11 ML {* val _ = recursive := false  *}

    12 

    13 (* example 7 from Peter Sewell's bestiary *)

    14 (* dest_Const raised

    15 nominal_datatype exp7 =

    16   EVar' name

    17 | EUnit'

    18 | EPair' exp7 exp7

    19 | ELetRec' l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l

    20 and lrb =

    21   Assign' name exp7

    22 and lrbs =

    23   Single' lrb

    24 | More' lrb lrbs

    25 binder

    26   b7 :: "lrb \<Rightarrow> atom set" and

    27   b7s :: "lrbs \<Rightarrow> atom set"

    28 where

    29   "b7 (Assign x e) = {atom x}"

    30 | "b7s (Single a) = b7 a"

    31 | "b7s (More a as) = (b7 a) \<union> (b7s as)"

    32 thm alpha_exp7_raw_alpha_lrb_raw_alpha_lrbs_raw.intros

    33 *)

    34 

    35 (* example 8 from Peter Sewell's bestiary *)

    36 (*

    37 *** fv_bn: recursive argument, but wrong datatype.

    38 *** At command "nominal_datatype".

    39 nominal_datatype exp8 =

    40   EVar' name

    41 | EUnit'

    42 | EPair' exp8 exp8

    43 | ELetRec' l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l

    44 and fnclause =

    45   K' x::name p::pat8 e::exp8 bind "b_pat p" in e

    46 and fnclauses =

    47   S' fnclause

    48 | ORs' fnclause fnclauses

    49 and lrb8 =

    50   Clause' fnclauses

    51 and lrbs8 =

    52   Single' lrb8

    53 | More' lrb8 lrbs8

    54 and pat8 =

    55   PVar'' name

    56 | PUnit''

    57 | PPair'' pat8 pat8

    58 binder

    59   b_lrbs8 :: "lrbs8 \<Rightarrow> atom set" and

    60   b_pat :: "pat8 \<Rightarrow> atom set" and

    61   b_fnclauses :: "fnclauses \<Rightarrow> atom set" and

    62   b_fnclause :: "fnclause \<Rightarrow> atom set" and

    63   b_lrb8 :: "lrb8 \<Rightarrow> atom set"

    64 where

    65   "b_lrbs8 (Single' l) = b_lrb8 l"

    66 | "b_lrbs8 (More' l ls) = b_lrb8 l \<union> b_lrbs8 ls"

    67 | "b_pat (PVar'' x) = {atom x}"

    68 | "b_pat (PUnit'') = {}"

    69 | "b_pat (PPair'' p1 p2) = b_pat p1 \<union> b_pat p2"

    70 | "b_fnclauses (S' fc) = (b_fnclause fc)"

    71 | "b_fnclauses (ORs' fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"

    72 | "b_lrb8 (Clause' fcs) = (b_fnclauses fcs)"

    73 | "b_fnclause (K' x pat exp8) = {atom x}"

    74 thm alpha_exp8_raw_alpha_fnclause_raw_alpha_fnclauses_raw_alpha_lrb8_raw_alpha_lrbs8_raw_alpha_pat8_raw.intros

    75 *)