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Diffstat (limited to 'src/Compilers/CommonSubexpressionEliminationProperties.v')
-rw-r--r-- | src/Compilers/CommonSubexpressionEliminationProperties.v | 189 |
1 files changed, 0 insertions, 189 deletions
diff --git a/src/Compilers/CommonSubexpressionEliminationProperties.v b/src/Compilers/CommonSubexpressionEliminationProperties.v deleted file mode 100644 index b52afcb18..000000000 --- a/src/Compilers/CommonSubexpressionEliminationProperties.v +++ /dev/null @@ -1,189 +0,0 @@ -(** * Common Subexpression Elimination for PHOAS Syntax *) -Require Import Coq.omega.Omega. -Require Import Coq.Lists.List. -Require Import Coq.FSets.FMapInterface. -Require Import Crypto.Compilers.Syntax. -Require Import Crypto.Compilers.Equality. -Require Import Crypto.Compilers.CommonSubexpressionElimination. -Require Import Crypto.Util.NatUtil. - -Local Open Scope list_scope. - -Local Open Scope ctype_scope. -Section symbolic. - (** Holds decidably-equal versions of raw expressions, for lookup. *) - Context (base_type_code : Type) - (op_code : Type) - (base_type_code_beq : base_type_code -> base_type_code -> bool) - (op_code_beq : op_code -> op_code -> bool) - (base_type_code_bl : forall x y, base_type_code_beq x y = true -> x = y) - (base_type_code_lb : forall x y, x = y -> base_type_code_beq x y = true) - (op_code_bl : forall x y, op_code_beq x y = true -> x = y) - (op_code_lb : forall x y, x = y -> op_code_beq x y = true) - (op : flat_type base_type_code -> flat_type base_type_code -> Type) - (symbolize_op : forall s d, op s d -> op_code) - (op_code_leb : op_code -> op_code -> bool) - (base_type_leb : base_type_code -> base_type_code -> bool) - (op_code_leb_total : forall x y, op_code_leb x y = true \/ op_code_leb y x = true) - (base_type_leb_total : forall x y, base_type_leb x y = true \/ base_type_leb y x = true) - (op_code_leb_antisymmetric : forall x y, op_code_leb x y = true -> op_code_leb y x = true -> op_code_beq x y = true) - (base_type_leb_antisymmetric : forall x y, base_type_leb x y = true -> base_type_leb y x = true -> base_type_code_beq x y = true). - Local Notation symbolic_expr := (symbolic_expr base_type_code op_code). - Context (normalize_symbolic_op_arguments : op_code -> symbolic_expr -> symbolic_expr). - - Local Notation symbolic_expr_beq := (@symbolic_expr_beq base_type_code op_code base_type_code_beq op_code_beq). - Local Notation symbolic_expr_lb := (@internal_symbolic_expr_dec_lb base_type_code op_code base_type_code_beq op_code_beq base_type_code_lb op_code_lb). - Local Notation symbolic_expr_bl := (@internal_symbolic_expr_dec_bl base_type_code op_code base_type_code_beq op_code_beq base_type_code_bl op_code_bl). - - Local Notation flat_type := (flat_type base_type_code). - Local Notation type := (type base_type_code). - Local Notation exprf := (@exprf base_type_code op). - Local Notation expr := (@expr base_type_code op). - Local Notation Expr := (@Expr base_type_code op). - - Local Notation symbolic_expr_leb := (@symbolic_expr_leb base_type_code op_code base_type_code_beq op_code_beq op_code_leb base_type_leb). - Local Notation flat_type_leb := (@flat_type_leb base_type_code base_type_code_beq base_type_leb). - Local Notation flat_type_beq := (@flat_type_beq base_type_code base_type_code_beq). - Local Notation flat_type_bl := (@internal_flat_type_dec_bl base_type_code base_type_code_beq base_type_code_bl). - Local Notation flat_type_lb := (@internal_flat_type_dec_lb base_type_code base_type_code_beq base_type_code_lb). - - Lemma base_type_leb_reflexive x : base_type_leb x x = true. - Proof using base_type_leb_total. destruct (base_type_leb_total x x); assumption. Qed. - - Lemma op_code_leb_reflexive x : op_code_leb x x = true. - Proof using op_code_leb_total. destruct (op_code_leb_total x x); assumption. Qed. - - Theorem flat_type_leb_total : forall a1 a2, flat_type_leb a1 a2 = true \/ flat_type_leb a2 a1 = true. - Proof using base_type_code_bl base_type_leb_total. - induction a1, a2; - repeat first [ progress simpl - | progress subst - | solve [ auto ] - | match goal with - | [ H : forall a2', ?leb ?a1 a2' = true \/ _ |- context[?leb ?a1 ?a2] ] - => let H' := fresh in destruct (H a2) as [H'|H']; rewrite H' - | [ H : flat_type_beq _ _ = true |- _ ] => apply flat_type_bl in H - | [ |- context[flat_type_beq ?x ?y] ] - => destruct (flat_type_beq x y) eqn:? - end ]. - Qed. - - Theorem flat_type_leb_reflexive x : flat_type_leb x x = true. - Proof using base_type_code_bl base_type_leb_total. destruct (flat_type_leb_total x x); assumption. Qed. - - Local Ltac rewrite_beq_leb_flat_type_op_code_reflexive := - repeat match goal with - | [ H : flat_type_beq _ _ = true |- _ ] => apply flat_type_bl in H - | [ H : op_code_beq _ _ = true |- _ ] => apply op_code_bl in H - | [ H : symbolic_expr_beq _ _ = true |- _ ] => apply symbolic_expr_bl in H - | [ H : context[flat_type_leb ?x ?x] |- _ ] - => rewrite (flat_type_leb_reflexive x) in H - | [ |- context[flat_type_leb ?x ?x] ] - => rewrite (flat_type_leb_reflexive x) - | [ H : context[flat_type_beq ?x ?x] |- _ ] - => rewrite (flat_type_lb x x eq_refl) in H - | [ |- context[flat_type_beq ?x ?x] ] - => rewrite (flat_type_lb x x eq_refl) - | [ H : context[op_code_leb ?x ?x] |- _ ] - => rewrite (op_code_leb_reflexive x) in H - | [ |- context[op_code_leb ?x ?x] ] - => rewrite (op_code_leb_reflexive x) - | [ H : context[op_code_beq ?x ?x] |- _ ] - => rewrite (op_code_lb x x eq_refl) in H - | [ |- context[op_code_beq ?x ?x] ] - => rewrite (op_code_lb x x eq_refl) - end. - - Theorem flat_type_leb_antisymmetric : forall a1 a2, flat_type_leb a1 a2 = true -> flat_type_leb a2 a1 = true -> flat_type_beq a1 a2 = true. - Proof using base_type_code_bl base_type_code_lb base_type_leb_antisymmetric base_type_leb_total. - induction a1, a2; - repeat first [ progress simpl - | progress subst - | solve [ auto ] - | progress rewrite ?andb_true_r, ?orb_false_r - | progress rewrite_beq_leb_flat_type_op_code_reflexive - | match goal with - | [ |- context[flat_type_beq ?x ?y] ] - => destruct (flat_type_beq x y) eqn:? - | [ H : forall a2, ?leb ?x a2 = true -> ?leb a2 ?x = true -> _, H0 : ?leb ?x ?a2' = true, H1 : ?leb ?a2' ?x = true |- _ ] - => specialize (H _ H0 H1) - end - | progress intros ]. - Qed. - - Theorem symbolic_expr_leb_total : forall a1 a2, symbolic_expr_leb a1 a2 = true \/ symbolic_expr_leb a2 a1 = true. - Proof using base_type_code_bl base_type_code_lb base_type_leb_total op_code_bl op_code_lb op_code_leb_total. - induction a1, a2; - repeat first [ rewrite !PeanoNat.Nat.leb_le - | progress subst - | progress simpl - | solve [ auto ] - | omega - | progress rewrite_beq_leb_flat_type_op_code_reflexive - | match goal with - | [ |- context[flat_type_beq ?x ?y] ] - => destruct (flat_type_beq x y) eqn:? - | [ |- context[op_code_beq ?x ?y] ] - => destruct (op_code_beq x y) eqn:? - | [ |- context[symbolic_expr_beq ?x ?y] ] - => destruct (symbolic_expr_beq x y) eqn:? - | [ H : forall a2', ?leb ?a1 a2' = true \/ _ |- context[?leb ?a1 ?a2] ] - => let H' := fresh in destruct (H a2) as [H'|H']; rewrite H' - | [ |- context[flat_type_leb ?a1 ?a2] ] - => let H' := fresh in destruct (flat_type_leb_total a1 a2) as [H'|H']; rewrite H' - | [ |- context[op_code_leb ?a1 ?a2] ] - => let H' := fresh in destruct (op_code_leb_total a1 a2) as [H'|H']; rewrite H' - end ]. - Qed. - - Theorem symbolic_expr_leb_reflexive x : symbolic_expr_leb x x = true. - Proof using base_type_code_bl base_type_code_lb base_type_leb_total op_code_bl op_code_lb op_code_leb_total. destruct (symbolic_expr_leb_total x x); assumption. Qed. - - Local Ltac rewrite_beq_leb_symbolic_expr_reflexive := - repeat match goal with - | [ H : symbolic_expr_beq _ _ = true |- _ ] => apply symbolic_expr_bl in H - | [ H : context[symbolic_expr_leb ?x ?x] |- _ ] - => rewrite (symbolic_expr_leb_reflexive x) in H - | [ |- context[symbolic_expr_leb ?x ?x] ] - => rewrite (symbolic_expr_leb_reflexive x) - | [ H : context[symbolic_expr_beq ?x ?x] |- _ ] - => rewrite (symbolic_expr_lb x x eq_refl) in H - | [ |- context[symbolic_expr_beq ?x ?x] ] - => rewrite (symbolic_expr_lb x x eq_refl) - end. - - Theorem symbolic_expr_leb_antisymmetric : forall a1 a2, symbolic_expr_leb a1 a2 = true -> symbolic_expr_leb a2 a1 = true -> symbolic_expr_beq a1 a2 = true. - Proof using base_type_code_bl base_type_code_lb base_type_leb_antisymmetric base_type_leb_total op_code_bl op_code_lb op_code_leb_antisymmetric op_code_leb_total. - induction a1, a2; - repeat first [ rewrite !PeanoNat.Nat.leb_le - | progress subst - | progress simpl - | solve [ auto ] - | omega - | progress rewrite ?andb_true_r, ?orb_false_r - | progress rewrite_beq_leb_flat_type_op_code_reflexive - | progress rewrite_beq_leb_symbolic_expr_reflexive - | match goal with - | [ |- context[flat_type_beq ?x ?y] ] - => destruct (flat_type_beq x y) eqn:? - | [ |- context[op_code_beq ?x ?y] ] - => destruct (op_code_beq x y) eqn:? - | [ |- context[symbolic_expr_beq ?x ?y] ] - => destruct (symbolic_expr_beq x y) eqn:? - | [ |- context[nat_beq ?x ?x] ] - => rewrite (internal_nat_dec_lb x x eq_refl) - | [ |- context[flat_type_leb ?a1 ?a2] ] - => let H' := fresh in destruct (flat_type_leb_total a1 a2) as [H'|H']; rewrite H' - | [ |- context[op_code_leb ?a1 ?a2] ] - => let H' := fresh in destruct (op_code_leb_total a1 a2) as [H'|H']; rewrite H' - | [ H : ?x <= ?y, H' : ?y <= ?x |- _ ] => assert (x = y) by omega; clear H H' - | [ H : forall a2, ?leb ?x a2 = true -> ?leb a2 ?x = true -> _, H0 : ?leb ?x ?a2' = true, H1 : ?leb ?a2' ?x = true |- _ ] - => specialize (H _ H0 H1) - | [ H0 : flat_type_leb ?x' ?y' = true, H1 : flat_type_leb ?y' ?x' = true |- _ ] - => pose proof (flat_type_leb_antisymmetric _ _ H0 H1); clear H0 H1 - | [ H : forall x y, ?leb x y = true -> ?leb y x = true -> _, H0 : ?leb ?x' ?y' = true, H1 : ?leb ?y' ?x' = true |- _ ] - => pose proof (H _ _ H0 H1); clear H0 H1 - end - | progress intros ]. - Qed. -End symbolic. |