header "Immutable Arrays with Code Generation"

theory IArray

imports Main

begin

text{* Immutable arrays are lists wrapped up in an additional constructor.

There are no update operations. Hence code generation can safely implement

this type by efficient target language arrays. Currently only SML is

provided. Should be extended to other target languages and more operations.

Note that arrays cannot be printed directly but only by turning them into

lists first. Arrays could be converted back into lists for printing if they

were wrapped up in an additional constructor. *}

datatype 'a iarray = IArray "'a list"

primrec list_of :: "'a iarray => 'a list" where

"list_of (IArray xs) = xs"

hide_const (open) list_of

definition of_fun :: "(nat => 'a) => nat => 'a iarray" where

[simp]: "of_fun f n = IArray (map f [0..<n])"

hide_const (open) of_fun

definition sub :: "'a iarray => nat => 'a" (infixl "!!" 100) where

[simp]: "as !! n = IArray.list_of as ! n"

hide_const (open) sub

definition length :: "'a iarray => nat" where

[simp]: "length as = List.length (IArray.list_of as)"

hide_const (open) length

lemma list_of_code [code]:

"IArray.list_of as = map (λn. as !! n) [0 ..< IArray.length as]"

by (cases as) (simp add: map_nth)

subsection "Code Generation"

code_reserved SML Vector

code_printing

type_constructor iarray \<rightharpoonup> (SML) "_ Vector.vector"

| constant IArray \<rightharpoonup> (SML) "Vector.fromList"

lemma [code]:

"size (as :: 'a iarray) = 0"

by (cases as) simp

lemma [code]:

"iarray_size f as = Suc (list_size f (IArray.list_of as))"

by (cases as) simp

lemma [code]:

"iarray_rec f as = f (IArray.list_of as)"

by (cases as) simp

lemma [code]:

"iarray_case f as = f (IArray.list_of as)"

by (cases as) simp

lemma [code]:

"HOL.equal as bs <-> HOL.equal (IArray.list_of as) (IArray.list_of bs)"

by (cases as, cases bs) (simp add: equal)

primrec tabulate :: "integer × (integer => 'a) => 'a iarray" where

"tabulate (n, f) = IArray (map (f o integer_of_nat) [0..<nat_of_integer n])"

hide_const (open) tabulate

lemma [code]:

"IArray.of_fun f n = IArray.tabulate (integer_of_nat n, f o nat_of_integer)"

by simp

code_printing

constant IArray.tabulate \<rightharpoonup> (SML) "Vector.tabulate"

primrec sub' :: "'a iarray × integer => 'a" where

"sub' (as, n) = IArray.list_of as ! nat_of_integer n"

hide_const (open) sub'

lemma [code]:

"as !! n = IArray.sub' (as, integer_of_nat n)"

by simp

code_printing

constant IArray.sub' \<rightharpoonup> (SML) "Vector.sub"

definition length' :: "'a iarray => integer" where

[simp]: "length' as = integer_of_nat (List.length (IArray.list_of as))"

hide_const (open) length'

lemma [code]:

"IArray.length as = nat_of_integer (IArray.length' as)"

by simp

code_printing

constant IArray.length' \<rightharpoonup> (SML) "Vector.length"

end