move CPS notations to Util.CPSNotations

1 files changed, 34 insertions, 0 deletions

diff --git a/src/Util/CPSNotations.v b/src/Util/CPSNotations.v
new file mode 100644
index 000000000..f6fa31f5e
--- /dev/null
+++ b/src/Util/CPSNotations.v
@@ -0,0 +1,34 @@
+Require Import Crypto.Util.Notations.
+
+(** [x <- f ; C] encodes a call to function [f] with [C] as the
+  continuation. In [C], [x] refers to the output of [f]. *)
+
+(* [cpscall] is a marker to get Coq to print code using this notation only when it was actually used *)
+Definition cpscall {R} (f:forall{T}(continuation:R->T),T) {T} (continuation:R->T)
+:= @f T continuation.
+Notation "x' <- v ; C" := (cpscall v (fun x' => C)).
+
+(** A value of type [~>R] accepts a continuation that takes an
+     argument of type [R].  It is meant to be used in [Definition] and
+     such; for example:
+<<
+     Definition add_cps (a b:nat) : ~> nat.
+>>
+     The return type of the continuation is not yet specified; every
+     [~> R] is universally quantified over the possible return types
+     of the continuations that it can be applied to.
+ *)
+Notation "~> R" := (forall {T} (_:R->T), T).
+
+(** The type [A ~> R] contains functions that takes an argument of
+  type [A] and pass a value of type [R] to the continuation. Functions
+  that take multiple arguments can be encoded as [A -> B ~> C] or [A
+  ~> B ~>C] -- the first form requires both arguments to be specified
+  before its output can be CPS-bound, the latter must be bound once it
+  is partially applied to one argument. *)
+Notation "A ~> R" := (A -> ~>R).
+
+(* [cpsreturn] is a marker to get Coq to print loop notations before a [return] *)
+Definition cpsreturn {T} (x:T) := x.
+(** [return x] passes [x] to the continuation implicit in the previous notations. *)
+Notation "'return' x" := (cpsreturn (fun {T} (continuation:_->T) => continuation x)).
\ No newline at end of file