src/ZF/ex/Primrec.thy
 author clasohm Sat Dec 09 13:36:11 1995 +0100 (1995-12-09 ago) changeset 1401 0c439768f45c parent 1155 928a16e02f9f child 1478 2b8c2a7547ab permissions -rw-r--r--
removed quotes from consts and syntax sections
```     1 (*  Title: 	ZF/ex/Primrec.thy
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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 Primitive Recursive Functions
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```     7
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```     8 Proof adopted from
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```     9 Nora Szasz,
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```    10 A Machine Checked Proof that Ackermann's Function is not Primitive Recursive,
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```    11 In: Huet & Plotkin, eds., Logical Environments (CUP, 1993), 317-338.
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```    12
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```    13 See also E. Mendelson, Introduction to Mathematical Logic.
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```    14 (Van Nostrand, 1964), page 250, exercise 11.
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```    15 *)
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```    16
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```    17 Primrec = List +
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```    18 consts
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```    19     primrec :: i
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```    20     SC      :: i
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```    21     CONST   :: i=>i
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```    22     PROJ    :: i=>i
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```    23     COMP    :: [i,i]=>i
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```    24     PREC    :: [i,i]=>i
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```    25     ACK	    :: i=>i
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```    26     ack	    :: [i,i]=>i
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```    27
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```    28 translations
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```    29   "ack(x,y)"  == "ACK(x) ` [y]"
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```    30
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```    31 defs
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```    32
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```    33   SC_def    "SC == lam l:list(nat).list_case(0, %x xs.succ(x), l)"
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```    34
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```    35   CONST_def "CONST(k) == lam l:list(nat).k"
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```    36
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```    37   PROJ_def  "PROJ(i) == lam l:list(nat). list_case(0, %x xs.x, drop(i,l))"
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```    38
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```    39   COMP_def  "COMP(g,fs) == lam l:list(nat). g ` map(%f. f`l, fs)"
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```    40
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```    41   (*Note that g is applied first to PREC(f,g)`y and then to y!*)
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```    42   PREC_def  "PREC(f,g) ==
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```    43             lam l:list(nat). list_case(0,
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```    44                       %x xs. rec(x, f`xs, %y r. g ` Cons(r, Cons(y, xs))), l)"
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```    45
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```    46   ACK_def   "ACK(i) == rec(i, SC,
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```    47                       %z r. PREC (CONST (r`[1]), COMP(r,[PROJ(0)])))"
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```    48
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```    49
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```    50 inductive
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```    51   domains "primrec" <= "list(nat)->nat"
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```    52   intrs
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```    53     SC       "SC : primrec"
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```    54     CONST    "k: nat ==> CONST(k) : primrec"
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```    55     PROJ     "i: nat ==> PROJ(i) : primrec"
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```    56     COMP     "[| g: primrec; fs: list(primrec) |] ==> COMP(g,fs): primrec"
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```    57     PREC     "[| f: primrec; g: primrec |] ==> PREC(f,g): primrec"
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```    58   monos      "[list_mono]"
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```    59   con_defs   "[SC_def,CONST_def,PROJ_def,COMP_def,PREC_def]"
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```    60   type_intrs "nat_typechecks @ list.intrs @
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```    61 	      [lam_type, list_case_type, drop_type, map_type,
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```    62 	      apply_type, rec_type]"
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```    63
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```    64 end
```