty] = 26 Syntax.const @{const_syntax typerep} $ 27 (Syntax.const @{syntax_const "_constrain"} $ Syntax.const @{const_syntax Pure.type} $ 28 (Syntax.const @{type_syntax itself} $ ty)) 29 | typerep_tr (*"_TYPEREP"*) ts = raise TERM ("typerep_tr", ts); 30 in [(@{syntax_const "_TYPEREP"}, K typerep_tr)] end 31\<close> 32 33typed_print_translation \<open> 34 let 35 fun typerep_tr' ctxt (*"typerep"*) 36 (Type (@{type_name fun}, [Type (@{type_name itself}, [T]), _])) 37 (Const (@{const_syntax Pure.type}, _) :: ts) = 38 Term.list_comb 39 (Syntax.const @{syntax_const "_TYPEREP"} $ Syntax_Phases.term_of_typ ctxt T, ts) 40 | typerep_tr' _ T ts = raise Match; 41 in [(@{const_syntax typerep}, typerep_tr')] end 42\<close> 43 44setup \<open> 45let 46 47fun add_typerep tyco thy = 48 let 49 val sorts = replicate (Sign.arity_number thy tyco) @{sort typerep}; 50 val vs = Name.invent_names Name.context "'a" sorts; 51 val ty = Type (tyco, map TFree vs); 52 val lhs = Const (@{const_name typerep}, Term.itselfT ty --> @{typ typerep}) 53 $ Free ("T", Term.itselfT ty); 54 val rhs = @{term Typerep} $ HOLogic.mk_literal tyco 55 $ HOLogic.mk_list @{typ typerep} (map (HOLogic.mk_typerep o TFree) vs); 56 val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs)); 57 in 58 thy 59 |> Class.instantiation ([tyco], vs, @{sort typerep}) 60 |> `(fn lthy => Syntax.check_term lthy eq) 61 |-> (fn eq => Specification.definition NONE [] [] (Binding.empty_atts, eq)) 62 |> snd 63 |> Class.prove_instantiation_exit (fn ctxt => Class.intro_classes_tac ctxt []) 64 end; 65 66fun ensure_typerep tyco thy = 67 if not (Sorts.has_instance (Sign.classes_of thy) tyco @{sort typerep}) 68 andalso Sorts.has_instance (Sign.classes_of thy) tyco @{sort type} 69 then add_typerep tyco thy else thy; 70 71in 72 73add_typerep @{type_name fun} 74#> Typedef.interpretation (Local_Theory.background_theory o ensure_typerep) 75#> Code.type_interpretation ensure_typerep 76 77end 78\<close> 79 80lemma [code]: 81 "HOL.equal (Typerep tyco1 tys1) (Typerep tyco2 tys2) \<longleftrightarrow> HOL.equal tyco1 tyco2 82 \<and> list_all2 HOL.equal tys1 tys2" 83 by (auto simp add: eq_equal [symmetric] list_all2_eq [symmetric]) 84 85lemma [code nbe]: 86 "HOL.equal (x :: typerep) x \<longleftrightarrow> True" 87 by (fact equal_refl) 88 89code_printing 90 type_constructor typerep \<rightharpoonup> (Eval) "Term.typ" 91| constant Typerep \<rightharpoonup> (Eval) "Term.Type/ (_, _)" 92 93code_reserved Eval Term 94 95hide_const (open) typerep Typerep 96 97end 98