MessagesAndRefinement: base syntax and semantics

MessagesAndRefinement.v

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+(** Formal Reasoning About Programs <http://adam.chlipala.net/frap/>
+  * Chapter 15: Pi-Calculus and Behavioral Refinement
+  * Author: Adam Chlipala
+  * License: https://creativecommons.org/licenses/by-nc-nd/4.0/ *)
+
+Require Import Frap.
+
+Set Implicit Arguments.
+Set Asymmetric Patterns.
+
+
+Notation channel := nat.
+
+Inductive proc :=
+| NewChannel (k : channel -> proc)
+| Send (ch : channel) {A : Set} (v : A) (k : proc)
+| Recv (ch : channel) {A : Set} (k : A -> proc)
+| Par (pr1 pr2 : proc)
+| Dup (pr : proc).
+
+Notation pid := nat.
+Notation procs := (fmap pid proc).
+Notation channels := (set channel).
+
+Inductive step : channels * procs -> channels * procs -> Prop :=
+| StepNew : forall chs ps i k ch,
+    ps $? i = Some (NewChannel k)
+    -> ~ch \in chs
+    -> step (chs, ps) (chs \cup {ch}, ps $+ (i, k ch))
+| StepSendRecv : forall chs ps i ch {A : Set} (v : A) k1 j k2,
+    ps $? i = Some (Send ch v k1)
+    -> ps $? j = Some (Recv ch k2)
+    -> step (chs, ps) (chs, ps $+ (i, k1) $+ (j, k2 v))
+| StepPar : forall chs ps i pr1 pr2 j,
+    ps $? i = Some (Par pr1 pr2)
+    -> ps $? j = None
+    -> step (chs, ps) (chs, ps $+ (i, pr1) $+ (j, pr2))
+| StepDup : forall chs ps i pr j,
+    ps $? i = Some (Dup pr)
+    -> ps $? j = None
+    -> step (chs, ps) (chs, ps $+ (i, Dup pr) $+ (j, pr)).