Add efficient extraction of [nat], [Z], and [string] to Haskell

This mirrors the existing extraction libraries for OCaml.

One wart: the extraction for [string] requires that the Haskell code
imports Data.Bits and Data.Char.  Coq has no way to add extra import
statements to the extracted code.  So we have to rely on the user to
somehow import these libraries (e.g., using the -pgmF ghc option).
See also https://coq.inria.fr/bugs/show_bug.cgi?id=4189

Message to github robot: this commit closes #65

1 files changed, 27 insertions, 0 deletions

diff --git a/plugins/extraction/ExtrHaskellNatNum.v b/plugins/extraction/ExtrHaskellNatNum.v
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index 000000000..979a1cdc4
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+++ b/plugins/extraction/ExtrHaskellNatNum.v
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+(**
+ * Efficient (but uncertified) extraction of usual [nat] functions
+ * into equivalent versions in Haskell's Prelude that are defined
+ * for any [Num] typeclass instances.  Useful in combination with
+ * [Extract Inductive nat] that maps [nat] onto a Haskell type that
+ * implements [Num].
+ *)
+
+Require Import Arith.
+Require Import EqNat.
+
+Extract Inlined Constant Nat.add => "(Prelude.+)".
+Extract Inlined Constant Nat.mul => "(Prelude.*)".
+Extract Inlined Constant Nat.div => "Prelude.div".
+Extract Inlined Constant Nat.max => "Prelude.max".
+Extract Inlined Constant Nat.min => "Prelude.min".
+Extract Inlined Constant Init.Nat.add => "(Prelude.+)".
+Extract Inlined Constant Init.Nat.mul => "(Prelude.*)".
+Extract Inlined Constant Compare_dec.lt_dec => "(Prelude.<)".
+Extract Inlined Constant Compare_dec.leb => "(Prelude.<=)".
+Extract Inlined Constant Compare_dec.le_lt_dec => "(Prelude.<=)".
+Extract Inlined Constant EqNat.beq_nat => "(Prelude.==)".
+Extract Inlined Constant EqNat.eq_nat_decide => "(Prelude.==)".
+Extract Inlined Constant Peano_dec.eq_nat_dec => "(Prelude.==)".
+
+Extract Constant pred => "(\n -> Prelude.max 0 (Prelude.pred n))".
+Extract Constant minus => "(\n m -> Prelude.max 0 (n Prelude.- m))".