| author | lcp |
| Thu, 12 Jan 1995 03:02:34 +0100 | |
| changeset 854 | 2e3ca37dfa14 |
| parent 71 | 729fe026c5f3 |
| permissions | -rw-r--r-- |
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(* Title: ZF/ex/primrec.thy |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1993 University of Cambridge |
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Primitive Recursive Functions |
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Proof adopted from |
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Nora Szasz, |
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A Machine Checked Proof that Ackermann's Function is not Primitive Recursive, |
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In: Huet & Plotkin, eds., Logical Environments (CUP, 1993), 317-338. |
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See also E. Mendelson, Introduction to Mathematical Logic. |
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(Van Nostrand, 1964), page 250, exercise 11. |
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*) |
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Primrec0 = ListFn + |
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consts |
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SC :: "i" |
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CONST :: "i=>i" |
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PROJ :: "i=>i" |
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COMP :: "[i,i]=>i" |
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PREC :: "[i,i]=>i" |
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primrec :: "i" |
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ACK :: "i=>i" |
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ack :: "[i,i]=>i" |
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translations |
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"ack(x,y)" == "ACK(x) ` [y]" |
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rules |
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SC_def "SC == lam l:list(nat).list_case(0, %x xs.succ(x), l)" |
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CONST_def "CONST(k) == lam l:list(nat).k" |
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PROJ_def "PROJ(i) == lam l:list(nat). list_case(0, %x xs.x, drop(i,l))" |
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COMP_def "COMP(g,fs) == lam l:list(nat). g ` map(%f. f`l, fs)" |
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(*Note that g is applied first to PREC(f,g)`y and then to y!*) |
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PREC_def "PREC(f,g) == \ |
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\ lam l:list(nat). list_case(0, \ |
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\ %x xs. rec(x, f`xs, %y r. g ` Cons(r, Cons(y, xs))), l)" |
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ACK_def "ACK(i) == rec(i, SC, \ |
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\ %z r. PREC (CONST (r`[1]), COMP(r,[PROJ(0)])))" |
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end |