Commit e7409376 authored by Robbert Krebbers's avatar Robbert Krebbers

Fundamental comments.

parent 6b2fd748
......@@ -17,6 +17,9 @@ Section fundamental.
Implicit Types τ : ty.
Implicit Types ρ : list (sem_ty Σ).
(** First we need to prove soundness of operator typing. We declare these
lemmas as instances so they will be used automatically in the proof of the
fundamental theorem. *)
Instance ty_unboxed_sound τ ρ : ty_unboxed τ SemTyUnboxed ( τ ρ).
Proof. destruct 1; simpl; apply _. Qed.
Instance ty_un_op_sound op τ σ ρ :
......@@ -26,7 +29,12 @@ Section fundamental.
ty_bin_op op τ1 τ2 σ SemTyBinOp op ( τ1 ρ) ( τ2 ρ) ( σ ρ).
Proof. destruct 1; simpl; apply _. Qed.
Lemma fundamental Γ e τ ρ
(** The fundamental theorem. Since the syntactic typing judgment is defined
in a mutual inductive fashion, we need to prove the fundamental theorem for
expressions mutually with the fundamental theorem for values. Note that for
such mutually inductive proofs, we need to make sure ourselves that the
induction hypotheses is only used on smaller derivations. *)
Theorem fundamental Γ e τ ρ
(Hty : Γ e : τ) : (interp_env Γ ρ e : τ ρ)%I
with fundamental_val v τ ρ
(Hty : v : τ) : ( v : τ ρ)%I.
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