diff options
Diffstat (limited to 'plugins/romega/ReflOmegaCore.v')
| -rw-r--r-- | plugins/romega/ReflOmegaCore.v | 46 |
1 files changed, 23 insertions, 23 deletions
diff --git a/plugins/romega/ReflOmegaCore.v b/plugins/romega/ReflOmegaCore.v index c82abfc8..56ae921e 100644 --- a/plugins/romega/ReflOmegaCore.v +++ b/plugins/romega/ReflOmegaCore.v @@ -868,11 +868,11 @@ Inductive term : Set := | Tvar : nat -> term. Delimit Scope romega_scope with term. -Arguments Scope Tint [Int_scope]. -Arguments Scope Tplus [romega_scope romega_scope]. -Arguments Scope Tmult [romega_scope romega_scope]. -Arguments Scope Tminus [romega_scope romega_scope]. -Arguments Scope Topp [romega_scope romega_scope]. +Arguments Tint _%I. +Arguments Tplus (_ _)%term. +Arguments Tmult (_ _)%term. +Arguments Tminus (_ _)%term. +Arguments Topp _%term. Infix "+" := Tplus : romega_scope. Infix "*" := Tmult : romega_scope. @@ -1014,7 +1014,7 @@ Inductive h_step : Set := (* This type allows to navigate in the logical constructors that form the predicats of the hypothesis in order to decompose them. This allows in particular to extract one hypothesis from a - conjonction with possibly the right level of negations. *) + conjunction with possibly the right level of negations. *) Inductive direction : Set := | D_left : direction @@ -2038,12 +2038,12 @@ Qed. (* \subsection{La fonction de normalisation des termes (moteur de réécriture)} *) -Fixpoint rewrite (s : step) : term -> term := +Fixpoint t_rewrite (s : step) : term -> term := match s with - | C_DO_BOTH s1 s2 => apply_both (rewrite s1) (rewrite s2) - | C_LEFT s => apply_left (rewrite s) - | C_RIGHT s => apply_right (rewrite s) - | C_SEQ s1 s2 => fun t : term => rewrite s2 (rewrite s1 t) + | C_DO_BOTH s1 s2 => apply_both (t_rewrite s1) (t_rewrite s2) + | C_LEFT s => apply_left (t_rewrite s) + | C_RIGHT s => apply_right (t_rewrite s) + | C_SEQ s1 s2 => fun t : term => t_rewrite s2 (t_rewrite s1 t) | C_NOP => fun t : term => t | C_OPP_PLUS => Topp_plus | C_OPP_OPP => Topp_opp @@ -2069,7 +2069,7 @@ Fixpoint rewrite (s : step) : term -> term := | C_MULT_COMM => Tmult_comm end. -Theorem rewrite_stable : forall s : step, term_stable (rewrite s). +Theorem t_rewrite_stable : forall s : step, term_stable (t_rewrite s). Proof. simple induction s; simpl in |- *; [ intros; apply apply_both_stable; auto @@ -2453,7 +2453,7 @@ Definition state (m : int) (s : step) (prop1 prop2 : proposition) := match prop2 with | EqTerm b2 b3 => if beq Null 0 - then EqTerm (Tint 0) (rewrite s (b1 + (- b3 + b2) * Tint m)%term) + then EqTerm (Tint 0) (t_rewrite s (b1 + (- b3 + b2) * Tint m)%term) else TrueTerm | _ => TrueTerm end @@ -2463,7 +2463,7 @@ Definition state (m : int) (s : step) (prop1 prop2 : proposition) := Theorem state_valid : forall (m : int) (s : step), valid2 (state m s). Proof. unfold valid2 in |- *; intros m s ep e p1 p2; unfold state in |- *; Simplify; - simpl in |- *; auto; elim (rewrite_stable s e); simpl in |- *; + simpl in |- *; auto; elim (t_rewrite_stable s e); simpl in |- *; intros H1 H2; elim H1. now rewrite H2, plus_opp_l, plus_0_l, mult_0_l. Qed. @@ -2585,19 +2585,19 @@ Qed. Definition move_right (s : step) (p : proposition) := match p with - | EqTerm t1 t2 => EqTerm (Tint 0) (rewrite s (t1 + - t2)%term) - | LeqTerm t1 t2 => LeqTerm (Tint 0) (rewrite s (t2 + - t1)%term) - | GeqTerm t1 t2 => LeqTerm (Tint 0) (rewrite s (t1 + - t2)%term) - | LtTerm t1 t2 => LeqTerm (Tint 0) (rewrite s (t2 + Tint (-(1)) + - t1)%term) - | GtTerm t1 t2 => LeqTerm (Tint 0) (rewrite s (t1 + Tint (-(1)) + - t2)%term) - | NeqTerm t1 t2 => NeqTerm (Tint 0) (rewrite s (t1 + - t2)%term) + | EqTerm t1 t2 => EqTerm (Tint 0) (t_rewrite s (t1 + - t2)%term) + | LeqTerm t1 t2 => LeqTerm (Tint 0) (t_rewrite s (t2 + - t1)%term) + | GeqTerm t1 t2 => LeqTerm (Tint 0) (t_rewrite s (t1 + - t2)%term) + | LtTerm t1 t2 => LeqTerm (Tint 0) (t_rewrite s (t2 + Tint (-(1)) + - t1)%term) + | GtTerm t1 t2 => LeqTerm (Tint 0) (t_rewrite s (t1 + Tint (-(1)) + - t2)%term) + | NeqTerm t1 t2 => NeqTerm (Tint 0) (t_rewrite s (t1 + - t2)%term) | p => p end. Theorem move_right_valid : forall s : step, valid1 (move_right s). Proof. unfold valid1, move_right in |- *; intros s ep e p; Simplify; simpl in |- *; - elim (rewrite_stable s e); simpl in |- *; + elim (t_rewrite_stable s e); simpl in |- *; [ symmetry in |- *; apply egal_left; assumption | intro; apply le_left; assumption | intro; apply le_left; rewrite <- ge_le_iff; assumption @@ -2950,14 +2950,14 @@ Qed. Theorem move_right_stable : forall s : step, prop_stable (move_right s). Proof. unfold move_right, prop_stable in |- *; intros s ep e p; split; - [ Simplify; simpl in |- *; elim (rewrite_stable s e); simpl in |- *; + [ Simplify; simpl in |- *; elim (t_rewrite_stable s e); simpl in |- *; [ symmetry in |- *; apply egal_left; assumption | intro; apply le_left; assumption | intro; apply le_left; rewrite <- ge_le_iff; assumption | intro; apply lt_left; rewrite <- gt_lt_iff; assumption | intro; apply lt_left; assumption | intro; apply ne_left_2; assumption ] - | case p; simpl in |- *; intros; auto; generalize H; elim (rewrite_stable s); + | case p; simpl in |- *; intros; auto; generalize H; elim (t_rewrite_stable s); simpl in |- *; intro H1; [ rewrite (plus_0_r_reverse (interp_term e t0)); rewrite H1; rewrite plus_permute; rewrite plus_opp_r; |