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Revising for next next lecture

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Adam Chlipala 2022-01-29 17:22:33 -05:00
parent 6c1d09bbbc
commit 0f72c50df0
1 changed files with 4 additions and 5 deletions
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9
Polymorphism.v
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@ -448,7 +448,6 @@ Inductive statement : Set :=
* almost-natural-looking embedded programs in Coq. *) * almost-natural-looking embedded programs in Coq. *)
Coercion Const : nat >-> expression. Coercion Const : nat >-> expression.
Coercion Var : string >-> expression. Coercion Var : string >-> expression.
(*Declare Scope embedded_scope.*)
Infix "+" := Plus : embedded_scope. Infix "+" := Plus : embedded_scope.
Infix "-" := Minus : embedded_scope. Infix "-" := Minus : embedded_scope.
Infix "*" := Times : embedded_scope. Infix "*" := Times : embedded_scope.
@ -542,7 +541,7 @@ Compute listifyStatement factorial.
(* At this point, I can't resist switching to a more automated proof style, (* At this point, I can't resist switching to a more automated proof style,
* though still a pretty tame one. *) * though still a pretty tame one. *)
Hint Rewrite length_app. Local Hint Rewrite length_app.
Lemma length_listifyExpression : forall e, Lemma length_listifyExpression : forall e,
length (listifyExpression e) = varsInExpression e. length (listifyExpression e) = varsInExpression e.
@ -550,7 +549,7 @@ Proof.
induct e; simplify; linear_arithmetic. induct e; simplify; linear_arithmetic.
Qed. Qed.
Hint Rewrite length_listifyExpression. Local Hint Rewrite length_listifyExpression.
Theorem length_listifyStatement : forall s, Theorem length_listifyStatement : forall s,
length (listifyStatement s) = varsInStatement s. length (listifyStatement s) = varsInStatement s.
@ -595,7 +594,7 @@ Proof.
induct ls1; simplify; equality. induct ls1; simplify; equality.
Qed. Qed.
Hint Rewrite swedishList_app. Local Hint Rewrite swedishList_app.
Lemma listifyExpression_swedishExpression : forall e, Lemma listifyExpression_swedishExpression : forall e,
listifyExpression (swedishExpression e) = swedishList (listifyExpression e). listifyExpression (swedishExpression e) = swedishList (listifyExpression e).
@ -603,7 +602,7 @@ Proof.
induct e; simplify; equality. induct e; simplify; equality.
Qed. Qed.
Hint Rewrite listifyExpression_swedishExpression. Local Hint Rewrite listifyExpression_swedishExpression.
Lemma listifyStatement_swedishStatement : forall s, Lemma listifyStatement_swedishStatement : forall s,
listifyStatement (swedishStatement s) = swedishList (listifyStatement s). listifyStatement (swedishStatement s) = swedishList (listifyStatement s).