boolSyntax.sep_type

STRUCTURE

SYNOPSIS

Calculates a pair of substitutions (theta1, theta2) such that instantiating the first argument with theta1 equals the second argument instatiated with theta2.

DESCRIPTION

If sep_type_unify ty1 ty2 succeeds, then

    type_subst (sep_type_unify ty1 ty2 |> fst) ty1 =
      type_subst (sep_type_unify ty1 ty2 |> snd) ty2

FAILURE

If no such substitution can be found.

EXAMPLE

- let val alpha_list = Type `:'a list`
  in
     sep_type_unify alpha alpha_list
  end;
> val it = ([{redex = “:α”, residue = “:α list”}], []):
   (hol_type, hol_type) Lib.subst * (hol_type, hol_type) subst

- let val ty1 = Type `:'a -> 'b -> 'b`
      val ty2 = Type `:'a list -> 'b list -> 'a list`
  in
    sep_type_unify ty1 ty2
  end;
> val it =
   ([{redex = “:β”, residue = “:α list”},
     {redex = “:α”, residue = “:α list”}], [{redex = “:β”, residue = “:α”}]):
   (hol_type, hol_type) Lib.subst * (hol_type, hol_type) subst

Note that in these examples, type_unify would fail due to an occurs check:

- let val ty1 = Type `:'a -> 'b -> 'b`
      val ty2 = Type `:'a list -> 'b list -> 'a list`
  in
    type_unify ty1 ty2
  end;

  Exception raised at boolSyntax.type_unify:
  occurs check
  Exception-
     HOL_ERR
       {message = "occurs check", origin_function = "type_unify",
        origin_structure = "boolSyntax"} raised

COMMENTS

sep_type_unify is similar to type_unify, but does not run into problems with occurs checks. It first renames all type variables, then attempt to unify the argument types, returning two separate substitutions as a result.

SEEALSO

type_unify, type_subst, inst