### view lib/ur/top.urs @ 2307:6ae9a2784a45

author Adam Chlipala Sun, 20 Dec 2015 14:39:50 -0500 9029e0e2c67c
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```(** Row folding *)

con folder :: K --> {K} -> Type

val fold : K --> tf :: ({K} -> Type)
-> (nm :: Name -> v :: K -> r :: {K} -> [[nm] ~ r] =>
tf r -> tf ([nm = v] ++ r))
-> tf []
-> r ::: {K} -> folder r -> tf r

structure Folder : sig
val nil : K --> folder (([]) :: {K})
val cons : K --> r ::: {K} -> nm :: Name -> v :: K
-> [[nm] ~ r] => folder r -> folder ([nm = v] ++ r)
val concat : K --> r1 ::: {K} -> r2 ::: {K}
-> [r1 ~ r2] => folder r1 -> folder r2 -> folder (r1 ++ r2)
val mp : K1 --> K2 --> f ::: (K1 -> K2) -> r ::: {K1}
-> folder r -> folder (map f r)
end

val not : bool -> bool

(* Type-level identity function *)
con ident = K ==> fn t :: K => t

(* Type-level function which yields the value-level record
described by the given type-level record *)
con record = fn t :: {Type} => \$t

con fst = K1 ==> K2 ==> fn t :: (K1 * K2) => t.1
con snd = K1 ==> K2 ==> fn t :: (K1 * K2) => t.2
con fst3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.1
con snd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.2
con thd3 = K1 ==> K2 ==> K3 ==> fn t :: (K1 * K2 * K3) => t.3

(* Convert a record of n Units into a type-level record where
each field has the same value (which describes a uniformly
typed record) *)
con mapU = K ==> fn f :: K => map (fn _ :: Unit => f)

(* Existential type former *)
con ex :: K --> (K -> Type) -> Type

(* Introduction of existential type *)
val ex_intro : K --> tf :: (K -> Type) -> choice :: K -> tf choice -> ex tf

(* Eliminator for existential type *)
val ex_elim : K --> tf ::: (K -> Type) -> ex tf -> res ::: Type -> (choice :: K -> tf choice -> res) -> res

(* Composition of ordinary (value-level) functions *)
val compose : t1 ::: Type -> t2 ::: Type -> t3 ::: Type
-> (t2 -> t3) -> (t1 -> t2) -> (t1 -> t3)

val show_option : t ::: Type -> show t -> show (option t)

val txt : t ::: Type -> ctx ::: {Unit} -> use ::: {Type} -> show t -> t
-> xml ctx use []

(* Given a polymorphic type (tf) and a means of constructing
"default" values of tf applied to arbitrary arguments,
constructs records consisting of those "default" values *)
val map0 : K --> tf :: (K -> Type)
-> (t :: K -> tf t)
-> r ::: {K} -> folder r -> \$(map tf r)

(* Given two polymorphic types (tf1 and tf2) and a means of
converting from tf1 t to tf2 t for arbitrary t,
converts records of tf1's to records of tf2's *)
val mp : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t)
-> r ::: {K} -> folder r -> \$(map tf1 r) -> \$(map tf2 r)

(* Two-argument conversion form of mp *)
val map2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t -> tf t)
-> r ::: {K} -> folder r -> \$(map tf1 r) -> \$(map tf2 r) -> \$(map tf r)

(* Three-argument conversion form of mp *)
val map3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) -> tf :: (K -> Type)
-> (t ::: K -> tf1 t -> tf2 t -> tf3 t -> tf t)
-> r ::: {K} -> folder r -> \$(map tf1 r) -> \$(map tf2 r) -> \$(map tf3 r) -> \$(map tf r)

(* Fold along a uniformly (homogenously) typed record *)
val foldUR : tf :: Type -> tr :: ({Unit} -> Type)
-> (nm :: Name -> rest :: {Unit}
-> [[nm] ~ rest] =>
tf -> tr rest -> tr ([nm] ++ rest))
-> tr [] -> r ::: {Unit} -> folder r -> \$(mapU tf r) -> tr r

(* Fold (generalized safe zip) along two equal-length uniformly-typed records *)
val foldUR2 : tf1 :: Type -> tf2 :: Type -> tr :: ({Unit} -> Type)
-> (nm :: Name -> rest :: {Unit}
-> [[nm] ~ rest] =>
tf1 -> tf2 -> tr rest -> tr ([nm] ++ rest))
-> tr [] -> r ::: {Unit} -> folder r -> \$(mapU tf1 r) -> \$(mapU tf2 r) -> tr r

(* Fold along a heterogenously-typed record *)
val foldR : K --> tf :: (K -> Type) -> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf t -> tr rest -> tr ([nm = t] ++ rest))
-> tr [] -> r ::: {K} -> folder r -> \$(map tf r) -> tr r

(* Fold (generalized safe zip) along two heterogenously-typed records *)
val foldR2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type)
-> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf1 t -> tf2 t -> tr rest -> tr ([nm = t] ++ rest))
-> tr []
-> r ::: {K} -> folder r -> \$(map tf1 r) -> \$(map tf2 r) -> tr r

(* Fold (generalized safe zip) along three heterogenously-typed records *)
val foldR3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type)
-> tr :: ({K} -> Type)
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf1 t -> tf2 t -> tf3 t -> tr rest -> tr ([nm = t] ++ rest))
-> tr []
-> r ::: {K} -> folder r -> \$(map tf1 r) -> \$(map tf2 r) -> \$(map tf3 r) -> tr r

(* Generate some XML by mapping over a uniformly-typed record *)
val mapUX : tf :: Type -> ctx :: {Unit}
-> (nm :: Name -> rest :: {Unit} -> [[nm] ~ rest] =>
tf -> xml ctx [] [])
-> r ::: {Unit} -> folder r -> \$(mapU tf r) -> xml ctx [] []

(* Generate some XML by mapping over a heterogenously-typed record *)
val mapX : K --> tf :: (K -> Type) -> ctx :: {Unit}
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf t -> xml ctx [] [])
-> r ::: {K} -> folder r -> \$(map tf r) -> xml ctx [] []

val mapUX2 : tf1 :: Type -> tf2 :: Type -> ctx :: {Unit}
-> (nm :: Name -> rest :: {Unit}
-> [[nm] ~ rest] =>
tf1 -> tf2 -> xml ctx [] [])
-> r ::: {Unit} -> folder r
-> \$(mapU tf1 r) -> \$(mapU tf2 r) -> xml ctx [] []

val mapX2 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> ctx :: {Unit}
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf1 t -> tf2 t -> xml ctx [] [])
-> r ::: {K} -> folder r
-> \$(map tf1 r) -> \$(map tf2 r) -> xml ctx [] []

val mapX3 : K --> tf1 :: (K -> Type) -> tf2 :: (K -> Type) -> tf3 :: (K -> Type) -> ctx :: {Unit}
-> (nm :: Name -> t :: K -> rest :: {K}
-> [[nm] ~ rest] =>
tf1 t -> tf2 t -> tf3 t -> xml ctx [] [])
-> r ::: {K} -> folder r
-> \$(map tf1 r) -> \$(map tf2 r) -> \$(map tf3 r) -> xml ctx [] []

(* Note that the next two functions return elements in the _reverse_ of the natural order!
* Such a choice interacts well with the time complexity of standard list operations.
* It's easy to regain the natural order by inverting a query's 'ORDER BY' condition. *)

val queryL : tables ::: {{Type}} -> exps ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> transaction (list \$(exps ++ map (fn fields :: {Type} => \$fields) tables))

val queryL1 : t ::: Name -> fs ::: {Type}
-> sql_query [] [] [t = fs] []
-> transaction (list \$fs)

val query1 : t ::: Name -> fs ::: {Type} -> state ::: Type
-> sql_query [] [] [t = fs] []
-> (\$fs -> state -> transaction state)
-> state
-> transaction state

val query1' : t ::: Name -> fs ::: {Type} -> state ::: Type
-> sql_query [] [] [t = fs] []
-> (\$fs -> state -> state)
-> state
-> transaction state

val queryI : tables ::: {{Type}} -> exps ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> (\$(exps ++ map (fn fields :: {Type} => \$fields) tables)
-> transaction unit)
-> transaction unit

val queryI1 : nm ::: Name -> fs ::: {Type}
-> sql_query [] [] [nm = fs] []
-> (\$fs -> transaction unit)
-> transaction unit

val queryX : tables ::: {{Type}} -> exps ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> (\$(exps ++ map (fn fields :: {Type} => \$fields) tables)
-> xml ctx inp [])
-> transaction (xml ctx inp [])

val queryXI : tables ::: {{Type}} -> exps ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> (int -> \$(exps ++ map (fn fields :: {Type} => \$fields) tables)
-> xml ctx inp [])
-> transaction (xml ctx inp [])

val queryX1 : nm ::: Name -> fs ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> sql_query [] [] [nm = fs] []
-> (\$fs -> xml ctx inp [])
-> transaction (xml ctx inp [])

val queryX1I : nm ::: Name -> fs ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> sql_query [] [] [nm = fs] []
-> (int -> \$fs -> xml ctx inp [])
-> transaction (xml ctx inp [])

val queryX' : tables ::: {{Type}} -> exps ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> (\$(exps ++ map (fn fields :: {Type} => \$fields) tables)
-> transaction (xml ctx inp []))
-> transaction (xml ctx inp [])
val queryX1' : nm ::: Name -> fs ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> sql_query [] [] [nm = fs] []
-> (\$fs -> transaction (xml ctx inp []))
-> transaction (xml ctx inp [])
val queryXE' : exps ::: {Type} -> ctx ::: {Unit} -> inp ::: {Type}
-> sql_query [] [] [] exps
-> (\$exps -> transaction (xml ctx inp []))
-> transaction (xml ctx inp [])

val hasRows : tables ::: {{Type}} -> exps ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> transaction bool

val oneOrNoRows : tables ::: {{Type}} -> exps ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> transaction
(option
\$(exps
++ map (fn fields :: {Type} => \$fields) tables))

val oneOrNoRows1 : nm ::: Name -> fs ::: {Type}
-> sql_query [] [] [nm = fs] []
-> transaction (option \$fs)

val oneOrNoRowsE1 : tabs ::: {Unit} -> nm ::: Name -> t ::: Type
-> [tabs ~ [nm]] =>
sql_query [] [] (mapU [] tabs) [nm = t]
-> transaction (option t)

val oneRow : tables ::: {{Type}} -> exps ::: {Type}
-> [tables ~ exps] =>
sql_query [] [] tables exps
-> transaction
\$(exps
++ map (fn fields :: {Type} => \$fields) tables)

val oneRow1 : nm ::: Name -> fs ::: {Type}
-> sql_query [] [] [nm = fs] []
-> transaction \$fs

val oneRowE1 : tabs ::: {Unit} -> nm ::: Name -> t ::: Type
-> [tabs ~ [nm]] =>
sql_query [] [] (mapU [] tabs) [nm = t]
-> transaction t

val nonempty : fs ::: {Type} -> us ::: {{Unit}} -> sql_table fs us
-> transaction bool

val eqNullable : tables ::: {{Type}} -> agg ::: {{Type}} -> exps ::: {Type}
-> t ::: Type -> sql_injectable (option t)
-> sql_exp tables agg exps (option t)
-> sql_exp tables agg exps (option t)
-> sql_exp tables agg exps bool

val eqNullable' : tables ::: {{Type}} -> agg ::: {{Type}} -> exps ::: {Type}
-> t ::: Type -> sql_injectable (option t)
-> sql_exp tables agg exps (option t)
-> option t
-> sql_exp tables agg exps bool

val mkRead' : t ::: Type -> (string -> option t) -> string -> read t

val postFields : postBody -> list (string * string)

val max : t ::: Type -> ord t -> t -> t -> t
val min : t ::: Type -> ord t -> t -> t -> t

val assert : t ::: Type
-> bool   (* Did we avoid something bad? *)
-> string (* Explanation of the bad thing *)
-> string (* Source location of the bad thing *)
-> t      (* Return this value if all went well. *)
-> t```