(* Title: HOL/Prolog/Type.thy
ID: $Id$
Author: David von Oheimb (based on a lecture on Lambda Prolog by Nadathur)
License: GPL (GNU GENERAL PUBLIC LICENSE)
type inference
*)
Type = Func +
types ty
arities ty :: type
consts bool :: ty
nat :: ty
"->" :: ty => ty => ty (infixr 20)
typeof :: [tm, ty] => bool
anyterm :: tm
rules common_typeof "
typeof (app M N) B :- typeof M (A -> B) & typeof N A..
typeof (cond C L R) A :- typeof C bool & typeof L A & typeof R A..
typeof (fix F) A :- (!x. typeof x A => typeof (F x) A)..
typeof true bool..
typeof false bool..
typeof (M and N) bool :- typeof M bool & typeof N bool..
typeof (M eq N) bool :- typeof M T & typeof N T ..
typeof Z nat..
typeof (S N) nat :- typeof N nat..
typeof (M + N) nat :- typeof M nat & typeof N nat..
typeof (M - N) nat :- typeof M nat & typeof N nat..
typeof (M * N) nat :- typeof M nat & typeof N nat"
rules good_typeof "
typeof (abs Bo) (A -> B) :- (!x. typeof x A => typeof (Bo x) B)"
rules bad1_typeof "
typeof (abs Bo) (A -> B) :- (typeof varterm A => typeof (Bo varterm) B)"
rules bad2_typeof "
typeof (abs Bo) (A -> B) :- (typeof anyterm A => typeof (Bo anyterm) B)"
end