src/HOL/Induct/Sexp.thy
 author wenzelm Mon, 08 May 2000 20:59:30 +0200 changeset 8840 18b76c137c41 child 10212 33fe2d701ddd permissions -rw-r--r--
moved theory Sexp to Induct examples;
```
(*  Title:      HOL/Induct/Sexp.thy
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

S-expressions, general binary trees for defining recursive data
structures by hand.
*)

Sexp = Univ + Inductive +
consts
sexp      :: 'a item set

sexp_case :: "['a=>'b, nat=>'b, ['a item, 'a item]=>'b,
'a item] => 'b"

sexp_rec  :: "['a item, 'a=>'b, nat=>'b,
['a item, 'a item, 'b, 'b]=>'b] => 'b"

pred_sexp :: "('a item * 'a item)set"

inductive sexp
intrs
LeafI  "Leaf(a): sexp"
NumbI  "Numb(i): sexp"
SconsI "[| M: sexp;  N: sexp |] ==> Scons M N : sexp"

defs

sexp_case_def
"sexp_case c d e M == @ z. (? x.   M=Leaf(x) & z=c(x))
| (? k.   M=Numb(k) & z=d(k))
| (? N1 N2. M = Scons N1 N2  & z=e N1 N2)"

pred_sexp_def
"pred_sexp == UN M: sexp. UN N: sexp. {(M, Scons M N), (N, Scons M N)}"

sexp_rec_def
"sexp_rec M c d e == wfrec pred_sexp
(%g. sexp_case c d (%N1 N2. e N1 N2 (g N1) (g N2))) M"
end
```