author wenzelm Wed Mar 08 10:50:59 2017 +0100 (2017-03-08) changeset 65151 a7394aa4d21c parent 62189 116f41763b2b child 66263 466d8e7ed170 permissions -rw-r--r--
tuned proofs;
```     1 (* Author: Alexander Krauss, TU Muenchen
```
```     2    Author: Christian Sternagel, University of Innsbruck
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```     3 *)
```
```     4
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```     5 section \<open>Monad notation for arbitrary types\<close>
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```     6
```
```     7 theory Monad_Syntax
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```     8 imports Main "~~/src/Tools/Adhoc_Overloading"
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```     9 begin
```
```    10
```
```    11 text \<open>
```
```    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 \<close>
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```    16
```
```    17 consts
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```    18   bind :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'd" (infixr "\<bind>" 54)
```
```    19
```
```    20 notation (ASCII)
```
```    21   bind (infixr ">>=" 54)
```
```    22
```
```    23
```
```    24 abbreviation (do_notation)
```
```    25   bind_do :: "['a, 'b \<Rightarrow> 'c] \<Rightarrow> 'd"
```
```    26   where "bind_do \<equiv> bind"
```
```    27
```
```    28 notation (output)
```
```    29   bind_do (infixr "\<bind>" 54)
```
```    30
```
```    31 notation (ASCII output)
```
```    32   bind_do (infixr ">>=" 54)
```
```    33
```
```    34
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```    35 nonterminal do_binds and do_bind
```
```    36 syntax
```
```    37   "_do_block" :: "do_binds \<Rightarrow> 'a" ("do {//(2  _)//}" [12] 62)
```
```    38   "_do_bind"  :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(2_ \<leftarrow>/ _)" 13)
```
```    39   "_do_let" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(2let _ =/ _)" [1000, 13] 13)
```
```    40   "_do_then" :: "'a \<Rightarrow> do_bind" ("_" [14] 13)
```
```    41   "_do_final" :: "'a \<Rightarrow> do_binds" ("_")
```
```    42   "_do_cons" :: "[do_bind, do_binds] \<Rightarrow> do_binds" ("_;//_" [13, 12] 12)
```
```    43   "_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixr "\<then>" 54)
```
```    44
```
```    45 syntax (ASCII)
```
```    46   "_do_bind" :: "[pttrn, 'a] \<Rightarrow> do_bind" ("(2_ <-/ _)" 13)
```
```    47   "_thenM" :: "['a, 'b] \<Rightarrow> 'c" (infixr ">>" 54)
```
```    48
```
```    49 translations
```
```    50   "_do_block (_do_cons (_do_then t) (_do_final e))"
```
```    51     \<rightleftharpoons> "CONST bind_do t (\<lambda>_. e)"
```
```    52   "_do_block (_do_cons (_do_bind p t) (_do_final e))"
```
```    53     \<rightleftharpoons> "CONST bind_do t (\<lambda>p. e)"
```
```    54   "_do_block (_do_cons (_do_let p t) bs)"
```
```    55     \<rightleftharpoons> "let p = t in _do_block bs"
```
```    56   "_do_block (_do_cons b (_do_cons c cs))"
```
```    57     \<rightleftharpoons> "_do_block (_do_cons b (_do_final (_do_block (_do_cons c cs))))"
```
```    58   "_do_cons (_do_let p t) (_do_final s)"
```
```    59     \<rightleftharpoons> "_do_final (let p = t in s)"
```
```    60   "_do_block (_do_final e)" \<rightharpoonup> "e"
```
```    61   "(m \<then> n)" \<rightharpoonup> "(m \<bind> (\<lambda>_. n))"
```
```    62
```
```    63 adhoc_overloading
```
```    64   bind Set.bind Predicate.bind Option.bind List.bind
```
```    65
```
```    66 end
```