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Manual: add a pointer to background reading on inference rule notation
author Adam Chlipala <adam@chlipala.net>
date Sun, 17 Nov 2013 07:54:59 -0500
parents a613cae954ca
children cbd294994c69
rev   line source
adamc@834 1 fun exec [m ::: Type -> Type] (_ : monad m) [ts ::: {Type}] r (fd : folder ts) =
adamc@1093 2 @foldR [m] [fn ts => m $ts]
adamc@1093 3 (fn [nm :: Name] [v :: Type] [rest :: {Type}] [[nm] ~ rest] action acc =>
adamc@1093 4 this <- action;
adamc@1093 5 others <- acc;
adamc@1093 6 return ({nm = this} ++ others))
adamc@1093 7 (return {}) fd r
adamc@898 8
adamc@898 9 fun ignore [m ::: Type -> Type] (_ : monad m) [t] (v : m t) = x <- v; return ()
adamc@905 10
adamc@917 11 fun mp [m] (_ : monad m) [a] [b] f m =
adamc@917 12 v <- m;
adamc@917 13 return (f v)
adamc@917 14
adam@1768 15 val liftM = @@mp
adam@1768 16
adamc@905 17 fun foldR [K] [m] (_ : monad m) [tf :: K -> Type] [tr :: {K} -> Type]
adamc@905 18 (f : nm :: Name -> t :: K -> rest :: {K}
adamc@905 19 -> [[nm] ~ rest] =>
adamc@905 20 tf t -> tr rest -> m (tr ([nm = t] ++ rest)))
adamc@1093 21 (i : tr []) [r ::: {K}] (fl : folder r) =
adamc@1093 22 @Top.fold [fn r :: {K} => $(map tf r) -> m (tr r)]
adamc@1093 23 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest]
adamc@1093 24 (acc : _ -> m (tr rest)) r =>
adamc@1093 25 acc' <- acc (r -- nm);
adam@1472 26 f [nm] [t] [rest] r.nm acc')
adamc@1093 27 (fn _ => return i)
adamc@1093 28 fl
adamc@905 29
adamc@905 30 fun foldR2 [K] [m] (_ : monad m) [tf1 :: K -> Type] [tf2 :: K -> Type] [tr :: {K} -> Type]
adamc@905 31 (f : nm :: Name -> t :: K -> rest :: {K}
adamc@905 32 -> [[nm] ~ rest] =>
adamc@905 33 tf1 t -> tf2 t -> tr rest -> m (tr ([nm = t] ++ rest)))
adamc@1093 34 (i : tr []) [r ::: {K}] (fl : folder r) =
adamc@1093 35 @Top.fold [fn r :: {K} => $(map tf1 r) -> $(map tf2 r) -> m (tr r)]
adamc@1093 36 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest]
adamc@1093 37 (acc : _ -> _ -> m (tr rest)) r1 r2 =>
adamc@1093 38 acc' <- acc (r1 -- nm) (r2 -- nm);
adam@1472 39 f [nm] [t] [rest] r1.nm r2.nm acc')
adamc@1093 40 (fn _ _ => return i)
adamc@1093 41 fl
adamc@905 42
adamc@910 43 fun foldR3 [K] [m] (_ : monad m) [tf1 :: K -> Type] [tf2 :: K -> Type] [tf3 :: K -> Type] [tr :: {K} -> Type]
adamc@910 44 (f : nm :: Name -> t :: K -> rest :: {K}
adamc@910 45 -> [[nm] ~ rest] =>
adamc@910 46 tf1 t -> tf2 t -> tf3 t -> tr rest -> m (tr ([nm = t] ++ rest)))
adamc@1093 47 (i : tr []) [r ::: {K}] (fl : folder r) =
adamc@1093 48 @Top.fold [fn r :: {K} => $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> m (tr r)]
adamc@1093 49 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest]
adamc@1093 50 (acc : _ -> _ -> _ -> m (tr rest)) r1 r2 r3 =>
adamc@1093 51 acc' <- acc (r1 -- nm) (r2 -- nm) (r3 -- nm);
adam@1472 52 f [nm] [t] [rest] r1.nm r2.nm r3.nm acc')
adamc@1093 53 (fn _ _ _ => return i)
adamc@1093 54 fl
adamc@910 55
adamc@1172 56 fun mapR0 [K] [m] (_ : monad m) [tr :: K -> Type]
adamc@1172 57 (f : nm :: Name -> t :: K -> m (tr t)) [r ::: {K}] (fl : folder r) =
adamc@1172 58 @Top.fold [fn r => m ($(map tr r))]
adamc@1172 59 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] (acc : m ($(map tr rest))) =>
adamc@1172 60 v <- f [nm] [t];
adamc@1172 61 vs <- acc;
adamc@1172 62 return (vs ++ {nm = v}))
adamc@1172 63 (return {})
adamc@1172 64 fl
adamc@1172 65
adamc@905 66 fun mapR [K] [m] (_ : monad m) [tf :: K -> Type] [tr :: K -> Type]
adamc@905 67 (f : nm :: Name -> t :: K -> tf t -> m (tr t)) =
adamc@905 68 @@foldR [m] _ [tf] [fn r => $(map tr r)]
adamc@905 69 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] (v : tf t)
adamc@905 70 (acc : $(map tr rest)) =>
adamc@905 71 v' <- f [nm] [t] v;
adamc@905 72 return (acc ++ {nm = v'}))
adamc@905 73 {}
adamc@937 74
adamc@937 75 fun mapR2 [K] [m] (_ : monad m) [tf1 :: K -> Type] [tf2 :: K -> Type] [tr :: K -> Type]
adamc@937 76 (f : nm :: Name -> t :: K -> tf1 t -> tf2 t -> m (tr t)) =
adamc@937 77 @@foldR2 [m] _ [tf1] [tf2] [fn r => $(map tr r)]
adamc@937 78 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] (v1 : tf1 t) (v2 : tf2 t)
adamc@937 79 (acc : $(map tr rest)) =>
adamc@937 80 v' <- f [nm] [t] v1 v2;
adamc@937 81 return (acc ++ {nm = v'}))
adamc@937 82 {}
adamc@1175 83
adamc@1175 84 fun foldMapR [K] [m] (_ : monad m) [tf :: K -> Type] [tf' :: K -> Type] [tr :: {K} -> Type]
adamc@1175 85 (f : nm :: Name -> t :: K -> rest :: {K}
adamc@1175 86 -> [[nm] ~ rest] =>
adamc@1175 87 tf t -> tr rest -> m (tf' t * tr ([nm = t] ++ rest)))
adamc@1175 88 (i : tr []) [r ::: {K}] (fl : folder r) =
adamc@1175 89 @Top.fold [fn r :: {K} => $(map tf r) -> m ($(map tf' r) * tr r)]
adamc@1175 90 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest]
adamc@1175 91 (acc : _ -> m ($(map tf' rest) * tr rest)) r =>
adamc@1175 92 p <- acc (r -- nm);
adam@1472 93 p' <- f [nm] [t] [rest] r.nm p.2;
adamc@1175 94 return ({nm = p'.1} ++ p.1, p'.2))
adamc@1175 95 (fn _ => return ({}, i))
adamc@1175 96 fl
adamc@1257 97
adam@1312 98 fun appR [K] [m] (_ : monad m) [tf :: K -> Type]
adam@1312 99 (f : nm :: Name -> t :: K -> tf t -> m unit)
adam@1312 100 [r ::: {K}] (fl : folder r) =
adam@1312 101 @Top.fold [fn r :: {K} => $(map tf r) -> m unit]
adam@1312 102 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] acc r =>
adam@1312 103 acc (r -- nm);
adam@1312 104 f [nm] [t] r.nm)
adam@1312 105 (fn _ => return ())
adam@1312 106 fl
adam@1312 107
adamc@1257 108 fun appR2 [K] [m] (_ : monad m) [tf1 :: K -> Type] [tf2 :: K -> Type]
adam@1310 109 (f : nm :: Name -> t :: K -> tf1 t -> tf2 t -> m unit)
adamc@1257 110 [r ::: {K}] (fl : folder r) =
adamc@1257 111 @Top.fold [fn r :: {K} => $(map tf1 r) -> $(map tf2 r) -> m unit]
adamc@1257 112 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] acc r1 r2 =>
adamc@1257 113 acc (r1 -- nm) (r2 -- nm);
adam@1310 114 f [nm] [t] r1.nm r2.nm)
adamc@1257 115 (fn _ _ => return ())
adamc@1257 116 fl
adam@1313 117
adam@1313 118 fun appR3 [K] [m] (_ : monad m) [tf1 :: K -> Type] [tf2 :: K -> Type] [tf3 :: K -> Type]
adam@1313 119 (f : nm :: Name -> t :: K -> tf1 t -> tf2 t -> tf3 t -> m unit)
adam@1313 120 [r ::: {K}] (fl : folder r) =
adam@1313 121 @Top.fold [fn r :: {K} => $(map tf1 r) -> $(map tf2 r) -> $(map tf3 r) -> m unit]
adam@1313 122 (fn [nm :: Name] [t :: K] [rest :: {K}] [[nm] ~ rest] acc r1 r2 r3 =>
adam@1313 123 acc (r1 -- nm) (r2 -- nm) (r3 -- nm);
adam@1313 124 f [nm] [t] r1.nm r2.nm r3.nm)
adam@1313 125 (fn _ _ _ => return ())
adam@1313 126 fl
adam@1768 127
adam@1768 128 fun liftM2 [m ::: Type -> Type] (_ : monad m) [a] [b] [c] (f : a -> b -> c) (mx : m a) (my : m b) : m c =
adam@1768 129 x <- mx;
adam@1768 130 y <- my;
adam@1768 131 return (f x y)