Merge pull request #34 from samuelgruetter/ltac_lecture

preparing Ltac lecture

IntroToProofScripting.v

@@ -483,6 +483,25 @@ Goal False.
   length (1 :: 2 :: 3 :: nil) ltac:(fun n => pose n).
 Abort.
 
+(* However, it's not always convenient to use continuation passing style
+ * everywhere, so cool kids use the following hack to sneak side effects
+ * into otherwise functional Ltac code: *)
+Module Import WithPrintingFixedWithoutContinuations.
+  Ltac length ls :=
+    let __ := match constr:(Set) with
+              | _ => (* put all your side effects here:*)
+                     idtac ls; assert (ls = ls) by equality
+              end in
+    match ls with
+    | nil => constr:(O)
+    | _ :: ?ls' => let L := length ls' in constr:(S L)
+    end.
+End WithPrintingFixedWithoutContinuations.
+
+Goal False.
+  let n := length (1 :: 2 :: 3 :: nil) in
+  pose n.
+Abort.
 
 (** * Recursive Proof Search *)
 

IntroToProofScripting_template.v

@@ -182,7 +182,7 @@ Section propositional.
   Admitted.
 End propositional.
 
-(* Backrtracking example #1 *)
+(* Backtracking example #1 *)
 
 Theorem m1 : True.
 Proof.

TransitionSystems.v

@@ -29,7 +29,7 @@ Inductive fact_state :=
  * throughout recursive invocations of a predicate (though this definition does
  * not use recursion).  After the colon, we give a type that expresses which
  * additional arguments exist, followed by [Prop] for "proposition."
- * Putting this inductive definition in [Prop] is what marks at as a predicate.
+ * Putting this inductive definition in [Prop] is what marks it as a predicate.
  * Our prior definitions have implicitly been in [Set], the normal universe
  * of mathematical objects. *)
 Inductive fact_init (original_input : nat) : fact_state -> Prop :=