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comparison lib/ur/top.urs @ 1480:aa0c6382aa57

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top.urs: More comments
author Robin Green <greenrd@greenrd.org>
date Tue, 28 Jun 2011 11:55:57 +0100
parents 44f78d6fec29
children 9253765d7724
comparison
equal deleted inserted replaced
1479:f561025bb68e 1480:aa0c6382aa57
19 end 19 end
20 20
21 21
22 val not : bool -> bool 22 val not : bool -> bool
23 23
24 (* Type-level identity function *)
24 con id = K ==> fn t :: K => t 25 con id = K ==> fn t :: K => t
26
27 (* Type-level function which yields the value-level record
28 described by the given type-level record *)
25 con record = fn t :: {Type} => $t 29 con record = fn t :: {Type} => $t
30
26 con fst = K1 ==> K2 ==> fn t :: (K1 * K2) => t.1 31 con fst = K1 ==> K2 ==> fn t :: (K1 * K2) => t.1
27 con snd = K1 ==> K2 ==> fn t :: (K1 * K2) => t.2 32 con snd = K1 ==> K2 ==> fn t :: (K1 * K2) => t.2
28 con fst3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.1 33 con fst3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.1
29 con snd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.2 34 con snd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.2
30 con thd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.3 35 con thd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.3
31 36
37 (* Convert a record of n Units into a type-level record where
38 each field has the same value (which describes a uniformly
39 typed record) *)
32 con mapU = K ==> fn f :: K => map (fn _ :: Unit => f) 40 con mapU = K ==> fn f :: K => map (fn _ :: Unit => f)
33 41
42 (* Existential type former *)
34 con ex :: K --> (K -> Type) -> Type 43 con ex :: K --> (K -> Type) -> Type
35 44
45 (* Introduction of existential type *)
36 val ex_intro : K --> tf :: (K -> Type) -> choice :: K -> tf choice -> ex tf 46 val ex_intro : K --> tf :: (K -> Type) -> choice :: K -> tf choice -> ex tf
47
48 (* Eliminator for existential type *)
37 val ex_elim : K --> tf ::: (K -> Type) -> ex tf -> res ::: Type -> (choice :: K -> tf choice -> res) -> res 49 val ex_elim : K --> tf ::: (K -> Type) -> ex tf -> res ::: Type -> (choice :: K -> tf choice -> res) -> res
38 50
51 (* Composition of ordinary (value-level) functions *)
39 val compose : t1 ::: Type -> t2 ::: Type -> t3 ::: Type 52 val compose : t1 ::: Type -> t2 ::: Type -> t3 ::: Type
40 -> (t2 -> t3) -> (t1 -> t2) -> (t1 -> t3) 53 -> (t2 -> t3) -> (t1 -> t2) -> (t1 -> t3)
41 54
42 val show_option : t ::: Type -> show t -> show (option t) 55 val show_option : t ::: Type -> show t -> show (option t)
43 val read_option : t ::: Type -> read t -> read (option t) 56 val read_option : t ::: Type -> read t -> read (option t)
44 57
45 val txt : t ::: Type -> ctx ::: {Unit} -> use ::: {Type} -> show t -> t 58 val txt : t ::: Type -> ctx ::: {Unit} -> use ::: {Type} -> show t -> t
46 -> xml ctx use [] 59 -> xml ctx use []
47 60
61 (* Given a polymorphic type (tf) and a means of constructing
62 "default" values of tf applied to arbitrary arguments,
63 constructs records consisting of those "default" values *)
48 val map0 : K --> tf :: (K -> Type) 64 val map0 : K --> tf :: (K -> Type)
49 -> (t :: K -> tf t) 65 -> (t :: K -> tf t)
50 -> r ::: {K} -> folder r -> $(map tf r) 66 -> r ::: {K} -> folder r -> $(map tf r)
67
68 (* Given two polymorphic types (tf1 and tf2) and a means of
69 converting from tf1 t to tf2 t for arbitrary t,
70 converts records of tf1's to records of tf2's *)
51 val mp : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) 71 val mp : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
52 -> (t ::: K -> tf1 t -> tf2 t) 72 -> (t ::: K -> tf1 t -> tf2 t)
53 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) 73 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r)
74
75 (* Two-argument conversion form of mp *)
54 val map2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf :: (K -> Type) 76 val map2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf :: (K -> Type)
55 -> (t ::: K -> tf1 t -> tf2 t -> tf t) 77 -> (t ::: K -> tf1 t -> tf2 t -> tf t)
56 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf r) 78 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf r)
79
80 (* Three-argument conversion form of mp *)
57 val map3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) -> tf :: (K -> Type) 81 val map3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) -> tf :: (K -> Type)
58 -> (t ::: K -> tf1 t -> tf2 t -> tf3 t -> tf t) 82 -> (t ::: K -> tf1 t -> tf2 t -> tf3 t -> tf t)
59 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> $(map tf r) 83 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> $(map tf r)
60 84
85 (* Fold along a uniformly (homogenously) typed record *)
61 val foldUR : tf :: Type -> tr :: ({Unit} -> Type) 86 val foldUR : tf :: Type -> tr :: ({Unit} -> Type)
62 -> (nm :: Name -> rest :: {Unit} 87 -> (nm :: Name -> rest :: {Unit}
63 -> [[nm] ~ rest] => 88 -> [[nm] ~ rest] =>
64 tf -> tr rest -> tr ([nm] ++ rest)) 89 tf -> tr rest -> tr ([nm] ++ rest))
65 -> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf r) -> tr r 90 -> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf r) -> tr r
66 91
92 (* Fold (generalized safe zip) along two equal-length uniformly-typed records *)
67 val foldUR2 : tf1 :: Type -> tf2 :: Type -> tr :: ({Unit} -> Type) 93 val foldUR2 : tf1 :: Type -> tf2 :: Type -> tr :: ({Unit} -> Type)
68 -> (nm :: Name -> rest :: {Unit} 94 -> (nm :: Name -> rest :: {Unit}
69 -> [[nm] ~ rest] => 95 -> [[nm] ~ rest] =>
70 tf1 -> tf2 -> tr rest -> tr ([nm] ++ rest)) 96 tf1 -> tf2 -> tr rest -> tr ([nm] ++ rest))
71 -> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf1 r) -> $(mapU tf2 r) -> tr r 97 -> tr [] -> r ::: {Unit} -> folder r -> $(mapU tf1 r) -> $(mapU tf2 r) -> tr r
72 98
99 (* Fold along a heterogenously-typed record *)
73 val foldR : K --> tf :: (K -> Type) -> tr :: ({K} -> Type) 100 val foldR : K --> tf :: (K -> Type) -> tr :: ({K} -> Type)
74 -> (nm :: Name -> t :: K -> rest :: {K} 101 -> (nm :: Name -> t :: K -> rest :: {K}
75 -> [[nm] ~ rest] => 102 -> [[nm] ~ rest] =>
76 tf t -> tr rest -> tr ([nm = t] ++ rest)) 103 tf t -> tr rest -> tr ([nm = t] ++ rest))
77 -> tr [] -> r ::: {K} -> folder r -> $(map tf r) -> tr r 104 -> tr [] -> r ::: {K} -> folder r -> $(map tf r) -> tr r
78 105
106 (* Fold (generalized safe zip) along two heterogenously-typed records *)
79 val foldR2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) 107 val foldR2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
80 -> tr :: ({K} -> Type) 108 -> tr :: ({K} -> Type)
81 -> (nm :: Name -> t :: K -> rest :: {K} 109 -> (nm :: Name -> t :: K -> rest :: {K}
82 -> [[nm] ~ rest] => 110 -> [[nm] ~ rest] =>
83 tf1 t -> tf2 t -> tr rest -> tr ([nm = t] ++ rest)) 111 tf1 t -> tf2 t -> tr rest -> tr ([nm = t] ++ rest))
84 -> tr [] 112 -> tr []
85 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> tr r 113 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> tr r
86 114
115 (* Fold (generalized safe zip) along three heterogenously-typed records *)
87 val foldR3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) 116 val foldR3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type)
88 -> tr :: ({K} -> Type) 117 -> tr :: ({K} -> Type)
89 -> (nm :: Name -> t :: K -> rest :: {K} 118 -> (nm :: Name -> t :: K -> rest :: {K}
90 -> [[nm] ~ rest] => 119 -> [[nm] ~ rest] =>
91 tf1 t -> tf2 t -> tf3 t -> tr rest -> tr ([nm = t] ++ rest)) 120 tf1 t -> tf2 t -> tf3 t -> tr rest -> tr ([nm = t] ++ rest))
92 -> tr [] 121 -> tr []
93 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> tr r 122 -> r ::: {K} -> folder r -> $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> tr r
94 123
124 (* Generate some XML by mapping over a uniformly-typed record *)
95 val mapUX : tf :: Type -> ctx :: {Unit} 125 val mapUX : tf :: Type -> ctx :: {Unit}
96 -> (nm :: Name -> rest :: {Unit} -> [[nm] ~ rest] => 126 -> (nm :: Name -> rest :: {Unit} -> [[nm] ~ rest] =>
97 tf -> xml ctx [] []) 127 tf -> xml ctx [] [])
98 -> r ::: {Unit} -> folder r -> $(mapU tf r) -> xml ctx [] [] 128 -> r ::: {Unit} -> folder r -> $(mapU tf r) -> xml ctx [] []
99 129
130 (* Generate some XML by mapping over a heterogenously-typed record *)
100 val mapX : K --> tf :: (K -> Type) -> ctx :: {Unit} 131 val mapX : K --> tf :: (K -> Type) -> ctx :: {Unit}
101 -> (nm :: Name -> t :: K -> rest :: {K} 132 -> (nm :: Name -> t :: K -> rest :: {K}
102 -> [[nm] ~ rest] => 133 -> [[nm] ~ rest] =>
103 tf t -> xml ctx [] []) 134 tf t -> xml ctx [] [])
104 -> r ::: {K} -> folder r -> $(map tf r) -> xml ctx [] [] 135 -> r ::: {K} -> folder r -> $(map tf r) -> xml ctx [] []