ML {*
fun strip_abs_split 0 t = ([], t)
| strip_abs_split i (Abs (s, T, t)) =
let
val s' = Codegen.new_name t s;
val v = Free (s', T)
in apfst (cons v) (strip_abs_split (i-1) (subst_bound (v, t))) end
| strip_abs_split i (u as Const ("split", _) $ t) = (case strip_abs_split (i+1) t of
(v :: v' :: vs, u) => (HOLogic.mk_prod (v, v') :: vs, u)
| _ => ([], u))
| strip_abs_split i t = ([], t);
fun let_codegen thy defs gr dep thyname brack t = (case strip_comb t of
(t1 as Const ("Let", _), t2 :: t3 :: ts) =>
let
fun dest_let (l as Const ("Let", _) $ t $ u) =
(case strip_abs_split 1 u of
([p], u') => apfst (cons (p, t)) (dest_let u')
| _ => ([], l))
| dest_let t = ([], t);
fun mk_code (gr, (l, r)) =
let
val (gr1, pl) = Codegen.invoke_codegen thy defs dep thyname false (gr, l);
val (gr2, pr) = Codegen.invoke_codegen thy defs dep thyname false (gr1, r);
in (gr2, (pl, pr)) end
in case dest_let (t1 $ t2 $ t3) of
([], _) => NONE
| (ps, u) =>
let
val (gr1, qs) = foldl_map mk_code (gr, ps);
val (gr2, pu) = Codegen.invoke_codegen thy defs dep thyname false (gr1, u);
val (gr3, pargs) = foldl_map
(Codegen.invoke_codegen thy defs dep thyname true) (gr2, ts)
in
SOME (gr3, Codegen.mk_app brack
(Pretty.blk (0, [Pretty.str "let ", Pretty.blk (0, List.concat
(separate [Pretty.str ";", Pretty.brk 1] (map (fn (pl, pr) =>
[Pretty.block [Pretty.str "val ", pl, Pretty.str " =",
Pretty.brk 1, pr]]) qs))),
Pretty.brk 1, Pretty.str "in ", pu,
Pretty.brk 1, Pretty.str "end"])) pargs)
end
end
| _ => NONE);
fun split_codegen thy defs gr dep thyname brack t = (case strip_comb t of
(t1 as Const ("split", _), t2 :: ts) =>
(case strip_abs_split 1 (t1 $ t2) of
([p], u) =>
let
val (gr1, q) = Codegen.invoke_codegen thy defs dep thyname false (gr, p);
val (gr2, pu) = Codegen.invoke_codegen thy defs dep thyname false (gr1, u);
val (gr3, pargs) = foldl_map
(Codegen.invoke_codegen thy defs dep thyname true) (gr2, ts)
in
SOME (gr2, Codegen.mk_app brack
(Pretty.block [Pretty.str "(fn ", q, Pretty.str " =>",
Pretty.brk 1, pu, Pretty.str ")"]) pargs)
end
| _ => NONE)
| _ => NONE);
val prod_codegen_setup =
Codegen.add_codegen "let_codegen" let_codegen #>
Codegen.add_codegen "split_codegen" split_codegen #>
CodegenPackage.add_appconst
("Let", ((2, 2), CodegenPackage.appgen_let strip_abs_split)) #>
CodegenPackage.add_appconst
("split", ((1, 1), CodegenPackage.appgen_split strip_abs_split));
*}
(* Title: HOL/Library/ExecutableRat.thy
ID: $Id$
Author: Florian Haftmann, TU Muenchen
*)
header {* Executable implementation of rational numbers in HOL *}
theory ExecutableRat
imports "~~/src/HOL/Real/Rational" "~~/src/HOL/NumberTheory/IntPrimes"
begin
text {*
Actually nothing is proved about the implementation.
*}
datatype erat = Rat bool int int
instance erat :: zero by intro_classes
instance erat :: one by intro_classes
instance erat :: plus by intro_classes
instance erat :: minus by intro_classes
instance erat :: times by intro_classes
instance erat :: inverse by intro_classes
instance erat :: ord by intro_classes
consts
norm :: "erat \<Rightarrow> erat"
common :: "(int * int) * (int * int) \<Rightarrow> (int * int) * int"
of_quotient :: "int * int \<Rightarrow> erat"
of_rat :: "rat \<Rightarrow> erat"
to_rat :: "erat \<Rightarrow> rat"
defs
norm_def [simp]: "norm r == case r of (Rat a p q) \<Rightarrow>
if p = 0 then Rat True 0 1
else
let
absp = abs p
in let
m = zgcd (absp, q)
in Rat (a = (0 <= p)) (absp div m) (q div m)"
common_def [simp]: "common r == case r of ((p1, q1), (p2, q2)) \<Rightarrow>
let q' = q1 * q2 div int (gcd (nat q1, nat q2))
in ((p1 * (q' div q1), p2 * (q' div q2)), q')"
of_quotient_def [simp]: "of_quotient r == case r of (a, b) \<Rightarrow>
norm (Rat True a b)"
of_rat_def [simp]: "of_rat r == of_quotient (THE s. s : Rep_Rat r)"
to_rat_def [simp]: "to_rat r == case r of (Rat a p q) \<Rightarrow>
if a then Fract p q else Fract (uminus p) q"
consts
zero :: erat
one :: erat
add :: "erat \<Rightarrow> erat \<Rightarrow> erat"
neg :: "erat \<Rightarrow> erat"
mult :: "erat \<Rightarrow> erat \<Rightarrow> erat"
inv :: "erat \<Rightarrow> erat"
le :: "erat \<Rightarrow> erat \<Rightarrow> bool"
defs (overloaded)
zero_rat_def [simp]: "0 == Rat False 0 1"
one_rat_def [simp]: "1 == Rat False 1 1"
add_rat_def [simp]: "r + s == case r of Rat a1 p1 q1 \<Rightarrow> case s of Rat a2 p2 q2 \<Rightarrow>
let
((r1, r2), den) = common ((p1, q1), (p2, q2))
in let
num = (if a1 then r1 else -r1) + (if a2 then r2 else -r2)
in norm (Rat True num den)"
uminus_rat_def [simp]: "- r == case r of Rat a p q \<Rightarrow>
if p = 0 then Rat a p q
else Rat (\<not> a) p q"
times_rat_def [simp]: "r * s == case r of Rat a1 p1 q1 \<Rightarrow> case s of Rat a2 p2 q2 \<Rightarrow>
norm (Rat (a1 = a2) (p1 * p2) (q1 * q2))"
inverse_rat_def [simp]: "inverse r == case r of Rat a p q \<Rightarrow>
if p = 0 then arbitrary
else Rat a q p"
le_rat_def [simp]: "r <= s == case r of Rat a1 p1 q1 \<Rightarrow> case s of Rat a2 p2 q2 \<Rightarrow>
(\<not> a1 \<and> a2) \<or>
(\<not> (a1 \<and> \<not> a2) \<and>
(let
((r1, r2), dummy) = common ((p1, q1), (p2, q2))
in if a1 then r1 <= r2 else r2 <= r1))"
code_syntax_tyco rat
ml (target_atom "{*erat*}")
haskell (target_atom "{*erat*}")
code_alias
(* an intermediate solution until name resolving of ad-hoc overloaded
constants is refined *)
"HOL.inverse" "Rational.inverse"
"HOL.divide" "Rational.divide"
code_syntax_const
Fract
ml ("{*of_quotient*}")
haskell ("{*of_quotient*}")
0 :: "rat"
ml ("{*0::erat*}")
haskell ("{*1::erat*}")
1 :: "rat"
ml ("{*1::erat*}")
haskell ("{*1::erat*}")
"op +" :: "rat \<Rightarrow> rat \<Rightarrow> rat"
ml ("{*op + :: erat \<Rightarrow> erat \<Rightarrow> erat*}")
haskell ("{*op + :: erat \<Rightarrow> erat \<Rightarrow> erat*}")
uminus :: "rat \<Rightarrow> rat"
ml ("{*uminus :: erat \<Rightarrow> erat*}")
haskell ("{*uminus :: erat \<Rightarrow> erat*}")
"op *" :: "rat \<Rightarrow> rat \<Rightarrow> rat"
ml ("{*op * :: erat \<Rightarrow> erat \<Rightarrow> erat*}")
haskell ("{*op * :: erat \<Rightarrow> erat \<Rightarrow> erat*}")
inverse :: "rat \<Rightarrow> rat"
ml ("{*inverse :: erat \<Rightarrow> erat*}")
haskell ("{*inverse :: erat \<Rightarrow> erat*}")
divide :: "rat \<Rightarrow> rat \<Rightarrow> rat"
ml ("{*op * :: erat \<Rightarrow> erat \<Rightarrow> erat*}/ _/ ({*inverse :: erat \<Rightarrow> erat*}/ _)")
haskell ("{*op * :: erat \<Rightarrow> erat \<Rightarrow> erat*}/ _/ ({*inverse :: erat \<Rightarrow> erat*}/ _)")
"op <=" :: "rat \<Rightarrow> rat \<Rightarrow> bool"
ml ("{*op <= :: erat \<Rightarrow> erat \<Rightarrow> bool*}")
haskell ("{*op <= :: erat \<Rightarrow> erat \<Rightarrow> bool*}")
end