(* Title: HOL/Library/Monad_Syntax.thy
Author: Alexander Krauss, TU Muenchen
Author: Christian Sternagel, University of Innsbruck
*)
section \<open>Monad notation for arbitrary types\<close>
theory Monad_Syntax
imports Main
begin
text \<open>
We provide a convenient do-notation for monadic expressions well-known from Haskell.
\<^const>\<open>Let\<close> is printed specially in do-expressions.
\<close>
consts
bind :: "'a \<Rightarrow> ('b \<Rightarrow> 'c) \<Rightarrow> 'd" (infixl \<open>\<bind>\<close> 54)
notation (ASCII)
bind (infixl \<open>>>=\<close> 54)
abbreviation (do_notation)
bind_do :: "'a \<Rightarrow> ('b \<Rightarrow> 'c) \<Rightarrow> 'd"
where "bind_do \<equiv> bind"
notation (output)
bind_do (infixl \<open>\<bind>\<close> 54)
notation (ASCII output)
bind_do (infixl \<open>>>=\<close> 54)
nonterminal do_binds and do_bind
syntax
"_do_block" :: "do_binds \<Rightarrow> 'a"
(\<open>(\<open>open_block notation=\<open>mixfix do block\<close>\<close>do {//(2 _)//})\<close> [12] 62)
"_do_bind" :: "[pttrn, 'a] \<Rightarrow> do_bind"
(\<open>(\<open>indent=2 notation=\<open>infix do bind\<close>\<close>_ \<leftarrow>/ _)\<close> 13)
"_do_let" :: "[pttrn, 'a] \<Rightarrow> do_bind"
(\<open>(\<open>indent=2 notation=\<open>infix do let\<close>\<close>let _ =/ _)\<close> [1000, 13] 13)
"_do_then" :: "'a \<Rightarrow> do_bind" (\<open>_\<close> [14] 13)
"_do_final" :: "'a \<Rightarrow> do_binds" (\<open>_\<close>)
"_do_cons" :: "[do_bind, do_binds] \<Rightarrow> do_binds"
(\<open>(\<open>open_block notation=\<open>infix do next\<close>\<close>_;//_)\<close> [13, 12] 12)
"_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixl \<open>\<then>\<close> 54)
syntax (ASCII)
"_do_bind" :: "[pttrn, 'a] \<Rightarrow> do_bind"
(\<open>(\<open>indent=2 notation=\<open>infix do bind\<close>\<close>_ <-/ _)\<close> 13)
"_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixl \<open>>>\<close> 54)
syntax_consts
"_do_block" "_do_cons" "_do_bind" "_do_then" \<rightleftharpoons> bind and
"_do_let" \<rightleftharpoons> Let
translations
"_do_block (_do_cons (_do_then t) (_do_final e))"
\<rightleftharpoons> "CONST bind_do t (\<lambda>_. e)"
"_do_block (_do_cons (_do_bind p t) (_do_final e))"
\<rightleftharpoons> "CONST bind_do t (\<lambda>p. e)"
"_do_block (_do_cons (_do_let p t) bs)"
\<rightleftharpoons> "let p = t in _do_block bs"
"_do_block (_do_cons b (_do_cons c cs))"
\<rightleftharpoons> "_do_block (_do_cons b (_do_final (_do_block (_do_cons c cs))))"
"_do_cons (_do_let p t) (_do_final s)"
\<rightleftharpoons> "_do_final (let p = t in s)"
"_do_block (_do_final e)" \<rightharpoonup> "e"
"(m \<then> n)" \<rightharpoonup> "(m \<bind> (\<lambda>_. n))"
adhoc_overloading
bind Set.bind Predicate.bind Option.bind List.bind
end