author wenzelm Sun Nov 02 17:20:45 2014 +0100 (2014-11-02) changeset 58881 b9556a055632 parent 53616 ff37dc246b10 child 59359 07b9893cd8a7 permissions -rw-r--r--
```     1 (* Author: Alexander Krauss, TU Muenchen
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```     2    Author: Christian Sternagel, University of Innsbruck
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```     3 *)
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```     4
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```     5 section {* Monad notation for arbitrary types *}
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```     6
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```     7 theory Monad_Syntax
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```     8 imports Main "~~/src/Tools/Adhoc_Overloading"
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```     9 begin
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```    10
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```    11 text {*
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```    12   We provide a convenient do-notation for monadic expressions
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```    13   well-known from Haskell.  @{const Let} is printed
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```    14   specially in do-expressions.
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```    15 *}
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```    16
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```    17 consts
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```    18   bind :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'd" (infixr ">>=" 54)
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```    19
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```    20 notation (xsymbols)
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```    21   bind (infixr "\<guillemotright>=" 54)
```
```    22
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```    23 notation (latex output)
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```    24   bind (infixr "\<bind>" 54)
```
```    25
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```    26 abbreviation (do_notation)
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```    27   bind_do :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'd"
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```    28 where
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```    29   "bind_do \<equiv> bind"
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```    30
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```    31 notation (output)
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```    32   bind_do (infixr ">>=" 54)
```
```    33
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```    34 notation (xsymbols output)
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```    35   bind_do (infixr "\<guillemotright>=" 54)
```
```    36
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```    37 notation (latex output)
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```    38   bind_do (infixr "\<bind>" 54)
```
```    39
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```    40 nonterminal do_binds and do_bind
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```    41
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```    42 syntax
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```    43   "_do_block" :: "do_binds \<Rightarrow> 'a" ("do {//(2  _)//}" [12] 62)
```
```    44   "_do_bind" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(_ <-/ _)" 13)
```
```    45   "_do_let" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(2let _ =/ _)" [1000, 13] 13)
```
```    46   "_do_then" :: "'a \<Rightarrow> do_bind" ("_" [14] 13)
```
```    47   "_do_final" :: "'a \<Rightarrow> do_binds" ("_")
```
```    48   "_do_cons" :: "[do_bind, do_binds] \<Rightarrow> do_binds" ("_;//_" [13, 12] 12)
```
```    49   "_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixr ">>" 54)
```
```    50
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```    51 syntax (xsymbols)
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```    52   "_do_bind"  :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(_ \<leftarrow>/ _)" 13)
```
```    53   "_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixr "\<guillemotright>" 54)
```
```    54
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```    55 syntax (latex output)
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```    56   "_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixr "\<then>" 54)
```
```    57
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```    58 translations
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```    59   "_do_block (_do_cons (_do_then t) (_do_final e))"
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```    60     == "CONST bind_do t (\<lambda>_. e)"
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```    61   "_do_block (_do_cons (_do_bind p t) (_do_final e))"
```
```    62     == "CONST bind_do t (\<lambda>p. e)"
```
```    63   "_do_block (_do_cons (_do_let p t) bs)"
```
```    64     == "let p = t in _do_block bs"
```
```    65   "_do_block (_do_cons b (_do_cons c cs))"
```
```    66     == "_do_block (_do_cons b (_do_final (_do_block (_do_cons c cs))))"
```
```    67   "_do_cons (_do_let p t) (_do_final s)"
```
```    68     == "_do_final (let p = t in s)"
```
```    69   "_do_block (_do_final e)" => "e"
```
```    70   "(m >> n)" => "(m >>= (\<lambda>_. n))"
```
```    71
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```    72 adhoc_overloading
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```    73   bind Set.bind Predicate.bind Option.bind List.bind
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```    74
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```    75 end
```