39 lines
1.0 KiB
OCaml
39 lines
1.0 KiB
OCaml
type id = string
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type ty_annot = id * Types.ty
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type lam =
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Fun of ty_annot * lam
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| App of lam * lam
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| Var of id
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| Exf of lam * Types.ty
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(** alpha renaming in a deterministic way *)
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let alpha_convert (e : lam) : lam =
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let cpt_var = ref 0 in (* id cpt for variables *)
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let generator (cpt : int ref) : id = (* id generator *)
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let v = "__"^(string_of_int !cpt)
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in incr cpt; v
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in let get_ren_var (var : id) (g : (id * id) list): id = (* returns var if not found *)
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match List.assoc_opt var g with
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| Some var' -> var'
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| None -> var
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in let rec alpha_aux (e : lam) (g : (id * id) list): lam = match e with (* actual renaming *)
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Fun ((v, t), e) ->
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let v' = generator cpt_var in
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Fun ((v', t), alpha_aux e ((v, v')::g))
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| App (e1, e2) -> App (alpha_aux e1 g, alpha_aux e2 g)
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| Var v -> Var (get_ren_var v g)
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| Exf (e, t) -> Exf (alpha_aux e g, t)
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in alpha_aux e []
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(** alpha equivalence *)
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let (=~) (e1 : lam) (e2 : lam) : bool =
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alpha_convert e1 = alpha_convert e2
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(** beta-reduction *)
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