diff options
Diffstat (limited to 'kernel/vars.mli')
| -rw-r--r-- | kernel/vars.mli | 92 |
1 files changed, 72 insertions, 20 deletions
diff --git a/kernel/vars.mli b/kernel/vars.mli index 501a5b85..574d50ec 100644 --- a/kernel/vars.mli +++ b/kernel/vars.mli @@ -8,7 +8,6 @@ open Names open Constr -open Context (** {6 Occur checks } *) @@ -42,32 +41,85 @@ val liftn : int -> int -> constr -> constr (** [lift n c] lifts by [n] the positive indexes in [c] *) val lift : int -> constr -> constr -(** [substnl [a1;...;an] k c] substitutes in parallel [a1],...,[an] +(** The type [substl] is the type of substitutions [u₁..un] of type + some context Δ and defined in some environment Γ. Typing of + substitutions is defined by: + - Γ ⊢ ∅ : ∅, + - Γ ⊢ u₁..u{_n-1} : Δ and Γ ⊢ u{_n} : An\[u₁..u{_n-1}\] implies + Γ ⊢ u₁..u{_n} : Δ,x{_n}:A{_n} + - Γ ⊢ u₁..u{_n-1} : Δ and Γ ⊢ un : A{_n}\[u₁..u{_n-1}\] implies + Γ ⊢ u₁..u{_n} : Δ,x{_n}:=c{_n}:A{_n} when Γ ⊢ u{_n} ≡ c{_n}\[u₁..u{_n-1}\] + + Note that [u₁..un] is represented as a list with [un] at the head of + the list, i.e. as [[un;...;u₁]]. *) + +type substl = constr list + +(** Let [Γ] be a context interleaving declarations [x₁:T₁..xn:Tn] + and definitions [y₁:=c₁..yp:=cp] in some context [Γ₀]. Let + [u₁..un] be an {e instance} of [Γ], i.e. an instance in [Γ₀] + of the [xi]. Then, [subst_of_rel_context_instance Γ u₁..un] + returns the corresponding {e substitution} of [Γ], i.e. the + appropriate interleaving [σ] of the [u₁..un] with the [c₁..cp], + all of them in [Γ₀], so that a derivation [Γ₀, Γ, Γ₁|- t:T] + can be instantiated into a derivation [Γ₀, Γ₁ |- t[σ]:T[σ]] using + [substnl σ |Γ₁| t]. + Note that the instance [u₁..un] is represented starting with [u₁], + as if usable in [applist] while the substitution is + represented the other way round, i.e. ending with either [u₁] or + [c₁], as if usable for [substl]. *) +val subst_of_rel_context_instance : Context.Rel.t -> constr list -> substl + +(** For compatibility: returns the substitution reversed *) +val adjust_subst_to_rel_context : Context.Rel.t -> constr list -> constr list + +(** [substnl [a₁;...;an] k c] substitutes in parallel [a₁],...,[an] for respectively [Rel(k+1)],...,[Rel(k+n)] in [c]; it relocates - accordingly indexes in [a1],...,[an] and [c] *) -val substnl : constr list -> int -> constr -> constr -val substl : constr list -> constr -> constr + accordingly indexes in [an],...,[a1] and [c]. In terms of typing, if + Γ ⊢ a{_n}..a₁ : Δ and Γ, Δ, Γ' ⊢ c : T with |Γ'|=k, then + Γ, Γ' ⊢ [substnl [a₁;...;an] k c] : [substnl [a₁;...;an] k T]. *) +val substnl : substl -> int -> constr -> constr + +(** [substl σ c] is a short-hand for [substnl σ 0 c] *) +val substl : substl -> constr -> constr + +(** [substl a c] is a short-hand for [substnl [a] 0 c] *) val subst1 : constr -> constr -> constr -val substnl_decl : constr list -> int -> rel_declaration -> rel_declaration -val substl_decl : constr list -> rel_declaration -> rel_declaration -val subst1_decl : constr -> rel_declaration -> rel_declaration +(** [substnl_decl [a₁;...;an] k Ω] substitutes in parallel [a₁], ..., [an] + for respectively [Rel(k+1)], ..., [Rel(k+n)] in [Ω]; it relocates + accordingly indexes in [a₁],...,[an] and [c]. In terms of typing, if + Γ ⊢ a{_n}..a₁ : Δ and Γ, Δ, Γ', Ω ⊢ with |Γ'|=[k], then + Γ, Γ', [substnl_decl [a₁;...;an]] k Ω ⊢. *) +val substnl_decl : substl -> int -> Context.Rel.Declaration.t -> Context.Rel.Declaration.t -val substnl_named_decl : constr list -> int -> named_declaration -> named_declaration -val subst1_named_decl : constr -> named_declaration -> named_declaration -val substl_named_decl : constr list -> named_declaration -> named_declaration +(** [substl_decl σ Ω] is a short-hand for [substnl_decl σ 0 Ω] *) +val substl_decl : substl -> Context.Rel.Declaration.t -> Context.Rel.Declaration.t +(** [subst1_decl a Ω] is a short-hand for [substnl_decl [a] 0 Ω] *) +val subst1_decl : constr -> Context.Rel.Declaration.t -> Context.Rel.Declaration.t + +(** [replace_vars k [(id₁,c₁);...;(idn,cn)] t] substitutes [Var idj] by + [cj] in [t]. *) val replace_vars : (Id.t * constr) list -> constr -> constr -(** (subst_var str t) substitute (VAR str) by (Rel 1) in t *) -val subst_var : Id.t -> constr -> constr -(** [subst_vars [id1;...;idn] t] substitute [VAR idj] by [Rel j] in [t] - if two names are identical, the one of least indice is kept *) +(** [substn_vars k [id₁;...;idn] t] substitutes [Var idj] by [Rel j+k-1] in [t]. + If two names are identical, the one of least index is kept. In terms of + typing, if Γ,x{_n}:U{_n},...,x₁:U₁,Γ' ⊢ t:T, together with id{_j}:T{_j} and + Γ,x{_n}:U{_n},...,x₁:U₁,Γ' ⊢ T{_j}\[id{_j+1}..id{_n}:=x{_j+1}..x{_n}\] ≡ Uj, + then Γ\\{id₁,...,id{_n}\},x{_n}:U{_n},...,x₁:U₁,Γ' ⊢ [substn_vars + (|Γ'|+1) [id₁;...;idn] t] : [substn_vars (|Γ'|+1) [id₁;...;idn] + T]. *) +val substn_vars : int -> Id.t list -> constr -> constr + +(** [subst_vars [id1;...;idn] t] is a short-hand for [substn_vars + [id1;...;idn] 1 t]: it substitutes [Var idj] by [Rel j] in [t]. If + two names are identical, the one of least index is kept. *) val subst_vars : Id.t list -> constr -> constr -(** [substn_vars n [id1;...;idk] t] substitute [VAR idj] by [Rel j+n-1] in [t] - if two names are identical, the one of least indice is kept *) -val substn_vars : int -> Id.t list -> constr -> constr +(** [subst_var id t] is a short-hand for [substn_vars [id] 1 t]: it + substitutes [Var id] by [Rel 1] in [t]. *) +val subst_var : Id.t -> constr -> constr (** {3 Substitution of universes} *) @@ -82,11 +134,11 @@ val subst_univs_constr : universe_subst -> constr -> constr (** Level substitutions for polymorphism. *) val subst_univs_level_constr : universe_level_subst -> constr -> constr -val subst_univs_level_context : Univ.universe_level_subst -> rel_context -> rel_context +val subst_univs_level_context : Univ.universe_level_subst -> Context.Rel.t -> Context.Rel.t (** Instance substitution for polymorphism. *) val subst_instance_constr : universe_instance -> constr -> constr -val subst_instance_context : universe_instance -> rel_context -> rel_context +val subst_instance_context : universe_instance -> Context.Rel.t -> Context.Rel.t type id_key = constant tableKey val eq_id_key : id_key -> id_key -> bool |