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chapter \<open>Generated by Lem from \<open>function.lem\<close>.\<close>
theory "Lem_function"
imports
Main
"Lem_bool"
"Lem_basic_classes"
begin
(******************************************************************************)
(* A library for common operations on functions *)
(******************************************************************************)
(*open import Bool Basic_classes*)
(*open import {coq} `Program.Basics`*)
(* ----------------------- *)
(* identity function *)
(* ----------------------- *)
(*val id : forall 'a. 'a -> 'a*)
(*let id x= x*)
(* ----------------------- *)
(* constant function *)
(* ----------------------- *)
(*val const : forall 'a 'b. 'a -> 'b -> 'a*)
(* ----------------------- *)
(* function composition *)
(* ----------------------- *)
(*val comb : forall 'a 'b 'c. ('b -> 'c) -> ('a -> 'b) -> ('a -> 'c)*)
(*let comb f g= (fun x -> f (g x))*)
(* ----------------------- *)
(* function application *)
(* ----------------------- *)
(*val $ [apply] : forall 'a 'b. ('a -> 'b) -> ('a -> 'b)*)
(*let $ f= (fun x -> f x)*)
(*val $> [rev_apply] : forall 'a 'b. 'a -> ('a -> 'b) -> 'b*)
(*let $> x f= f x*)
(* ----------------------- *)
(* flipping argument order *)
(* ----------------------- *)
(*val flip : forall 'a 'b 'c. ('a -> 'b -> 'c) -> ('b -> 'a -> 'c)*)
(*let flip f= (fun x y -> f y x)*)
(* currying / uncurrying *)
(*val curry : forall 'a 'b 'c. (('a * 'b) -> 'c) -> 'a -> 'b -> 'c*)
definition curry :: "('a*'b \<Rightarrow> 'c)\<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> 'c " where
" curry f = ( (\<lambda> a b . f (a, b)))"
(*val uncurry : forall 'a 'b 'c. ('a -> 'b -> 'c) -> ('a * 'b -> 'c)*)
fun uncurry :: "('a \<Rightarrow> 'b \<Rightarrow> 'c)\<Rightarrow> 'a*'b \<Rightarrow> 'c " where
" uncurry f (a,b) = ( f a b )"
end
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