Module `Term`

Derived constructors

val mkArrow : Constr.types -> Sorts.relevance -> Constr.types -> Constr.constr: non-dependent product t1 -> t2, an alias for forall (_:t1), t2. Beware t_2 is NOT lifted. Eg: in context A:Prop, A->A is built by (mkArrow (mkRel 1) (mkRel 2))

val mkArrowR : Constr.types -> Constr.types -> Constr.constr: For an always-relevant domain

val mkNamedLambda : Names.Id.t Context.binder_annot -> Constr.types -> Constr.constr -> Constr.constr: Named version of the functions from Term.

val mkNamedLetIn : Names.Id.t Context.binder_annot -> Constr.constr -> Constr.types -> Constr.constr -> Constr.constr
val mkNamedProd : Names.Id.t Context.binder_annot -> Constr.types -> Constr.types -> Constr.types
val mkProd_or_LetIn : Constr.rel_declaration -> Constr.types -> Constr.types: Constructs either (x:t)c or [x=b:t]c

val mkProd_wo_LetIn : Constr.rel_declaration -> Constr.types -> Constr.types
val mkNamedProd_or_LetIn : Constr.named_declaration -> Constr.types -> Constr.types
val mkNamedProd_wo_LetIn : Constr.named_declaration -> Constr.types -> Constr.types
val mkLambda_or_LetIn : Constr.rel_declaration -> Constr.constr -> Constr.constr: Constructs either [x:t]c or [x=b:t]c

val mkNamedLambda_or_LetIn : Constr.named_declaration -> Constr.constr -> Constr.constr

Other term constructors.

val applist : (Constr.constr * Constr.constr list) -> Constr.constr
val applistc : Constr.constr -> Constr.constr list -> Constr.constr
val appvect : (Constr.constr * Constr.constr array) -> Constr.constr
val appvectc : Constr.constr -> Constr.constr array -> Constr.constr
val prodn : int -> (Names.Name.t Context.binder_annot * Constr.constr) list -> Constr.constr -> Constr.constr: prodn n l b = forall (x_1:T_1)...(x_n:T_n), b where l is (x_n,T_n)...(x_1,T_1)....

val compose_prod : (Names.Name.t Context.binder_annot * Constr.constr) list -> Constr.constr -> Constr.constr

compose_prod l b

returns: forall (x_1:T_1)...(x_n:T_n), b where l is (x_n,T_n)...(x_1,T_1). Inverse of decompose_prod.

val lamn : int -> (Names.Name.t Context.binder_annot * Constr.constr) list -> Constr.constr -> Constr.constr

lamn n l b

returns: fun (x_1:T_1)...(x_n:T_n) => b where l is (x_n,T_n)...(x_1,T_1)....

val compose_lam : (Names.Name.t Context.binder_annot * Constr.constr) list -> Constr.constr -> Constr.constr

compose_lam l b

returns: fun (x_1:T_1)...(x_n:T_n) => b where l is (x_n,T_n)...(x_1,T_1). Inverse of it_destLam

val to_lambda : int -> Constr.constr -> Constr.constr

to_lambda n l

returns: fun (x_1:T_1)...(x_n:T_n) => T where l is forall (x_1:T_1)...(x_n:T_n), T

val to_prod : int -> Constr.constr -> Constr.constr

to_prod n l

returns: forall (x_1:T_1)...(x_n:T_n), T where l is fun (x_1:T_1)...(x_n:T_n) => T

val it_mkLambda_or_LetIn : Constr.constr -> Constr.rel_context -> Constr.constr
val it_mkProd_or_LetIn : Constr.types -> Constr.rel_context -> Constr.types
val lambda_applist : Constr.constr -> Constr.constr list -> Constr.constr: In lambda_applist c args, c is supposed to have the form λΓ.c with Γ without let-in; it returns c with the variables of Γ instantiated by args.

val lambda_appvect : Constr.constr -> Constr.constr array -> Constr.constr
val lambda_applist_assum : int -> Constr.constr -> Constr.constr list -> Constr.constr: In lambda_applist_assum n c args, c is supposed to have the form λΓ.c with Γ of length n and possibly with let-ins; it returns c with the assumptions of Γ instantiated by args and the local definitions of Γ expanded.

val lambda_appvect_assum : int -> Constr.constr -> Constr.constr array -> Constr.constr

val prod_appvect : Constr.types -> Constr.constr array -> Constr.types

prod_appvect forall (x1:B1;...;xn:Bn), B a1...an

returns: B[a1...an]

val prod_applist : Constr.types -> Constr.constr list -> Constr.types
val prod_appvect_assum : int -> Constr.types -> Constr.constr array -> Constr.types: In prod_appvect_assum n c args, c is supposed to have the form ∀Γ.c with Γ of length n and possibly with let-ins; it returns c with the assumptions of Γ instantiated by args and the local definitions of Γ expanded.

val prod_applist_assum : int -> Constr.types -> Constr.constr list -> Constr.types

Other term destructors.

val decompose_prod : Constr.constr -> (Names.Name.t Context.binder_annot * Constr.constr) list * Constr.constr: Transforms a product term $ (x_1:T_1)..(x_n:T_n)T $ into the pair $ ((x_n,T_n);...;(x_1,T_1),T) $ , where $ T $ is not a product.

val decompose_lam : Constr.constr -> (Names.Name.t Context.binder_annot * Constr.constr) list * Constr.constr: Transforms a lambda term $ x_1:T_1..x_n:T_nT $ into the pair $ ((x_n,T_n);...;(x_1,T_1),T) $ , where $ T $ is not a lambda.

val decompose_prod_n : int -> Constr.constr -> (Names.Name.t Context.binder_annot * Constr.constr) list * Constr.constr: Given a positive integer n, decompose a product term $ (x_1:T_1)..(x_n:T_n)T $ into the pair $ ((xn,Tn);...;(x1,T1),T) $ . Raise a user error if not enough products.

val decompose_lam_n : int -> Constr.constr -> (Names.Name.t Context.binder_annot * Constr.constr) list * Constr.constr: Given a positive integer $ n $ , decompose a lambda term $ x_1:T_1..x_n:T_nT $ into the pair $ ((x_n,T_n);...;(x_1,T_1),T) $ . Raise a user error if not enough lambdas.

val decompose_prod_assum : Constr.types -> Constr.rel_context * Constr.types: Extract the premisses and the conclusion of a term of the form "(xi:Ti) ... (xj:=cj:Tj) ..., T" where T is not a product nor a let

val decompose_lam_assum : Constr.constr -> Constr.rel_context * Constr.constr: Idem with lambda's and let's

val decompose_prod_n_assum : int -> Constr.types -> Constr.rel_context * Constr.types: Idem but extract the first n premisses, counting let-ins.

val decompose_lam_n_assum : int -> Constr.constr -> Constr.rel_context * Constr.constr: Idem for lambdas, _not_ counting let-ins

val decompose_lam_n_decls : int -> Constr.constr -> Constr.rel_context * Constr.constr: Idem, counting let-ins

val prod_assum : Constr.types -> Constr.rel_context: Return the premisses/parameters of a type/term (let-in included)

val lam_assum : Constr.constr -> Constr.rel_context
val prod_n_assum : int -> Constr.types -> Constr.rel_context: Return the first n-th premisses/parameters of a type (let included and counted)

val lam_n_assum : int -> Constr.constr -> Constr.rel_context: Return the first n-th premisses/parameters of a term (let included but not counted)

val strip_prod : Constr.types -> Constr.types: Remove the premisses/parameters of a type/term

val strip_lam : Constr.constr -> Constr.constr
val strip_prod_n : int -> Constr.types -> Constr.types: Remove the first n-th premisses/parameters of a type/term

val strip_lam_n : int -> Constr.constr -> Constr.constr
val strip_prod_assum : Constr.types -> Constr.types: Remove the premisses/parameters of a type/term (including let-in)

val strip_lam_assum : Constr.constr -> Constr.constr

...

type arity = Constr.rel_context * Sorts.t

val mkArity : arity -> Constr.types: Build an "arity" from its canonical form

val destArity : Constr.types -> arity: Destruct an "arity" into its canonical form

val isArity : Constr.types -> bool: Tell if a term has the form of an arity

type sorts_family = Sorts.family = | InSProp | InProp | InSet | InType
type sorts = private Sorts.t = | SProp | Prop | Set | Type of Univ.Universe.t Type

`\|` `SProp`
`\|` `Prop`
`\|` `Set`
`\|` `Type of Univ.Universe.t`	Type