30 split :: "[['a, 'b] => 'c, 'a * 'b] => 'c" |
34 split :: "[['a, 'b] => 'c, 'a * 'b] => 'c" |
31 prod_fun :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd" |
35 prod_fun :: "['a => 'b, 'c => 'd, 'a * 'c] => 'b * 'd" |
32 Pair :: "['a, 'b] => 'a * 'b" |
36 Pair :: "['a, 'b] => 'a * 'b" |
33 Sigma :: "['a set, 'a => 'b set] => ('a * 'b) set" |
37 Sigma :: "['a set, 'a => 'b set] => ('a * 'b) set" |
34 |
38 |
35 (** Patterns -- extends pre-defined type "pttrn" used in abstractions **) |
39 |
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40 (* patterns -- extends pre-defined type "pttrn" used in abstractions *) |
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41 |
36 types pttrns |
42 types pttrns |
37 |
43 |
38 syntax |
44 syntax |
39 "@Tuple" :: "['a, args] => 'a * 'b" ("(1'(_,/ _'))") |
45 "@Tuple" :: "['a, args] => 'a * 'b" ("(1'(_,/ _'))") |
40 |
46 |
41 "@pttrn" :: [pttrn,pttrns] => pttrn ("'(_,/_')") |
47 "@pttrn" :: [pttrn, pttrns] => pttrn ("'(_,/_')") |
42 "" :: pttrn => pttrns ("_") |
48 "" :: pttrn => pttrns ("_") |
43 "@pttrns" :: [pttrn,pttrns] => pttrns ("_,/_") |
49 "@pttrns" :: [pttrn, pttrns] => pttrns ("_,/_") |
44 |
50 |
45 "@Sigma" :: "[idt,'a set,'b set] => ('a * 'b)set" |
51 "@Sigma" :: "[idt, 'a set, 'b set] => ('a * 'b) set" ("(3SIGMA _:_./ _)" 10) |
46 ("(3SIGMA _:_./ _)" 10) |
52 "@Times" :: "['a set, 'a => 'b set] => ('a * 'b) set" ("_ Times _" [81, 80] 80) |
47 "@Times" :: "['a set, 'a => 'b set] => ('a * 'b) set" |
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48 ("_ Times _" [81,80] 80) |
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49 |
53 |
50 translations |
54 translations |
51 "(x, y, z)" == "(x, (y, z))" |
55 "(x, y, z)" == "(x, (y, z))" |
52 "(x, y)" == "Pair x y" |
56 "(x, y)" == "Pair x y" |
53 |
57 |
54 "%(x,y,zs).b" == "split(%x (y,zs).b)" |
58 "%(x,y,zs).b" == "split(%x (y,zs).b)" |
55 "%(x,y).b" == "split(%x y.b)" |
59 "%(x,y).b" == "split(%x y.b)" |
56 |
60 |
57 "SIGMA x:A. B" => "Sigma A (%x.B)" |
61 "SIGMA x:A.B" => "Sigma A (%x.B)" |
58 "A Times B" => "Sigma A (_K B)" |
62 "A Times B" => "Sigma A (_K B)" |
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63 |
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64 syntax (symbols) |
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65 "@Sigma" :: "[idt, 'a set, 'b set] => ('a * 'b) set" ("(3\\<Sigma> _\\<in>_./ _)" 10) |
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66 "@Times" :: "['a set, 'a => 'b set] => ('a * 'b) set" ("_ \\<times> _" [81, 80] 80) |
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67 |
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68 |
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69 (* definitions *) |
59 |
70 |
60 defs |
71 defs |
61 Pair_def "Pair a b == Abs_Prod(Pair_Rep a b)" |
72 Pair_def "Pair a b == Abs_Prod(Pair_Rep a b)" |
62 fst_def "fst(p) == @a. ? b. p = (a, b)" |
73 fst_def "fst(p) == @a. ? b. p = (a, b)" |
63 snd_def "snd(p) == @b. ? a. p = (a, b)" |
74 snd_def "snd(p) == @b. ? a. p = (a, b)" |
64 split_def "split == (%c p. c (fst p) (snd p))" |
75 split_def "split == (%c p. c (fst p) (snd p))" |
65 prod_fun_def "prod_fun f g == split(%x y.(f(x), g(y)))" |
76 prod_fun_def "prod_fun f g == split(%x y.(f(x), g(y)))" |
66 Sigma_def "Sigma A B == UN x:A. UN y:B(x). {(x, y)}" |
77 Sigma_def "Sigma A B == UN x:A. UN y:B(x). {(x, y)}" |
67 |
78 |
68 (** Unit **) |
79 |
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80 |
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81 (** unit **) |
69 |
82 |
70 typedef (Unit) |
83 typedef (Unit) |
71 unit = "{p. p = True}" |
84 unit = "{p. p = True}" |
72 |
85 |
73 consts |
86 consts |