1 (* Title: CCL/wfd.thy |
1 (* Title: CCL/Wfd.thy |
2 ID: $Id$ |
2 ID: $Id$ |
3 Author: Martin Coen, Cambridge University Computer Laboratory |
3 Author: Martin Coen, Cambridge University Computer Laboratory |
4 Copyright 1993 University of Cambridge |
4 Copyright 1993 University of Cambridge |
5 |
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6 Well-founded relations in CCL. |
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7 *) |
5 *) |
8 |
6 |
9 Wfd = Trancl + Type + |
7 header {* Well-founded relations in CCL *} |
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8 |
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9 theory Wfd |
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10 imports Trancl Type Hered |
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11 uses ("wfd.ML") ("genrec.ML") ("typecheck.ML") ("eval.ML") |
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12 begin |
10 |
13 |
11 consts |
14 consts |
12 (*** Predicates ***) |
15 (*** Predicates ***) |
13 Wfd :: "[i set] => o" |
16 Wfd :: "[i set] => o" |
14 (*** Relations ***) |
17 (*** Relations ***) |
16 wmap :: "[i=>i,i set] => i set" |
19 wmap :: "[i=>i,i set] => i set" |
17 "**" :: "[i set,i set] => i set" (infixl 70) |
20 "**" :: "[i set,i set] => i set" (infixl 70) |
18 NatPR :: "i set" |
21 NatPR :: "i set" |
19 ListPR :: "i set => i set" |
22 ListPR :: "i set => i set" |
20 |
23 |
21 rules |
24 axioms |
22 |
25 |
23 Wfd_def |
26 Wfd_def: |
24 "Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a. a:P)" |
27 "Wfd(R) == ALL P.(ALL x.(ALL y.<y,x> : R --> y:P) --> x:P) --> (ALL a. a:P)" |
25 |
28 |
26 wf_def "wf(R) == {x. x:R & Wfd(R)}" |
29 wf_def: "wf(R) == {x. x:R & Wfd(R)}" |
27 |
30 |
28 wmap_def "wmap(f,R) == {p. EX x y. p=<x,y> & <f(x),f(y)> : R}" |
31 wmap_def: "wmap(f,R) == {p. EX x y. p=<x,y> & <f(x),f(y)> : R}" |
29 lex_def |
32 lex_def: |
30 "ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}" |
33 "ra**rb == {p. EX a a' b b'. p = <<a,b>,<a',b'>> & (<a,a'> : ra | (a=a' & <b,b'> : rb))}" |
31 |
34 |
32 NatPR_def "NatPR == {p. EX x:Nat. p=<x,succ(x)>}" |
35 NatPR_def: "NatPR == {p. EX x:Nat. p=<x,succ(x)>}" |
33 ListPR_def "ListPR(A) == {p. EX h:A. EX t:List(A). p=<t,h$t>}" |
36 ListPR_def: "ListPR(A) == {p. EX h:A. EX t:List(A). p=<t,h$t>}" |
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37 |
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38 ML {* use_legacy_bindings (the_context ()) *} |
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39 |
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40 use "wfd.ML" |
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41 use "genrec.ML" |
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42 use "typecheck.ML" |
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43 use "eval.ML" |
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44 |
34 end |
45 end |