src/HOL/Library/Monad_Syntax.thy
author haftmann
Wed Jul 14 15:49:29 2010 +0200 (2010-07-14)
changeset 37823 194a7d543a70
parent 37818 dd65033fed78
child 37848 a33ecf47f0a0
permissions -rw-r--r--
corrected import
     1 (* Author: Alexander Krauss, TU Muenchen
     2    Author: Christian Sternagel, University of Innsbruck
     3 *)
     4 
     5 header {* Monad notation for arbitrary types *}
     6 
     7 theory Monad_Syntax
     8 imports Main "~~/src/Tools/Adhoc_Overloading"
     9 begin
    10 
    11 text {*
    12   We provide a convenient do-notation for monadic expressions
    13   well-known from Haskell.  @{const Let} is printed
    14   specially in do-expressions.
    15 *}
    16 
    17 consts
    18   bind :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'c" (infixr ">>=" 54)
    19 
    20 notation (xsymbols)
    21   bind (infixr "\<guillemotright>=" 54)
    22 
    23 abbreviation (do_notation)
    24   bind_do :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'c"
    25 where
    26   "bind_do \<equiv> bind"
    27 
    28 notation (output)
    29   bind_do (infixr ">>=" 54)
    30 
    31 notation (xsymbols output)
    32   bind_do (infixr "\<guillemotright>=" 54)
    33 
    34 nonterminals
    35   do_binds do_bind
    36 
    37 syntax
    38   "_do_block" :: "do_binds \<Rightarrow> 'a" ("do {//(2  _)//}" [12] 62)
    39   "_do_bind" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(_ <-/ _)" 13)
    40   "_do_let" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(2let _ =/ _)" [1000, 13] 13)
    41   "_do_then" :: "'a \<Rightarrow> do_bind" ("_" [14] 13)
    42   "_do_final" :: "'a \<Rightarrow> do_binds" ("_")
    43   "_do_cons" :: "[do_bind, do_binds] \<Rightarrow> do_binds" ("_;//_" [13, 12] 12)
    44   "_thenM" :: "['a, 'b] \<Rightarrow> 'b" (infixr ">>" 54)
    45 
    46 syntax (xsymbols)
    47   "_do_bind"  :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(_ \<leftarrow>/ _)" 13)
    48   "_thenM" :: "['a, 'b] \<Rightarrow> 'b" (infixr "\<guillemotright>" 54)
    49 
    50 translations
    51   "_do_block (_do_cons (_do_then t) (_do_final e))"
    52     == "CONST bind_do t (\<lambda>_. e)"
    53   "_do_block (_do_cons (_do_bind p t) (_do_final e))"
    54     == "CONST bind_do t (\<lambda>p. e)"
    55   "_do_block (_do_cons (_do_let p t) bs)"
    56     == "let p = t in _do_block bs"
    57   "_do_block (_do_cons b (_do_cons c cs))"
    58     == "_do_block (_do_cons b (_do_final (_do_block (_do_cons c cs))))"
    59   "_do_cons (_do_let p t) (_do_final s)"
    60     == "_do_final (let p = t in s)"
    61   "_do_block (_do_final e)" => "e"
    62   "(m >> n)" => "(m >>= (\<lambda>_. n))"
    63 
    64 setup {*
    65   Adhoc_Overloading.add_overloaded @{const_name bind}
    66   #> Adhoc_Overloading.add_variant @{const_name bind} @{const_name Predicate.bind}
    67 *}
    68 
    69 end