Finish semantics for Featherweight Ur

1 files changed, 71 insertions, 0 deletions

diff --git a/src/coq/Name.v b/src/coq/Name.v
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+(* Copyright (c) 2009, Adam Chlipala
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions are met:
+ *
+ * - Redistributions of source code must retain the above copyright notice,
+ *   this list of conditions and the following disclaimer.
+ * - Redistributions in binary form must reproduce the above copyright notice,
+ *   this list of conditions and the following disclaimer in the documentation
+ *   and/or other materials provided with the distribution.
+ * - The names of contributors may not be used to endorse or promote products
+ *   derived from this software without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+ * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+ * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+ * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+ * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+ * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *)
+
+Set Implicit Arguments.
+
+
+Fixpoint name' (n : nat) : Type :=
+  match n with
+    | O => Empty_set
+    | S n' => option (name' n')
+  end.
+
+Definition name'_eq_dec : forall n (x y : name' n), {x = y} + {x <> y}.
+  Hint Extern 1 (_ = _ -> False) => congruence.
+
+  induction n; simpl; intuition;
+    repeat match goal with
+             | [ x : Empty_set |- _ ] => destruct x
+             | [ x : option _ |- _ ] => destruct x
+           end; intuition;
+    match goal with
+      | [ IH : _, n1 : name' _, n2 : name' _ |- _ ] =>
+        destruct (IHn n1 n0); subst; intuition
+    end.
+Qed.
+
+Definition badName' n (P : name' n -> bool) :
+  {nm : _ | P nm = false} + {forall nm, P nm = true}.
+  Hint Constructors sig.
+  Hint Extern 1 (_ = true) =>
+    match goal with
+      | [ nm : option _ |- _ ] => destruct nm
+    end; auto.
+
+  induction n; simpl; intuition;
+    match goal with
+      | [ IH : forall P : _ -> _,_ |- _ ] =>
+        case_eq (P None);
+        destruct (IH (fun nm => P (Some nm))); firstorder eauto
+    end.
+Qed.
+
+Parameter numNames : nat.
+Definition name := name' (S numNames).
+Definition name_eq_dec : forall (x y : name), {x = y} + {x <> y} := @name'_eq_dec _.
+Definition badName : forall P : name -> bool, {nm : _ | P nm = false} + {forall nm, P nm = true} := @badName' _.
+Definition defaultName : name := None.