From d31101103fae2d2b85d83d628183b91f90912782 Mon Sep 17 00:00:00 2001 From: Michael Sippel Date: Tue, 24 Sep 2024 12:08:00 +0200 Subject: [PATCH] coq: add expr_fv_type --- coq/terms/debruijn.v | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/coq/terms/debruijn.v b/coq/terms/debruijn.v index f6e0505..9ecf6bc 100644 --- a/coq/terms/debruijn.v +++ b/coq/terms/debruijn.v @@ -187,6 +187,21 @@ Fixpoint expr_fv (e : expr_DeBruijn) {struct e} : atoms := | ex_descend τ t' => (expr_fv t') end. +(* get the list of all free type variables in an expression *) +Fixpoint expr_fv_type (e : expr_DeBruijn) {struct e} : atoms := + match e with + | ex_fvar n => {} + | ex_bvar y => {} + | ex_ty_abs t' => {} + | ex_ty_app t' σ => (expr_fv_type t') `union` (type_fv σ) + | ex_morph σ t' => (type_fv σ) `union` (expr_fv_type t') + | ex_abs σ t' => (type_fv σ) `union` (expr_fv_type t') + | ex_app t1 t2 => (expr_fv_type t1) `union` (expr_fv_type t2) + | ex_let t1 t2 => (expr_fv_type t1) `union` (expr_fv_type t2) + | ex_ascend τ t' => (expr_fv_type t') + | ex_descend τ t' => (expr_fv_type t') + end. + (* substitute free variable x with expression s in t *) Fixpoint expr_subst (x:atom) (s:expr_DeBruijn) (t:expr_DeBruijn) {struct t} : expr_DeBruijn := match t with