wenzelm@9536
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(* Title: Pure/term.ML
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clasohm@0
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ID: $Id$
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wenzelm@9536
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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clasohm@0
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Copyright Cambridge University 1992
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clasohm@1364
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wenzelm@4444
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Simply typed lambda-calculus: types, terms, and basic operations.
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clasohm@0
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*)
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clasohm@0
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clasohm@1364
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infix 9 $;
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clasohm@1364
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infixr 5 -->;
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wenzelm@4444
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infixr --->;
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wenzelm@4444
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infix aconv;
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clasohm@0
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wenzelm@4444
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signature BASIC_TERM =
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wenzelm@4444
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sig
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wenzelm@4444
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type indexname
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wenzelm@4444
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type class
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wenzelm@4444
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type sort
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wenzelm@14829
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type arity
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wenzelm@4444
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datatype typ =
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wenzelm@4444
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Type of string * typ list |
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wenzelm@4444
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TFree of string * sort |
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wenzelm@4444
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TVar of indexname * sort
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wenzelm@16537
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datatype term =
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wenzelm@16537
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Const of string * typ |
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wenzelm@16537
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Free of string * typ |
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wenzelm@16537
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Var of indexname * typ |
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wenzelm@16537
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Bound of int |
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wenzelm@16537
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Abs of string * typ * term |
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wenzelm@16537
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op $ of term * term
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wenzelm@16537
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exception TYPE of string * typ list * term list
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wenzelm@16537
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exception TERM of string * term list
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wenzelm@4444
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val --> : typ * typ -> typ
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wenzelm@4444
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val ---> : typ list * typ -> typ
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wenzelm@4444
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val is_TVar: typ -> bool
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paulson@15573
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val is_funtype: typ -> bool
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wenzelm@4444
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val domain_type: typ -> typ
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wenzelm@4480
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val range_type: typ -> typ
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wenzelm@4444
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val binder_types: typ -> typ list
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wenzelm@4444
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val body_type: typ -> typ
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wenzelm@4444
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val strip_type: typ -> typ list * typ
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nipkow@7318
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val is_Bound: term -> bool
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wenzelm@4444
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val is_Const: term -> bool
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wenzelm@4444
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val is_Free: term -> bool
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wenzelm@4444
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val is_Var: term -> bool
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paulson@15573
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val is_first_order: term -> bool
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paulson@6033
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val dest_Type: typ -> string * typ list
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dixon@15914
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val dest_TVar: typ -> indexname * sort
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dixon@15914
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val dest_TFree: typ -> string * sort
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wenzelm@4444
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val dest_Const: term -> string * typ
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wenzelm@4444
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val dest_Free: term -> string * typ
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wenzelm@4444
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val dest_Var: term -> indexname * typ
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wenzelm@4444
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val type_of: term -> typ
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wenzelm@4444
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val type_of1: typ list * term -> typ
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wenzelm@4444
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val fastype_of: term -> typ
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wenzelm@4444
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val fastype_of1: typ list * term -> typ
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wenzelm@10806
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val list_abs: (string * typ) list * term -> term
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wenzelm@4444
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val strip_abs_body: term -> term
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wenzelm@4444
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val strip_abs_vars: term -> (string * typ) list
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wenzelm@4444
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val strip_qnt_body: string -> term -> term
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wenzelm@4444
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val strip_qnt_vars: string -> term -> (string * typ) list
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wenzelm@4444
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val list_comb: term * term list -> term
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wenzelm@4444
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val strip_comb: term -> term * term list
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wenzelm@4444
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val head_of: term -> term
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wenzelm@4444
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val size_of_term: term -> int
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wenzelm@4444
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val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
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wenzelm@4444
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val map_type_tfree: (string * sort -> typ) -> typ -> typ
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wenzelm@4444
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val map_term_types: (typ -> typ) -> term -> term
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wenzelm@4444
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val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
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wenzelm@16537
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structure Vartab: TABLE
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wenzelm@16537
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structure Typtab: TABLE
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wenzelm@16537
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structure Termtab: TABLE
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wenzelm@16537
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val aconv: term * term -> bool
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wenzelm@16537
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val aconvs: term list * term list -> bool
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wenzelm@4444
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val foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a
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wenzelm@8609
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val foldl_term_types: (term -> 'a * typ -> 'a) -> 'a * term -> 'a
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wenzelm@4444
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val foldl_types: ('a * typ -> 'a) -> 'a * term -> 'a
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wenzelm@4444
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val foldl_aterms: ('a * term -> 'a) -> 'a * term -> 'a
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wenzelm@6548
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val foldl_map_aterms: ('a * term -> 'a * term) -> 'a * term -> 'a * term
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wenzelm@15025
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val add_term_varnames: indexname list * term -> indexname list
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wenzelm@15025
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val term_varnames: term -> indexname list
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wenzelm@4444
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val dummyT: typ
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wenzelm@4444
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val itselfT: typ -> typ
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wenzelm@4444
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val a_itselfT: typ
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wenzelm@4444
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val propT: typ
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wenzelm@4444
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val implies: term
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wenzelm@4444
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val all: typ -> term
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wenzelm@4444
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val equals: typ -> term
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wenzelm@4444
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val strip_all_body: term -> term
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wenzelm@4444
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val strip_all_vars: term -> (string * typ) list
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wenzelm@4444
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val incr_bv: int * int * term -> term
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wenzelm@4444
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val incr_boundvars: int -> term -> term
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wenzelm@4444
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val add_loose_bnos: term * int * int list -> int list
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wenzelm@4444
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val loose_bnos: term -> int list
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wenzelm@4444
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val loose_bvar: term * int -> bool
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wenzelm@4444
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val loose_bvar1: term * int -> bool
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wenzelm@4444
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val subst_bounds: term list * term -> term
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wenzelm@4444
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val subst_bound: term * term -> term
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wenzelm@4444
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val subst_TVars: (indexname * typ) list -> term -> term
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wenzelm@4444
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val betapply: term * term -> term
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wenzelm@4444
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val eq_ix: indexname * indexname -> bool
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wenzelm@4444
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val ins_ix: indexname * indexname list -> indexname list
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wenzelm@4444
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val mem_ix: indexname * indexname list -> bool
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wenzelm@4444
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val mem_term: term * term list -> bool
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wenzelm@4444
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val subset_term: term list * term list -> bool
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wenzelm@4444
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val eq_set_term: term list * term list -> bool
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wenzelm@4444
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val ins_term: term * term list -> term list
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wenzelm@4444
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val union_term: term list * term list -> term list
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paulson@5585
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val inter_term: term list * term list -> term list
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wenzelm@4444
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val could_unify: term * term -> bool
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wenzelm@4444
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val subst_free: (term * term) list -> term -> term
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wenzelm@4444
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val subst_atomic: (term * term) list -> term -> term
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berghofe@15797
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val typ_subst_atomic: (typ * typ) list -> typ -> typ
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wenzelm@4444
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val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
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wenzelm@4444
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val typ_subst_TVars: (indexname * typ) list -> typ -> typ
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wenzelm@4444
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val subst_Vars: (indexname * term) list -> term -> term
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wenzelm@4444
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val incr_tvar: int -> typ -> typ
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wenzelm@4444
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val xless: (string * int) * indexname -> bool
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wenzelm@4444
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val atless: term * term -> bool
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wenzelm@4444
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val insert_aterm: term * term list -> term list
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wenzelm@4444
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val abstract_over: term * term -> term
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wenzelm@11922
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val lambda: term -> term -> term
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wenzelm@4444
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val absfree: string * typ * term -> term
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wenzelm@4444
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val list_abs_free: (string * typ) list * term -> term
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wenzelm@4444
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val list_all_free: (string * typ) list * term -> term
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wenzelm@4444
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val list_all: (string * typ) list * term -> term
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wenzelm@4444
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val maxidx_of_typ: typ -> int
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wenzelm@4444
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val maxidx_of_typs: typ list -> int
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wenzelm@4444
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val maxidx_of_term: term -> int
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berghofe@13665
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val maxidx_of_terms: term list -> int
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wenzelm@4444
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val variant: string list -> string -> string
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wenzelm@4444
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val variantlist: string list * string list -> string list
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wenzelm@16537
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(*note reversed order of args wrt. variant!*)
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wenzelm@4444
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val variant_abs: string * typ * term -> string * term
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wenzelm@4444
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val rename_wrt_term: term -> (string * typ) list -> (string * typ) list
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wenzelm@4444
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val add_new_id: string list * string -> string list
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wenzelm@4444
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val add_typ_classes: typ * class list -> class list
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wenzelm@4444
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val add_typ_ixns: indexname list * typ -> indexname list
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wenzelm@4444
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val add_typ_tfree_names: typ * string list -> string list
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wenzelm@4444
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val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
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wenzelm@4444
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val typ_tfrees: typ -> (string * sort) list
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wenzelm@4444
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val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
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wenzelm@4444
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val typ_tvars: typ -> (indexname * sort) list
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wenzelm@4444
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val add_typ_tycons: typ * string list -> string list
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wenzelm@4444
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val add_typ_varnames: typ * string list -> string list
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wenzelm@4444
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val add_term_classes: term * class list -> class list
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wenzelm@4444
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val add_term_consts: term * string list -> string list
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nipkow@13646
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val term_consts: term -> string list
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obua@16108
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val term_constsT: term -> (string * typ) list
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wenzelm@4444
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val add_term_frees: term * term list -> term list
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wenzelm@4444
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val term_frees: term -> term list
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wenzelm@12802
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val add_term_free_names: term * string list -> string list
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wenzelm@4444
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val add_term_names: term * string list -> string list
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wenzelm@4444
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val add_term_tfree_names: term * string list -> string list
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wenzelm@4444
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val add_term_tfrees: term * (string * sort) list -> (string * sort) list
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wenzelm@4444
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val term_tfrees: term -> (string * sort) list
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wenzelm@4444
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val add_term_tvar_ixns: term * indexname list -> indexname list
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wenzelm@4444
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val add_term_tvarnames: term * string list -> string list
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wenzelm@4444
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val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
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wenzelm@4444
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val term_tvars: term -> (indexname * sort) list
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wenzelm@4444
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val add_term_tycons: term * string list -> string list
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wenzelm@4444
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val add_term_vars: term * term list -> term list
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wenzelm@4444
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val term_vars: term -> term list
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wenzelm@4444
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val exists_Const: (string * typ -> bool) -> term -> bool
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nipkow@4631
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val exists_subterm: (term -> bool) -> term -> bool
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wenzelm@4444
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val compress_type: typ -> typ
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wenzelm@4444
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val compress_term: term -> term
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wenzelm@15986
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val show_question_marks: bool ref
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wenzelm@4444
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end;
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clasohm@0
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wenzelm@4444
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signature TERM =
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wenzelm@4444
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sig
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wenzelm@4444
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include BASIC_TERM
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wenzelm@16537
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val indexname_ord: indexname * indexname -> order
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wenzelm@16537
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val sort_ord: sort * sort -> order
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wenzelm@16537
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val typ_ord: typ * typ -> order
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wenzelm@16537
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val typs_ord: typ list * typ list -> order
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wenzelm@16537
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val term_ord: term * term -> order
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wenzelm@16537
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val terms_ord: term list * term list -> order
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wenzelm@16537
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val hd_ord: term * term -> order
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wenzelm@16537
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val termless: term * term -> bool
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wenzelm@12981
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val match_bvars: (term * term) * (string * string) list -> (string * string) list
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wenzelm@12981
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val rename_abs: term -> term -> term -> term option
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wenzelm@12499
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val invent_names: string list -> string -> int -> string list
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wenzelm@16338
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val map_typ: (string -> string) -> (string -> string) -> typ -> typ
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wenzelm@16338
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val map_term: (string -> string) -> (string -> string) -> (string -> string) -> term -> term
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wenzelm@12499
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val add_tvarsT: (indexname * sort) list * typ -> (indexname * sort) list
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wenzelm@12499
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val add_tvars: (indexname * sort) list * term -> (indexname * sort) list
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wenzelm@12499
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val add_vars: (indexname * typ) list * term -> (indexname * typ) list
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wenzelm@12499
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val add_frees: (string * typ) list * term -> (string * typ) list
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wenzelm@14786
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val no_dummyT: typ -> typ
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wenzelm@9536
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val dummy_patternN: string
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wenzelm@9536
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val no_dummy_patterns: term -> term
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wenzelm@9536
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val replace_dummy_patterns: int * term -> int * term
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wenzelm@10552
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val is_replaced_dummy_pattern: indexname -> bool
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wenzelm@16035
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val show_dummy_patterns: term -> term
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wenzelm@13484
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val adhoc_freeze_vars: term -> term * string list
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wenzelm@14786
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val string_of_vname: indexname -> string
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wenzelm@14786
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val string_of_vname': indexname -> string
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nipkow@15612
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val string_of_term: term -> string
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wenzelm@4444
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end;
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wenzelm@4444
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wenzelm@4444
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structure Term: TERM =
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clasohm@1364
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struct
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clasohm@0
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205 |
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clasohm@0
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206 |
(*Indexnames can be quickly renamed by adding an offset to the integer part,
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clasohm@0
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207 |
for resolution.*)
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wenzelm@16537
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208 |
type indexname = string * int;
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clasohm@0
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209 |
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wenzelm@4626
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(* Types are classified by sorts. *)
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clasohm@0
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211 |
type class = string;
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clasohm@0
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212 |
type sort = class list;
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wenzelm@14829
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type arity = string * sort list * sort;
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clasohm@0
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clasohm@0
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215 |
(* The sorts attached to TFrees and TVars specify the sort of that variable *)
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clasohm@0
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216 |
datatype typ = Type of string * typ list
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clasohm@0
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217 |
| TFree of string * sort
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wenzelm@9536
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218 |
| TVar of indexname * sort;
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clasohm@0
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219 |
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paulson@6033
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220 |
(*Terms. Bound variables are indicated by depth number.
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clasohm@0
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221 |
Free variables, (scheme) variables and constants have names.
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wenzelm@4626
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222 |
An term is "closed" if every bound variable of level "lev"
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wenzelm@13000
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223 |
is enclosed by at least "lev" abstractions.
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clasohm@0
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224 |
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clasohm@0
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225 |
It is possible to create meaningless terms containing loose bound vars
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clasohm@0
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226 |
or type mismatches. But such terms are not allowed in rules. *)
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clasohm@0
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227 |
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wenzelm@13000
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228 |
datatype term =
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clasohm@0
|
229 |
Const of string * typ
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wenzelm@13000
|
230 |
| Free of string * typ
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clasohm@0
|
231 |
| Var of indexname * typ
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clasohm@0
|
232 |
| Bound of int
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clasohm@0
|
233 |
| Abs of string*typ*term
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wenzelm@3965
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234 |
| op $ of term*term;
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clasohm@0
|
235 |
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wenzelm@16537
|
236 |
(*Errors involving type mismatches*)
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clasohm@0
|
237 |
exception TYPE of string * typ list * term list;
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clasohm@0
|
238 |
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wenzelm@16537
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239 |
(*Errors errors involving terms*)
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clasohm@0
|
240 |
exception TERM of string * term list;
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clasohm@0
|
241 |
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clasohm@0
|
242 |
(*Note variable naming conventions!
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clasohm@0
|
243 |
a,b,c: string
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clasohm@0
|
244 |
f,g,h: functions (including terms of function type)
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clasohm@0
|
245 |
i,j,m,n: int
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clasohm@0
|
246 |
t,u: term
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clasohm@0
|
247 |
v,w: indexnames
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clasohm@0
|
248 |
x,y: any
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clasohm@0
|
249 |
A,B,C: term (denoting formulae)
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clasohm@0
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250 |
T,U: typ
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clasohm@0
|
251 |
*)
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clasohm@0
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252 |
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clasohm@0
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253 |
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paulson@6033
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254 |
(** Types **)
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paulson@6033
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255 |
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wenzelm@16537
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256 |
(*dummy type for parsing and printing etc.*)
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wenzelm@16537
|
257 |
val dummyT = Type ("dummy", []);
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wenzelm@16537
|
258 |
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wenzelm@16537
|
259 |
fun no_dummyT typ =
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wenzelm@16537
|
260 |
let
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wenzelm@16537
|
261 |
fun check (T as Type ("dummy", _)) =
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wenzelm@16537
|
262 |
raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
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wenzelm@16537
|
263 |
| check (Type (_, Ts)) = List.app check Ts
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wenzelm@16537
|
264 |
| check _ = ();
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wenzelm@16537
|
265 |
in check typ; typ end;
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wenzelm@16537
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266 |
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paulson@6033
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267 |
fun S --> T = Type("fun",[S,T]);
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paulson@6033
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268 |
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paulson@6033
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269 |
(*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*)
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skalberg@15570
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270 |
val op ---> = Library.foldr (op -->);
|
paulson@6033
|
271 |
|
paulson@6033
|
272 |
fun dest_Type (Type x) = x
|
paulson@6033
|
273 |
| dest_Type T = raise TYPE ("dest_Type", [T], []);
|
dixon@15914
|
274 |
fun dest_TVar (TVar x) = x
|
dixon@15914
|
275 |
| dest_TVar T = raise TYPE ("dest_TVar", [T], []);
|
dixon@15914
|
276 |
fun dest_TFree (TFree x) = x
|
dixon@15914
|
277 |
| dest_TFree T = raise TYPE ("dest_TFree", [T], []);
|
paulson@6033
|
278 |
|
wenzelm@16537
|
279 |
|
clasohm@0
|
280 |
(** Discriminators **)
|
clasohm@0
|
281 |
|
nipkow@7318
|
282 |
fun is_Bound (Bound _) = true
|
nipkow@7318
|
283 |
| is_Bound _ = false;
|
nipkow@7318
|
284 |
|
clasohm@0
|
285 |
fun is_Const (Const _) = true
|
clasohm@0
|
286 |
| is_Const _ = false;
|
clasohm@0
|
287 |
|
clasohm@0
|
288 |
fun is_Free (Free _) = true
|
clasohm@0
|
289 |
| is_Free _ = false;
|
clasohm@0
|
290 |
|
clasohm@0
|
291 |
fun is_Var (Var _) = true
|
clasohm@0
|
292 |
| is_Var _ = false;
|
clasohm@0
|
293 |
|
clasohm@0
|
294 |
fun is_TVar (TVar _) = true
|
clasohm@0
|
295 |
| is_TVar _ = false;
|
clasohm@0
|
296 |
|
paulson@15573
|
297 |
(*Differs from proofterm/is_fun in its treatment of TVar*)
|
paulson@15573
|
298 |
fun is_funtype (Type("fun",[_,_])) = true
|
paulson@15573
|
299 |
| is_funtype _ = false;
|
paulson@15573
|
300 |
|
wenzelm@16537
|
301 |
|
clasohm@0
|
302 |
(** Destructors **)
|
clasohm@0
|
303 |
|
clasohm@0
|
304 |
fun dest_Const (Const x) = x
|
clasohm@0
|
305 |
| dest_Const t = raise TERM("dest_Const", [t]);
|
clasohm@0
|
306 |
|
clasohm@0
|
307 |
fun dest_Free (Free x) = x
|
clasohm@0
|
308 |
| dest_Free t = raise TERM("dest_Free", [t]);
|
clasohm@0
|
309 |
|
clasohm@0
|
310 |
fun dest_Var (Var x) = x
|
clasohm@0
|
311 |
| dest_Var t = raise TERM("dest_Var", [t]);
|
clasohm@0
|
312 |
|
clasohm@0
|
313 |
|
paulson@4464
|
314 |
fun domain_type (Type("fun", [T,_])) = T
|
paulson@4464
|
315 |
and range_type (Type("fun", [_,T])) = T;
|
paulson@4064
|
316 |
|
clasohm@0
|
317 |
(* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*)
|
clasohm@0
|
318 |
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
|
clasohm@0
|
319 |
| binder_types _ = [];
|
clasohm@0
|
320 |
|
clasohm@0
|
321 |
(* maps [T1,...,Tn]--->T to T*)
|
clasohm@0
|
322 |
fun body_type (Type("fun",[S,T])) = body_type T
|
clasohm@0
|
323 |
| body_type T = T;
|
clasohm@0
|
324 |
|
clasohm@0
|
325 |
(* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *)
|
clasohm@0
|
326 |
fun strip_type T : typ list * typ =
|
clasohm@0
|
327 |
(binder_types T, body_type T);
|
clasohm@0
|
328 |
|
clasohm@0
|
329 |
|
clasohm@0
|
330 |
(*Compute the type of the term, checking that combinations are well-typed
|
clasohm@0
|
331 |
Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
|
clasohm@0
|
332 |
fun type_of1 (Ts, Const (_,T)) = T
|
clasohm@0
|
333 |
| type_of1 (Ts, Free (_,T)) = T
|
skalberg@15570
|
334 |
| type_of1 (Ts, Bound i) = (List.nth (Ts,i)
|
skalberg@15570
|
335 |
handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
|
clasohm@0
|
336 |
| type_of1 (Ts, Var (_,T)) = T
|
clasohm@0
|
337 |
| type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
|
wenzelm@13000
|
338 |
| type_of1 (Ts, f$u) =
|
clasohm@0
|
339 |
let val U = type_of1(Ts,u)
|
clasohm@0
|
340 |
and T = type_of1(Ts,f)
|
clasohm@0
|
341 |
in case T of
|
wenzelm@9536
|
342 |
Type("fun",[T1,T2]) =>
|
wenzelm@9536
|
343 |
if T1=U then T2 else raise TYPE
|
wenzelm@9536
|
344 |
("type_of: type mismatch in application", [T1,U], [f$u])
|
wenzelm@13000
|
345 |
| _ => raise TYPE
|
wenzelm@9536
|
346 |
("type_of: function type is expected in application",
|
wenzelm@9536
|
347 |
[T,U], [f$u])
|
clasohm@0
|
348 |
end;
|
clasohm@0
|
349 |
|
clasohm@0
|
350 |
fun type_of t : typ = type_of1 ([],t);
|
clasohm@0
|
351 |
|
clasohm@0
|
352 |
(*Determines the type of a term, with minimal checking*)
|
wenzelm@13000
|
353 |
fun fastype_of1 (Ts, f$u) =
|
lcp@61
|
354 |
(case fastype_of1 (Ts,f) of
|
wenzelm@9536
|
355 |
Type("fun",[_,T]) => T
|
wenzelm@9536
|
356 |
| _ => raise TERM("fastype_of: expected function type", [f$u]))
|
lcp@61
|
357 |
| fastype_of1 (_, Const (_,T)) = T
|
lcp@61
|
358 |
| fastype_of1 (_, Free (_,T)) = T
|
skalberg@15570
|
359 |
| fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
|
skalberg@15570
|
360 |
handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
|
wenzelm@13000
|
361 |
| fastype_of1 (_, Var (_,T)) = T
|
lcp@61
|
362 |
| fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
|
lcp@61
|
363 |
|
lcp@61
|
364 |
fun fastype_of t : typ = fastype_of1 ([],t);
|
clasohm@0
|
365 |
|
clasohm@0
|
366 |
|
skalberg@15570
|
367 |
val list_abs = Library.foldr (fn ((x, T), t) => Abs (x, T, t));
|
wenzelm@10806
|
368 |
|
clasohm@0
|
369 |
(* maps (x1,...,xn)t to t *)
|
wenzelm@13000
|
370 |
fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t
|
clasohm@0
|
371 |
| strip_abs_body u = u;
|
clasohm@0
|
372 |
|
clasohm@0
|
373 |
(* maps (x1,...,xn)t to [x1, ..., xn] *)
|
wenzelm@13000
|
374 |
fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t
|
clasohm@0
|
375 |
| strip_abs_vars u = [] : (string*typ) list;
|
clasohm@0
|
376 |
|
clasohm@0
|
377 |
|
clasohm@0
|
378 |
fun strip_qnt_body qnt =
|
clasohm@0
|
379 |
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
|
clasohm@0
|
380 |
| strip t = t
|
clasohm@0
|
381 |
in strip end;
|
clasohm@0
|
382 |
|
clasohm@0
|
383 |
fun strip_qnt_vars qnt =
|
clasohm@0
|
384 |
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
|
clasohm@0
|
385 |
| strip t = [] : (string*typ) list
|
clasohm@0
|
386 |
in strip end;
|
clasohm@0
|
387 |
|
clasohm@0
|
388 |
|
clasohm@0
|
389 |
(* maps (f, [t1,...,tn]) to f(t1,...,tn) *)
|
skalberg@15570
|
390 |
val list_comb : term * term list -> term = Library.foldl (op $);
|
clasohm@0
|
391 |
|
clasohm@0
|
392 |
|
clasohm@0
|
393 |
(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*)
|
wenzelm@13000
|
394 |
fun strip_comb u : term * term list =
|
clasohm@0
|
395 |
let fun stripc (f$t, ts) = stripc (f, t::ts)
|
wenzelm@13000
|
396 |
| stripc x = x
|
clasohm@0
|
397 |
in stripc(u,[]) end;
|
clasohm@0
|
398 |
|
clasohm@0
|
399 |
|
clasohm@0
|
400 |
(* maps f(t1,...,tn) to f , which is never a combination *)
|
clasohm@0
|
401 |
fun head_of (f$t) = head_of f
|
clasohm@0
|
402 |
| head_of u = u;
|
clasohm@0
|
403 |
|
clasohm@0
|
404 |
|
clasohm@0
|
405 |
(*Number of atoms and abstractions in a term*)
|
clasohm@0
|
406 |
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
|
clasohm@0
|
407 |
| size_of_term (f$t) = size_of_term f + size_of_term t
|
clasohm@0
|
408 |
| size_of_term _ = 1;
|
clasohm@0
|
409 |
|
nipkow@949
|
410 |
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
|
nipkow@949
|
411 |
| map_type_tvar f (T as TFree _) = T
|
nipkow@949
|
412 |
| map_type_tvar f (TVar x) = f x;
|
nipkow@949
|
413 |
|
nipkow@949
|
414 |
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
|
nipkow@949
|
415 |
| map_type_tfree f (TFree x) = f x
|
nipkow@949
|
416 |
| map_type_tfree f (T as TVar _) = T;
|
nipkow@949
|
417 |
|
clasohm@0
|
418 |
(* apply a function to all types in a term *)
|
clasohm@0
|
419 |
fun map_term_types f =
|
clasohm@0
|
420 |
let fun map(Const(a,T)) = Const(a, f T)
|
clasohm@0
|
421 |
| map(Free(a,T)) = Free(a, f T)
|
clasohm@0
|
422 |
| map(Var(v,T)) = Var(v, f T)
|
clasohm@0
|
423 |
| map(t as Bound _) = t
|
clasohm@0
|
424 |
| map(Abs(a,T,t)) = Abs(a, f T, map t)
|
clasohm@0
|
425 |
| map(f$t) = map f $ map t;
|
clasohm@0
|
426 |
in map end;
|
clasohm@0
|
427 |
|
clasohm@0
|
428 |
(* iterate a function over all types in a term *)
|
clasohm@0
|
429 |
fun it_term_types f =
|
clasohm@0
|
430 |
let fun iter(Const(_,T), a) = f(T,a)
|
clasohm@0
|
431 |
| iter(Free(_,T), a) = f(T,a)
|
clasohm@0
|
432 |
| iter(Var(_,T), a) = f(T,a)
|
clasohm@0
|
433 |
| iter(Abs(_,T,t), a) = iter(t,f(T,a))
|
clasohm@0
|
434 |
| iter(f$u, a) = iter(f, iter(u, a))
|
clasohm@0
|
435 |
| iter(Bound _, a) = a
|
clasohm@0
|
436 |
in iter end
|
clasohm@0
|
437 |
|
clasohm@0
|
438 |
|
wenzelm@16537
|
439 |
(** Comparing terms, types etc. **)
|
wenzelm@16537
|
440 |
|
wenzelm@16537
|
441 |
fun indexname_ord ((x, i), (y, j)) =
|
wenzelm@16537
|
442 |
(case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
|
wenzelm@16537
|
443 |
|
wenzelm@16537
|
444 |
val sort_ord = list_ord string_ord;
|
wenzelm@16537
|
445 |
|
wenzelm@16537
|
446 |
|
wenzelm@16537
|
447 |
(* typ_ord *)
|
wenzelm@16537
|
448 |
|
wenzelm@16537
|
449 |
fun typ_ord TU =
|
wenzelm@16537
|
450 |
if pointer_eq TU then EQUAL
|
wenzelm@16537
|
451 |
else
|
wenzelm@16537
|
452 |
(case TU of
|
wenzelm@16537
|
453 |
(Type x, Type y) => prod_ord string_ord typs_ord (x, y)
|
wenzelm@16537
|
454 |
| (Type _, _) => GREATER
|
wenzelm@16537
|
455 |
| (TFree _, Type _) => LESS
|
wenzelm@16537
|
456 |
| (TFree x, TFree y) => prod_ord string_ord sort_ord (x, y)
|
wenzelm@16537
|
457 |
| (TFree _, TVar _) => GREATER
|
wenzelm@16537
|
458 |
| (TVar _, Type _) => LESS
|
wenzelm@16537
|
459 |
| (TVar _, TFree _) => LESS
|
wenzelm@16537
|
460 |
| (TVar x, TVar y) => prod_ord indexname_ord sort_ord (x, y))
|
wenzelm@16537
|
461 |
and typs_ord Ts_Us = list_ord typ_ord Ts_Us;
|
wenzelm@16537
|
462 |
|
wenzelm@16537
|
463 |
|
wenzelm@16537
|
464 |
(* term_ord *)
|
wenzelm@16537
|
465 |
|
wenzelm@16537
|
466 |
(*a linear well-founded AC-compatible ordering for terms:
|
wenzelm@16537
|
467 |
s < t <=> 1. size(s) < size(t) or
|
wenzelm@16537
|
468 |
2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
|
wenzelm@16537
|
469 |
3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
|
wenzelm@16537
|
470 |
(s1..sn) < (t1..tn) (lexicographically)*)
|
wenzelm@16537
|
471 |
|
wenzelm@16537
|
472 |
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
|
wenzelm@16537
|
473 |
| dest_hd (Free (a, T)) = (((a, 0), T), 1)
|
wenzelm@16537
|
474 |
| dest_hd (Var v) = (v, 2)
|
wenzelm@16537
|
475 |
| dest_hd (Bound i) = ((("", i), dummyT), 3)
|
wenzelm@16537
|
476 |
| dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
|
wenzelm@16537
|
477 |
|
wenzelm@16537
|
478 |
fun term_ord tu =
|
wenzelm@16537
|
479 |
if pointer_eq tu then EQUAL
|
wenzelm@16537
|
480 |
else
|
wenzelm@16537
|
481 |
(case tu of
|
wenzelm@16537
|
482 |
(Abs (_, T, t), Abs(_, U, u)) =>
|
wenzelm@16537
|
483 |
(case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
|
wenzelm@16537
|
484 |
| (t, u) =>
|
wenzelm@16537
|
485 |
(case int_ord (size_of_term t, size_of_term u) of
|
wenzelm@16537
|
486 |
EQUAL =>
|
wenzelm@16537
|
487 |
let
|
wenzelm@16537
|
488 |
val (f, ts) = strip_comb t
|
wenzelm@16537
|
489 |
and (g, us) = strip_comb u
|
wenzelm@16537
|
490 |
in case hd_ord (f, g) of EQUAL => terms_ord (ts, us) | ord => ord end
|
wenzelm@16537
|
491 |
| ord => ord))
|
wenzelm@16537
|
492 |
and hd_ord (f, g) =
|
wenzelm@16537
|
493 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
|
wenzelm@16537
|
494 |
and terms_ord (ts, us) = list_ord term_ord (ts, us);
|
wenzelm@16537
|
495 |
|
wenzelm@16537
|
496 |
fun op aconv tu = (term_ord tu = EQUAL);
|
wenzelm@16537
|
497 |
fun aconvs ts_us = (list_ord term_ord ts_us = EQUAL);
|
wenzelm@16537
|
498 |
fun termless tu = (term_ord tu = LESS);
|
wenzelm@16537
|
499 |
|
wenzelm@16537
|
500 |
structure Vartab = TableFun(type key = indexname val ord = indexname_ord);
|
wenzelm@16537
|
501 |
structure Typtab = TableFun(type key = typ val ord = typ_ord);
|
wenzelm@16537
|
502 |
structure Termtab = TableFun(type key = term val ord = term_ord);
|
wenzelm@16537
|
503 |
|
wenzelm@16537
|
504 |
|
clasohm@0
|
505 |
(** Connectives of higher order logic **)
|
clasohm@0
|
506 |
|
wenzelm@375
|
507 |
fun itselfT ty = Type ("itself", [ty]);
|
wenzelm@14854
|
508 |
val a_itselfT = itselfT (TFree ("'a", []));
|
wenzelm@375
|
509 |
|
clasohm@0
|
510 |
val propT : typ = Type("prop",[]);
|
clasohm@0
|
511 |
|
clasohm@0
|
512 |
val implies = Const("==>", propT-->propT-->propT);
|
clasohm@0
|
513 |
|
clasohm@0
|
514 |
fun all T = Const("all", (T-->propT)-->propT);
|
clasohm@0
|
515 |
|
clasohm@0
|
516 |
fun equals T = Const("==", T-->T-->propT);
|
clasohm@0
|
517 |
|
clasohm@0
|
518 |
(* maps !!x1...xn. t to t *)
|
wenzelm@13000
|
519 |
fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t
|
clasohm@0
|
520 |
| strip_all_body t = t;
|
clasohm@0
|
521 |
|
clasohm@0
|
522 |
(* maps !!x1...xn. t to [x1, ..., xn] *)
|
clasohm@0
|
523 |
fun strip_all_vars (Const("all",_)$Abs(a,T,t)) =
|
wenzelm@13000
|
524 |
(a,T) :: strip_all_vars t
|
clasohm@0
|
525 |
| strip_all_vars t = [] : (string*typ) list;
|
clasohm@0
|
526 |
|
clasohm@0
|
527 |
(*increments a term's non-local bound variables
|
clasohm@0
|
528 |
required when moving a term within abstractions
|
clasohm@0
|
529 |
inc is increment for bound variables
|
clasohm@0
|
530 |
lev is level at which a bound variable is considered 'loose'*)
|
wenzelm@13000
|
531 |
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
|
clasohm@0
|
532 |
| incr_bv (inc, lev, Abs(a,T,body)) =
|
wenzelm@9536
|
533 |
Abs(a, T, incr_bv(inc,lev+1,body))
|
wenzelm@13000
|
534 |
| incr_bv (inc, lev, f$t) =
|
clasohm@0
|
535 |
incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
|
clasohm@0
|
536 |
| incr_bv (inc, lev, u) = u;
|
clasohm@0
|
537 |
|
clasohm@0
|
538 |
fun incr_boundvars 0 t = t
|
clasohm@0
|
539 |
| incr_boundvars inc t = incr_bv(inc,0,t);
|
clasohm@0
|
540 |
|
wenzelm@12981
|
541 |
(*Scan a pair of terms; while they are similar,
|
wenzelm@12981
|
542 |
accumulate corresponding bound vars in "al"*)
|
wenzelm@12981
|
543 |
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
|
wenzelm@12981
|
544 |
match_bvs(s, t, if x="" orelse y="" then al
|
wenzelm@12981
|
545 |
else (x,y)::al)
|
wenzelm@12981
|
546 |
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
|
wenzelm@12981
|
547 |
| match_bvs(_,_,al) = al;
|
wenzelm@12981
|
548 |
|
wenzelm@12981
|
549 |
(* strip abstractions created by parameters *)
|
wenzelm@12981
|
550 |
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
|
wenzelm@12981
|
551 |
|
wenzelm@12981
|
552 |
fun rename_abs pat obj t =
|
wenzelm@12981
|
553 |
let
|
wenzelm@12981
|
554 |
val ren = match_bvs (pat, obj, []);
|
wenzelm@12981
|
555 |
fun ren_abs (Abs (x, T, b)) =
|
skalberg@15570
|
556 |
Abs (getOpt (assoc_string (ren, x), x), T, ren_abs b)
|
wenzelm@12981
|
557 |
| ren_abs (f $ t) = ren_abs f $ ren_abs t
|
wenzelm@12981
|
558 |
| ren_abs t = t
|
skalberg@15531
|
559 |
in if null ren then NONE else SOME (ren_abs t) end;
|
clasohm@0
|
560 |
|
clasohm@0
|
561 |
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
|
clasohm@0
|
562 |
(Bound 0) is loose at level 0 *)
|
wenzelm@13000
|
563 |
fun add_loose_bnos (Bound i, lev, js) =
|
wenzelm@9536
|
564 |
if i<lev then js else (i-lev) ins_int js
|
clasohm@0
|
565 |
| add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
|
clasohm@0
|
566 |
| add_loose_bnos (f$t, lev, js) =
|
wenzelm@13000
|
567 |
add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
|
clasohm@0
|
568 |
| add_loose_bnos (_, _, js) = js;
|
clasohm@0
|
569 |
|
clasohm@0
|
570 |
fun loose_bnos t = add_loose_bnos (t, 0, []);
|
clasohm@0
|
571 |
|
clasohm@0
|
572 |
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
|
clasohm@0
|
573 |
level k or beyond. *)
|
clasohm@0
|
574 |
fun loose_bvar(Bound i,k) = i >= k
|
clasohm@0
|
575 |
| loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
|
clasohm@0
|
576 |
| loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
|
clasohm@0
|
577 |
| loose_bvar _ = false;
|
clasohm@0
|
578 |
|
nipkow@2792
|
579 |
fun loose_bvar1(Bound i,k) = i = k
|
nipkow@2792
|
580 |
| loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
|
nipkow@2792
|
581 |
| loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
|
nipkow@2792
|
582 |
| loose_bvar1 _ = false;
|
clasohm@0
|
583 |
|
clasohm@0
|
584 |
(*Substitute arguments for loose bound variables.
|
clasohm@0
|
585 |
Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
|
wenzelm@4626
|
586 |
Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
|
wenzelm@9536
|
587 |
and the appropriate call is subst_bounds([b,a], c) .
|
clasohm@0
|
588 |
Loose bound variables >=n are reduced by "n" to
|
clasohm@0
|
589 |
compensate for the disappearance of lambdas.
|
clasohm@0
|
590 |
*)
|
wenzelm@13000
|
591 |
fun subst_bounds (args: term list, t) : term =
|
clasohm@0
|
592 |
let val n = length args;
|
clasohm@0
|
593 |
fun subst (t as Bound i, lev) =
|
wenzelm@9536
|
594 |
(if i<lev then t (*var is locally bound*)
|
wenzelm@9536
|
595 |
else incr_boundvars lev (List.nth(args, i-lev))
|
wenzelm@9536
|
596 |
handle Subscript => Bound(i-n) (*loose: change it*))
|
wenzelm@9536
|
597 |
| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1))
|
wenzelm@9536
|
598 |
| subst (f$t, lev) = subst(f,lev) $ subst(t,lev)
|
wenzelm@9536
|
599 |
| subst (t,lev) = t
|
clasohm@0
|
600 |
in case args of [] => t | _ => subst (t,0) end;
|
clasohm@0
|
601 |
|
paulson@2192
|
602 |
(*Special case: one argument*)
|
wenzelm@13000
|
603 |
fun subst_bound (arg, t) : term =
|
paulson@2192
|
604 |
let fun subst (t as Bound i, lev) =
|
wenzelm@9536
|
605 |
if i<lev then t (*var is locally bound*)
|
wenzelm@9536
|
606 |
else if i=lev then incr_boundvars lev arg
|
wenzelm@9536
|
607 |
else Bound(i-1) (*loose: change it*)
|
wenzelm@9536
|
608 |
| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1))
|
wenzelm@9536
|
609 |
| subst (f$t, lev) = subst(f,lev) $ subst(t,lev)
|
wenzelm@9536
|
610 |
| subst (t,lev) = t
|
paulson@2192
|
611 |
in subst (t,0) end;
|
paulson@2192
|
612 |
|
clasohm@0
|
613 |
(*beta-reduce if possible, else form application*)
|
paulson@2192
|
614 |
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
|
clasohm@0
|
615 |
| betapply (f,u) = f$u;
|
clasohm@0
|
616 |
|
wenzelm@14786
|
617 |
|
paulson@2192
|
618 |
(** Equality, membership and insertion of indexnames (string*ints) **)
|
paulson@2192
|
619 |
|
paulson@2192
|
620 |
(*optimized equality test for indexnames. Yields a huge gain under Poly/ML*)
|
wenzelm@2959
|
621 |
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
|
paulson@2192
|
622 |
|
paulson@2192
|
623 |
(*membership in a list, optimized version for indexnames*)
|
wenzelm@2959
|
624 |
fun mem_ix (_, []) = false
|
paulson@2192
|
625 |
| mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
|
paulson@2192
|
626 |
|
paulson@2192
|
627 |
(*insertion into list, optimized version for indexnames*)
|
paulson@2192
|
628 |
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
|
paulson@2192
|
629 |
|
clasohm@0
|
630 |
|
paulson@2176
|
631 |
(** Membership, insertion, union for terms **)
|
paulson@2176
|
632 |
|
paulson@2176
|
633 |
fun mem_term (_, []) = false
|
paulson@2176
|
634 |
| mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
|
paulson@2176
|
635 |
|
paulson@2182
|
636 |
fun subset_term ([], ys) = true
|
paulson@2182
|
637 |
| subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
|
paulson@2182
|
638 |
|
paulson@2182
|
639 |
fun eq_set_term (xs, ys) =
|
paulson@2182
|
640 |
xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
|
paulson@2182
|
641 |
|
paulson@2176
|
642 |
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
|
paulson@2176
|
643 |
|
paulson@2176
|
644 |
fun union_term (xs, []) = xs
|
paulson@2176
|
645 |
| union_term ([], ys) = ys
|
paulson@2176
|
646 |
| union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
|
paulson@2176
|
647 |
|
paulson@5585
|
648 |
fun inter_term ([], ys) = []
|
paulson@5585
|
649 |
| inter_term (x::xs, ys) =
|
paulson@5585
|
650 |
if mem_term (x,ys) then x :: inter_term(xs,ys) else inter_term(xs,ys);
|
paulson@5585
|
651 |
|
wenzelm@13000
|
652 |
(*A fast unification filter: true unless the two terms cannot be unified.
|
clasohm@0
|
653 |
Terms must be NORMAL. Treats all Vars as distinct. *)
|
clasohm@0
|
654 |
fun could_unify (t,u) =
|
clasohm@0
|
655 |
let fun matchrands (f$t, g$u) = could_unify(t,u) andalso matchrands(f,g)
|
wenzelm@9536
|
656 |
| matchrands _ = true
|
clasohm@0
|
657 |
in case (head_of t , head_of u) of
|
wenzelm@9536
|
658 |
(_, Var _) => true
|
clasohm@0
|
659 |
| (Var _, _) => true
|
clasohm@0
|
660 |
| (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u)
|
clasohm@0
|
661 |
| (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u)
|
clasohm@0
|
662 |
| (Bound i, Bound j) => i=j andalso matchrands(t,u)
|
clasohm@0
|
663 |
| (Abs _, _) => true (*because of possible eta equality*)
|
clasohm@0
|
664 |
| (_, Abs _) => true
|
clasohm@0
|
665 |
| _ => false
|
clasohm@0
|
666 |
end;
|
clasohm@0
|
667 |
|
clasohm@0
|
668 |
(*Substitute new for free occurrences of old in a term*)
|
clasohm@0
|
669 |
fun subst_free [] = (fn t=>t)
|
clasohm@0
|
670 |
| subst_free pairs =
|
wenzelm@13000
|
671 |
let fun substf u =
|
wenzelm@9536
|
672 |
case gen_assoc (op aconv) (pairs, u) of
|
skalberg@15531
|
673 |
SOME u' => u'
|
skalberg@15531
|
674 |
| NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
|
wenzelm@9536
|
675 |
| t$u' => substf t $ substf u'
|
wenzelm@9536
|
676 |
| _ => u)
|
clasohm@0
|
677 |
in substf end;
|
clasohm@0
|
678 |
|
clasohm@0
|
679 |
(*a total, irreflexive ordering on index names*)
|
clasohm@0
|
680 |
fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b);
|
clasohm@0
|
681 |
|
clasohm@0
|
682 |
|
wenzelm@13000
|
683 |
(*Abstraction of the term "body" over its occurrences of v,
|
clasohm@0
|
684 |
which must contain no loose bound variables.
|
clasohm@0
|
685 |
The resulting term is ready to become the body of an Abs.*)
|
clasohm@0
|
686 |
fun abstract_over (v,body) =
|
clasohm@0
|
687 |
let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
|
clasohm@0
|
688 |
(case u of
|
clasohm@0
|
689 |
Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
|
wenzelm@9536
|
690 |
| f$rand => abst(lev,f) $ abst(lev,rand)
|
wenzelm@9536
|
691 |
| _ => u)
|
clasohm@0
|
692 |
in abst(0,body) end;
|
clasohm@0
|
693 |
|
berghofe@13665
|
694 |
fun lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
|
berghofe@13665
|
695 |
| lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
|
berghofe@13665
|
696 |
| lambda v t = raise TERM ("lambda", [v, t]);
|
clasohm@0
|
697 |
|
clasohm@0
|
698 |
(*Form an abstraction over a free variable.*)
|
clasohm@0
|
699 |
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
|
clasohm@0
|
700 |
|
clasohm@0
|
701 |
(*Abstraction over a list of free variables*)
|
clasohm@0
|
702 |
fun list_abs_free ([ ] , t) = t
|
wenzelm@13000
|
703 |
| list_abs_free ((a,T)::vars, t) =
|
clasohm@0
|
704 |
absfree(a, T, list_abs_free(vars,t));
|
clasohm@0
|
705 |
|
clasohm@0
|
706 |
(*Quantification over a list of free variables*)
|
clasohm@0
|
707 |
fun list_all_free ([], t: term) = t
|
wenzelm@13000
|
708 |
| list_all_free ((a,T)::vars, t) =
|
clasohm@0
|
709 |
(all T) $ (absfree(a, T, list_all_free(vars,t)));
|
clasohm@0
|
710 |
|
clasohm@0
|
711 |
(*Quantification over a list of variables (already bound in body) *)
|
clasohm@0
|
712 |
fun list_all ([], t) = t
|
wenzelm@13000
|
713 |
| list_all ((a,T)::vars, t) =
|
clasohm@0
|
714 |
(all T) $ (Abs(a, T, list_all(vars,t)));
|
clasohm@0
|
715 |
|
wenzelm@13000
|
716 |
(*Replace the ATOMIC term ti by ui; instl = [(t1,u1), ..., (tn,un)].
|
clasohm@0
|
717 |
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *)
|
clasohm@0
|
718 |
fun subst_atomic [] t = t : term
|
clasohm@0
|
719 |
| subst_atomic (instl: (term*term) list) t =
|
clasohm@0
|
720 |
let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
|
wenzelm@9536
|
721 |
| subst (f$t') = subst f $ subst t'
|
skalberg@15570
|
722 |
| subst t = getOpt (assoc(instl,t),t)
|
clasohm@0
|
723 |
in subst t end;
|
clasohm@0
|
724 |
|
berghofe@15797
|
725 |
(*Replace the ATOMIC type Ti by Ui; instl = [(T1,U1), ..., (Tn,Un)].*)
|
berghofe@15797
|
726 |
fun typ_subst_atomic [] T = T
|
berghofe@15797
|
727 |
| typ_subst_atomic instl (Type (s, Ts)) =
|
berghofe@15797
|
728 |
Type (s, map (typ_subst_atomic instl) Ts)
|
berghofe@15797
|
729 |
| typ_subst_atomic instl T = getOpt (assoc (instl, T), T);
|
berghofe@15797
|
730 |
|
lcp@728
|
731 |
(*Substitute for type Vars in a type*)
|
clasohm@0
|
732 |
fun typ_subst_TVars iTs T = if null iTs then T else
|
clasohm@0
|
733 |
let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
|
wenzelm@9536
|
734 |
| subst(T as TFree _) = T
|
skalberg@15570
|
735 |
| subst(T as TVar(ixn,_)) = getOpt (assoc(iTs,ixn),T)
|
clasohm@0
|
736 |
in subst T end;
|
clasohm@0
|
737 |
|
lcp@728
|
738 |
(*Substitute for type Vars in a term*)
|
clasohm@0
|
739 |
val subst_TVars = map_term_types o typ_subst_TVars;
|
clasohm@0
|
740 |
|
lcp@728
|
741 |
(*Substitute for Vars in a term; see also envir/norm_term*)
|
clasohm@0
|
742 |
fun subst_Vars itms t = if null itms then t else
|
skalberg@15570
|
743 |
let fun subst(v as Var(ixn,_)) = getOpt (assoc(itms,ixn),v)
|
clasohm@0
|
744 |
| subst(Abs(a,T,t)) = Abs(a,T,subst t)
|
clasohm@0
|
745 |
| subst(f$t) = subst f $ subst t
|
clasohm@0
|
746 |
| subst(t) = t
|
clasohm@0
|
747 |
in subst t end;
|
clasohm@0
|
748 |
|
lcp@728
|
749 |
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
|
clasohm@0
|
750 |
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
|
clasohm@0
|
751 |
let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
|
clasohm@0
|
752 |
| subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
|
clasohm@0
|
753 |
| subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
|
skalberg@15531
|
754 |
NONE => Var(ixn,typ_subst_TVars iTs T)
|
skalberg@15531
|
755 |
| SOME t => t)
|
clasohm@0
|
756 |
| subst(b as Bound _) = b
|
clasohm@0
|
757 |
| subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
|
clasohm@0
|
758 |
| subst(f$t) = subst f $ subst t
|
clasohm@0
|
759 |
in subst end;
|
clasohm@0
|
760 |
|
clasohm@0
|
761 |
|
paulson@15573
|
762 |
(** Identifying first-order terms **)
|
paulson@15573
|
763 |
|
paulson@15573
|
764 |
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
|
paulson@15573
|
765 |
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
|
paulson@15573
|
766 |
|
wenzelm@16537
|
767 |
(*First order means in all terms of the form f(t1,...,tn) no argument has a
|
wenzelm@16537
|
768 |
function type. The meta-quantifier "all" is excluded--its argument always
|
kleing@15962
|
769 |
has a function type--through a recursive call into its body.*)
|
paulson@15573
|
770 |
fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
|
wenzelm@16537
|
771 |
| first_order1 Ts (Const("all",_)$Abs(a,T,body)) =
|
paulson@15954
|
772 |
not (is_funtype T) andalso first_order1 (T::Ts) body
|
paulson@15573
|
773 |
| first_order1 Ts t =
|
paulson@15573
|
774 |
case strip_comb t of
|
wenzelm@16537
|
775 |
(Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
|
wenzelm@16537
|
776 |
| (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
|
wenzelm@16537
|
777 |
| (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
|
wenzelm@16537
|
778 |
| (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
|
wenzelm@16537
|
779 |
| (Abs _, ts) => false (*not in beta-normal form*)
|
wenzelm@16537
|
780 |
| _ => error "first_order: unexpected case";
|
paulson@15573
|
781 |
|
paulson@15573
|
782 |
val is_first_order = first_order1 [];
|
paulson@15573
|
783 |
|
clasohm@0
|
784 |
(*Computing the maximum index of a typ*)
|
paulson@2146
|
785 |
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
|
clasohm@0
|
786 |
| maxidx_of_typ(TFree _) = ~1
|
paulson@2146
|
787 |
| maxidx_of_typ(TVar((_,i),_)) = i
|
paulson@2146
|
788 |
and maxidx_of_typs [] = ~1
|
paulson@2146
|
789 |
| maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
|
clasohm@0
|
790 |
|
clasohm@0
|
791 |
|
clasohm@0
|
792 |
(*Computing the maximum index of a term*)
|
clasohm@0
|
793 |
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
|
clasohm@0
|
794 |
| maxidx_of_term (Bound _) = ~1
|
clasohm@0
|
795 |
| maxidx_of_term (Free(_,T)) = maxidx_of_typ T
|
paulson@2146
|
796 |
| maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
|
paulson@2146
|
797 |
| maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
|
paulson@2146
|
798 |
| maxidx_of_term (f$t) = Int.max(maxidx_of_term f, maxidx_of_term t);
|
clasohm@0
|
799 |
|
skalberg@15570
|
800 |
fun maxidx_of_terms ts = Library.foldl Int.max (~1, map maxidx_of_term ts);
|
berghofe@13665
|
801 |
|
clasohm@0
|
802 |
|
clasohm@0
|
803 |
(* Increment the index of all Poly's in T by k *)
|
nipkow@949
|
804 |
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
|
clasohm@0
|
805 |
|
clasohm@0
|
806 |
|
clasohm@0
|
807 |
(**** Syntax-related declarations ****)
|
clasohm@0
|
808 |
|
clasohm@0
|
809 |
(*** Printing ***)
|
clasohm@0
|
810 |
|
wenzelm@14676
|
811 |
(*Makes a variant of a name distinct from the names in bs.
|
wenzelm@14676
|
812 |
First attaches the suffix and then increments this;
|
wenzelm@12306
|
813 |
preserves a suffix of underscores "_". *)
|
wenzelm@12306
|
814 |
fun variant bs name =
|
wenzelm@12306
|
815 |
let
|
wenzelm@12306
|
816 |
val (c, u) = pairself implode (Library.take_suffix (equal "_") (Symbol.explode name));
|
wenzelm@12902
|
817 |
fun vary2 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_string c) else c;
|
wenzelm@14676
|
818 |
fun vary1 c = if ((c ^ u) mem_string bs) then vary2 (Symbol.bump_init c) else c;
|
wenzelm@12306
|
819 |
in vary1 (if c = "" then "u" else c) ^ u end;
|
clasohm@0
|
820 |
|
clasohm@0
|
821 |
(*Create variants of the list of names, with priority to the first ones*)
|
clasohm@0
|
822 |
fun variantlist ([], used) = []
|
wenzelm@13000
|
823 |
| variantlist(b::bs, used) =
|
clasohm@0
|
824 |
let val b' = variant used b
|
clasohm@0
|
825 |
in b' :: variantlist (bs, b'::used) end;
|
clasohm@0
|
826 |
|
wenzelm@14695
|
827 |
(*Invent fresh names*)
|
wenzelm@14695
|
828 |
fun invent_names _ _ 0 = []
|
wenzelm@14695
|
829 |
| invent_names used a n =
|
wenzelm@14695
|
830 |
let val b = Symbol.bump_string a in
|
wenzelm@14695
|
831 |
if a mem_string used then invent_names used b n
|
wenzelm@14695
|
832 |
else a :: invent_names used b (n - 1)
|
wenzelm@14695
|
833 |
end;
|
wenzelm@11353
|
834 |
|
wenzelm@16537
|
835 |
|
wenzelm@4017
|
836 |
(** Consts etc. **)
|
wenzelm@4017
|
837 |
|
skalberg@15574
|
838 |
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes cs Ts
|
wenzelm@4017
|
839 |
| add_typ_classes (TFree (_, S), cs) = S union cs
|
wenzelm@4017
|
840 |
| add_typ_classes (TVar (_, S), cs) = S union cs;
|
wenzelm@4017
|
841 |
|
wenzelm@16294
|
842 |
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (c ins_string cs) Ts
|
wenzelm@4017
|
843 |
| add_typ_tycons (_, cs) = cs;
|
wenzelm@4017
|
844 |
|
wenzelm@4017
|
845 |
val add_term_classes = it_term_types add_typ_classes;
|
wenzelm@4017
|
846 |
val add_term_tycons = it_term_types add_typ_tycons;
|
wenzelm@4017
|
847 |
|
wenzelm@9319
|
848 |
fun add_term_consts (Const (c, _), cs) = c ins_string cs
|
wenzelm@4017
|
849 |
| add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
|
wenzelm@4017
|
850 |
| add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
|
wenzelm@4017
|
851 |
| add_term_consts (_, cs) = cs;
|
wenzelm@4017
|
852 |
|
obua@16108
|
853 |
fun add_term_constsT (Const c, cs) = c::cs
|
obua@16108
|
854 |
| add_term_constsT (t $ u, cs) = add_term_constsT (t, add_term_constsT (u, cs))
|
obua@16108
|
855 |
| add_term_constsT (Abs (_, _, t), cs) = add_term_constsT (t, cs)
|
obua@16108
|
856 |
| add_term_constsT (_, cs) = cs;
|
obua@16108
|
857 |
|
nipkow@13646
|
858 |
fun term_consts t = add_term_consts(t,[]);
|
nipkow@13646
|
859 |
|
obua@16108
|
860 |
fun term_constsT t = add_term_constsT(t,[]);
|
obua@16108
|
861 |
|
oheimb@4185
|
862 |
fun exists_Const P t = let
|
wenzelm@9536
|
863 |
fun ex (Const c ) = P c
|
wenzelm@9536
|
864 |
| ex (t $ u ) = ex t orelse ex u
|
wenzelm@9536
|
865 |
| ex (Abs (_, _, t)) = ex t
|
wenzelm@9536
|
866 |
| ex _ = false
|
oheimb@4185
|
867 |
in ex t end;
|
wenzelm@4017
|
868 |
|
nipkow@4631
|
869 |
fun exists_subterm P =
|
nipkow@4631
|
870 |
let fun ex t = P t orelse
|
nipkow@4631
|
871 |
(case t of
|
nipkow@4631
|
872 |
u $ v => ex u orelse ex v
|
nipkow@4631
|
873 |
| Abs(_, _, u) => ex u
|
nipkow@4631
|
874 |
| _ => false)
|
nipkow@4631
|
875 |
in ex end;
|
nipkow@4631
|
876 |
|
wenzelm@4017
|
877 |
(*map classes, tycons*)
|
wenzelm@4017
|
878 |
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
|
wenzelm@4017
|
879 |
| map_typ f _ (TFree (x, S)) = TFree (x, map f S)
|
wenzelm@4017
|
880 |
| map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
|
wenzelm@4017
|
881 |
|
wenzelm@4017
|
882 |
(*map classes, tycons, consts*)
|
wenzelm@4017
|
883 |
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
|
wenzelm@4017
|
884 |
| map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
|
wenzelm@4017
|
885 |
| map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
|
wenzelm@4017
|
886 |
| map_term _ _ _ (t as Bound _) = t
|
wenzelm@4017
|
887 |
| map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
|
wenzelm@4017
|
888 |
| map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
|
wenzelm@4017
|
889 |
|
wenzelm@4017
|
890 |
|
clasohm@0
|
891 |
(** TFrees and TVars **)
|
clasohm@0
|
892 |
|
clasohm@0
|
893 |
(*maps (bs,v) to v'::bs this reverses the identifiers bs*)
|
clasohm@0
|
894 |
fun add_new_id (bs, c) : string list = variant bs c :: bs;
|
clasohm@0
|
895 |
|
wenzelm@12802
|
896 |
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
|
wenzelm@12802
|
897 |
fun add_term_free_names (Free(a,_), bs) = a ins_string bs
|
wenzelm@12802
|
898 |
| add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
|
wenzelm@12802
|
899 |
| add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
|
wenzelm@12802
|
900 |
| add_term_free_names (_, bs) = bs;
|
wenzelm@12802
|
901 |
|
clasohm@0
|
902 |
(*Accumulates the names in the term, suppressing duplicates.
|
clasohm@0
|
903 |
Includes Frees and Consts. For choosing unambiguous bound var names.*)
|
wenzelm@10666
|
904 |
fun add_term_names (Const(a,_), bs) = NameSpace.base a ins_string bs
|
paulson@2176
|
905 |
| add_term_names (Free(a,_), bs) = a ins_string bs
|
clasohm@0
|
906 |
| add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
|
clasohm@0
|
907 |
| add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
|
clasohm@0
|
908 |
| add_term_names (_, bs) = bs;
|
clasohm@0
|
909 |
|
clasohm@0
|
910 |
(*Accumulates the TVars in a type, suppressing duplicates. *)
|
skalberg@15574
|
911 |
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
|
clasohm@0
|
912 |
| add_typ_tvars(TFree(_),vs) = vs
|
wenzelm@16294
|
913 |
| add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
|
clasohm@0
|
914 |
|
clasohm@0
|
915 |
(*Accumulates the TFrees in a type, suppressing duplicates. *)
|
skalberg@15574
|
916 |
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
|
paulson@2176
|
917 |
| add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
|
clasohm@0
|
918 |
| add_typ_tfree_names(TVar(_),fs) = fs;
|
clasohm@0
|
919 |
|
skalberg@15574
|
920 |
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
|
wenzelm@16294
|
921 |
| add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
|
clasohm@0
|
922 |
| add_typ_tfrees(TVar(_),fs) = fs;
|
clasohm@0
|
923 |
|
skalberg@15574
|
924 |
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
|
paulson@2176
|
925 |
| add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
|
paulson@2176
|
926 |
| add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
|
nipkow@949
|
927 |
|
clasohm@0
|
928 |
(*Accumulates the TVars in a term, suppressing duplicates. *)
|
clasohm@0
|
929 |
val add_term_tvars = it_term_types add_typ_tvars;
|
clasohm@0
|
930 |
|
clasohm@0
|
931 |
(*Accumulates the TFrees in a term, suppressing duplicates. *)
|
clasohm@0
|
932 |
val add_term_tfrees = it_term_types add_typ_tfrees;
|
clasohm@0
|
933 |
val add_term_tfree_names = it_term_types add_typ_tfree_names;
|
clasohm@0
|
934 |
|
nipkow@949
|
935 |
val add_term_tvarnames = it_term_types add_typ_varnames;
|
nipkow@949
|
936 |
|
clasohm@0
|
937 |
(*Non-list versions*)
|
clasohm@0
|
938 |
fun typ_tfrees T = add_typ_tfrees(T,[]);
|
clasohm@0
|
939 |
fun typ_tvars T = add_typ_tvars(T,[]);
|
clasohm@0
|
940 |
fun term_tfrees t = add_term_tfrees(t,[]);
|
clasohm@0
|
941 |
fun term_tvars t = add_term_tvars(t,[]);
|
clasohm@0
|
942 |
|
nipkow@949
|
943 |
(*special code to enforce left-to-right collection of TVar-indexnames*)
|
nipkow@949
|
944 |
|
skalberg@15570
|
945 |
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
|
wenzelm@13000
|
946 |
| add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns
|
wenzelm@9536
|
947 |
else ixns@[ixn]
|
nipkow@949
|
948 |
| add_typ_ixns(ixns,TFree(_)) = ixns;
|
nipkow@949
|
949 |
|
nipkow@949
|
950 |
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
|
nipkow@949
|
951 |
| add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
|
nipkow@949
|
952 |
| add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
|
nipkow@949
|
953 |
| add_term_tvar_ixns(Bound _,ixns) = ixns
|
nipkow@949
|
954 |
| add_term_tvar_ixns(Abs(_,T,t),ixns) =
|
nipkow@949
|
955 |
add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
|
nipkow@949
|
956 |
| add_term_tvar_ixns(f$t,ixns) =
|
nipkow@949
|
957 |
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
|
nipkow@949
|
958 |
|
wenzelm@16537
|
959 |
|
clasohm@0
|
960 |
(** Frees and Vars **)
|
clasohm@0
|
961 |
|
clasohm@0
|
962 |
(*a partial ordering (not reflexive) for atomic terms*)
|
clasohm@0
|
963 |
fun atless (Const (a,_), Const (b,_)) = a<b
|
clasohm@0
|
964 |
| atless (Free (a,_), Free (b,_)) = a<b
|
clasohm@0
|
965 |
| atless (Var(v,_), Var(w,_)) = xless(v,w)
|
clasohm@0
|
966 |
| atless (Bound i, Bound j) = i<j
|
clasohm@0
|
967 |
| atless _ = false;
|
clasohm@0
|
968 |
|
clasohm@0
|
969 |
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
|
clasohm@0
|
970 |
fun insert_aterm (t,us) =
|
clasohm@0
|
971 |
let fun inserta [] = [t]
|
wenzelm@13000
|
972 |
| inserta (us as u::us') =
|
wenzelm@9536
|
973 |
if atless(t,u) then t::us
|
wenzelm@9536
|
974 |
else if t=u then us (*duplicate*)
|
wenzelm@9536
|
975 |
else u :: inserta(us')
|
clasohm@0
|
976 |
in inserta us end;
|
clasohm@0
|
977 |
|
clasohm@0
|
978 |
(*Accumulates the Vars in the term, suppressing duplicates*)
|
clasohm@0
|
979 |
fun add_term_vars (t, vars: term list) = case t of
|
clasohm@0
|
980 |
Var _ => insert_aterm(t,vars)
|
clasohm@0
|
981 |
| Abs (_,_,body) => add_term_vars(body,vars)
|
clasohm@0
|
982 |
| f$t => add_term_vars (f, add_term_vars(t, vars))
|
clasohm@0
|
983 |
| _ => vars;
|
clasohm@0
|
984 |
|
clasohm@0
|
985 |
fun term_vars t = add_term_vars(t,[]);
|
clasohm@0
|
986 |
|
clasohm@0
|
987 |
(*Accumulates the Frees in the term, suppressing duplicates*)
|
clasohm@0
|
988 |
fun add_term_frees (t, frees: term list) = case t of
|
clasohm@0
|
989 |
Free _ => insert_aterm(t,frees)
|
clasohm@0
|
990 |
| Abs (_,_,body) => add_term_frees(body,frees)
|
clasohm@0
|
991 |
| f$t => add_term_frees (f, add_term_frees(t, frees))
|
clasohm@0
|
992 |
| _ => frees;
|
clasohm@0
|
993 |
|
clasohm@0
|
994 |
fun term_frees t = add_term_frees(t,[]);
|
clasohm@0
|
995 |
|
clasohm@0
|
996 |
(*Given an abstraction over P, replaces the bound variable by a Free variable
|
clasohm@0
|
997 |
having a unique name. *)
|
clasohm@0
|
998 |
fun variant_abs (a,T,P) =
|
clasohm@0
|
999 |
let val b = variant (add_term_names(P,[])) a
|
paulson@2192
|
1000 |
in (b, subst_bound (Free(b,T), P)) end;
|
clasohm@0
|
1001 |
|
clasohm@0
|
1002 |
(* renames and reverses the strings in vars away from names *)
|
clasohm@0
|
1003 |
fun rename_aTs names vars : (string*typ)list =
|
clasohm@0
|
1004 |
let fun rename_aT (vars,(a,T)) =
|
wenzelm@9536
|
1005 |
(variant (map #1 vars @ names) a, T) :: vars
|
skalberg@15570
|
1006 |
in Library.foldl rename_aT ([],vars) end;
|
clasohm@0
|
1007 |
|
clasohm@0
|
1008 |
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
|
clasohm@1364
|
1009 |
|
paulson@1417
|
1010 |
|
wenzelm@4286
|
1011 |
(* left-ro-right traversal *)
|
wenzelm@4286
|
1012 |
|
wenzelm@4286
|
1013 |
(*foldl atoms of type*)
|
skalberg@15570
|
1014 |
fun foldl_atyps f (x, Type (_, Ts)) = Library.foldl (foldl_atyps f) (x, Ts)
|
wenzelm@4286
|
1015 |
| foldl_atyps f x_atom = f x_atom;
|
wenzelm@4286
|
1016 |
|
wenzelm@4286
|
1017 |
(*foldl atoms of term*)
|
wenzelm@4286
|
1018 |
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
|
wenzelm@4286
|
1019 |
| foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
|
wenzelm@4286
|
1020 |
| foldl_aterms f x_atom = f x_atom;
|
wenzelm@4286
|
1021 |
|
wenzelm@6548
|
1022 |
fun foldl_map_aterms f (x, t $ u) =
|
wenzelm@6548
|
1023 |
let val (x', t') = foldl_map_aterms f (x, t); val (x'', u') = foldl_map_aterms f (x', u);
|
wenzelm@6548
|
1024 |
in (x'', t' $ u') end
|
wenzelm@6548
|
1025 |
| foldl_map_aterms f (x, Abs (a, T, t)) =
|
wenzelm@6548
|
1026 |
let val (x', t') = foldl_map_aterms f (x, t) in (x', Abs (a, T, t')) end
|
wenzelm@6548
|
1027 |
| foldl_map_aterms f x_atom = f x_atom;
|
wenzelm@6548
|
1028 |
|
wenzelm@4286
|
1029 |
(*foldl types of term*)
|
wenzelm@8609
|
1030 |
fun foldl_term_types f (x, t as Const (_, T)) = f t (x, T)
|
wenzelm@8609
|
1031 |
| foldl_term_types f (x, t as Free (_, T)) = f t (x, T)
|
wenzelm@8609
|
1032 |
| foldl_term_types f (x, t as Var (_, T)) = f t (x, T)
|
wenzelm@8609
|
1033 |
| foldl_term_types f (x, Bound _) = x
|
wenzelm@8609
|
1034 |
| foldl_term_types f (x, t as Abs (_, T, b)) = foldl_term_types f (f t (x, T), b)
|
wenzelm@8609
|
1035 |
| foldl_term_types f (x, t $ u) = foldl_term_types f (foldl_term_types f (x, t), u);
|
wenzelm@8609
|
1036 |
|
wenzelm@8609
|
1037 |
fun foldl_types f = foldl_term_types (fn _ => f);
|
wenzelm@4286
|
1038 |
|
wenzelm@12499
|
1039 |
(*collect variables*)
|
wenzelm@16294
|
1040 |
val add_tvarsT = foldl_atyps (fn (vs, TVar v) => insert (op =) v vs | (vs, _) => vs);
|
wenzelm@12499
|
1041 |
val add_tvars = foldl_types add_tvarsT;
|
wenzelm@16294
|
1042 |
val add_vars = foldl_aterms (fn (vs, Var v) => insert (op =) v vs | (vs, _) => vs);
|
wenzelm@16294
|
1043 |
val add_frees = foldl_aterms (fn (vs, Free v) => insert (op =) v vs | (vs, _) => vs);
|
wenzelm@12499
|
1044 |
|
wenzelm@15025
|
1045 |
(*collect variable names*)
|
wenzelm@15025
|
1046 |
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
|
wenzelm@15025
|
1047 |
fun term_varnames t = add_term_varnames ([], t);
|
wenzelm@4286
|
1048 |
|
paulson@1417
|
1049 |
|
wenzelm@4444
|
1050 |
|
wenzelm@13000
|
1051 |
(*** Compression of terms and types by sharing common subtrees.
|
wenzelm@13000
|
1052 |
Saves 50-75% on storage requirements. As it is a bit slow,
|
wenzelm@13000
|
1053 |
it should be called only for axioms, stored theorems, etc.
|
wenzelm@13000
|
1054 |
Recorded term and type fragments are never disposed. ***)
|
paulson@1417
|
1055 |
|
wenzelm@16338
|
1056 |
|
paulson@1417
|
1057 |
(** Sharing of types **)
|
paulson@1417
|
1058 |
|
wenzelm@13000
|
1059 |
val memo_types = ref (Typtab.empty: typ Typtab.table);
|
paulson@1417
|
1060 |
|
paulson@1417
|
1061 |
fun compress_type T =
|
wenzelm@13000
|
1062 |
(case Typtab.lookup (! memo_types, T) of
|
skalberg@15531
|
1063 |
SOME T' => T'
|
skalberg@15531
|
1064 |
| NONE =>
|
wenzelm@13000
|
1065 |
let val T' = (case T of Type (a, Ts) => Type (a, map compress_type Ts) | _ => T)
|
wenzelm@13000
|
1066 |
in memo_types := Typtab.update ((T', T'), ! memo_types); T' end);
|
wenzelm@13000
|
1067 |
|
paulson@1417
|
1068 |
|
paulson@1417
|
1069 |
(** Sharing of atomic terms **)
|
paulson@1417
|
1070 |
|
wenzelm@13000
|
1071 |
val memo_terms = ref (Termtab.empty : term Termtab.table);
|
paulson@1417
|
1072 |
|
paulson@1417
|
1073 |
fun share_term (t $ u) = share_term t $ share_term u
|
wenzelm@13000
|
1074 |
| share_term (Abs (a, T, u)) = Abs (a, T, share_term u)
|
paulson@1417
|
1075 |
| share_term t =
|
wenzelm@13000
|
1076 |
(case Termtab.lookup (! memo_terms, t) of
|
skalberg@15531
|
1077 |
SOME t' => t'
|
skalberg@15531
|
1078 |
| NONE => (memo_terms := Termtab.update ((t, t), ! memo_terms); t));
|
paulson@1417
|
1079 |
|
paulson@1417
|
1080 |
val compress_term = share_term o map_term_types compress_type;
|
paulson@1417
|
1081 |
|
wenzelm@4444
|
1082 |
|
wenzelm@9536
|
1083 |
(* dummy patterns *)
|
wenzelm@9536
|
1084 |
|
wenzelm@9536
|
1085 |
val dummy_patternN = "dummy_pattern";
|
wenzelm@9536
|
1086 |
|
wenzelm@9536
|
1087 |
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
|
wenzelm@9536
|
1088 |
| is_dummy_pattern _ = false;
|
wenzelm@9536
|
1089 |
|
wenzelm@9536
|
1090 |
fun no_dummy_patterns tm =
|
wenzelm@9536
|
1091 |
if not (foldl_aterms (fn (b, t) => b orelse is_dummy_pattern t) (false, tm)) then tm
|
wenzelm@9536
|
1092 |
else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
|
wenzelm@9536
|
1093 |
|
wenzelm@11903
|
1094 |
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
|
wenzelm@11903
|
1095 |
(i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
|
wenzelm@11903
|
1096 |
| replace_dummy Ts (i, Abs (x, T, t)) =
|
wenzelm@11903
|
1097 |
let val (i', t') = replace_dummy (T :: Ts) (i, t)
|
wenzelm@11903
|
1098 |
in (i', Abs (x, T, t')) end
|
wenzelm@11903
|
1099 |
| replace_dummy Ts (i, t $ u) =
|
wenzelm@11903
|
1100 |
let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
|
wenzelm@11903
|
1101 |
in (i'', t' $ u') end
|
wenzelm@11903
|
1102 |
| replace_dummy _ (i, a) = (i, a);
|
wenzelm@11903
|
1103 |
|
wenzelm@11903
|
1104 |
val replace_dummy_patterns = replace_dummy [];
|
wenzelm@9536
|
1105 |
|
wenzelm@10552
|
1106 |
fun is_replaced_dummy_pattern ("_dummy_", _) = true
|
wenzelm@10552
|
1107 |
| is_replaced_dummy_pattern _ = false;
|
wenzelm@9536
|
1108 |
|
wenzelm@16035
|
1109 |
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
|
wenzelm@16035
|
1110 |
| show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
|
wenzelm@16035
|
1111 |
| show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
|
wenzelm@16035
|
1112 |
| show_dummy_patterns a = a;
|
wenzelm@16035
|
1113 |
|
wenzelm@13484
|
1114 |
|
wenzelm@13484
|
1115 |
(* adhoc freezing *)
|
wenzelm@13484
|
1116 |
|
wenzelm@13484
|
1117 |
fun adhoc_freeze_vars tm =
|
wenzelm@13484
|
1118 |
let
|
wenzelm@13484
|
1119 |
fun mk_inst (var as Var ((a, i), T)) =
|
wenzelm@13484
|
1120 |
let val x = a ^ Library.gensym "_" ^ string_of_int i
|
wenzelm@13484
|
1121 |
in ((var, Free(x, T)), x) end;
|
wenzelm@13484
|
1122 |
val (insts, xs) = split_list (map mk_inst (term_vars tm));
|
wenzelm@13484
|
1123 |
in (subst_atomic insts tm, xs) end;
|
wenzelm@13484
|
1124 |
|
wenzelm@13484
|
1125 |
|
wenzelm@14786
|
1126 |
(* string_of_vname *)
|
wenzelm@14786
|
1127 |
|
wenzelm@15986
|
1128 |
val show_question_marks = ref true;
|
berghofe@15472
|
1129 |
|
wenzelm@14786
|
1130 |
fun string_of_vname (x, i) =
|
wenzelm@14786
|
1131 |
let
|
wenzelm@15986
|
1132 |
val question_mark = if ! show_question_marks then "?" else "";
|
wenzelm@15986
|
1133 |
val idx = string_of_int i;
|
wenzelm@15986
|
1134 |
val dot =
|
wenzelm@15986
|
1135 |
(case rev (Symbol.explode x) of
|
wenzelm@15986
|
1136 |
_ :: "\\<^isub>" :: _ => false
|
wenzelm@15986
|
1137 |
| _ :: "\\<^isup>" :: _ => false
|
wenzelm@15986
|
1138 |
| c :: _ => Symbol.is_digit c
|
wenzelm@15986
|
1139 |
| _ => true);
|
wenzelm@14786
|
1140 |
in
|
wenzelm@15986
|
1141 |
if dot then question_mark ^ x ^ "." ^ idx
|
wenzelm@15986
|
1142 |
else if i <> 0 then question_mark ^ x ^ idx
|
wenzelm@15986
|
1143 |
else question_mark ^ x
|
wenzelm@14786
|
1144 |
end;
|
wenzelm@14786
|
1145 |
|
wenzelm@14786
|
1146 |
fun string_of_vname' (x, ~1) = x
|
wenzelm@14786
|
1147 |
| string_of_vname' xi = string_of_vname xi;
|
wenzelm@14786
|
1148 |
|
nipkow@15612
|
1149 |
fun string_of_term (Const(s,_)) = s
|
nipkow@15612
|
1150 |
| string_of_term (Free(s,_)) = s
|
nipkow@15612
|
1151 |
| string_of_term (Var(ix,_)) = string_of_vname ix
|
nipkow@15612
|
1152 |
| string_of_term (Bound i) = string_of_int i
|
nipkow@15612
|
1153 |
| string_of_term (Abs(x,_,t)) = "%" ^ x ^ ". " ^ string_of_term t
|
nipkow@15612
|
1154 |
| string_of_term (s $ t) =
|
nipkow@15612
|
1155 |
"(" ^ string_of_term s ^ " " ^ string_of_term t ^ ")"
|
nipkow@15612
|
1156 |
|
clasohm@1364
|
1157 |
end;
|
clasohm@1364
|
1158 |
|
wenzelm@4444
|
1159 |
structure BasicTerm: BASIC_TERM = Term;
|
wenzelm@4444
|
1160 |
open BasicTerm;
|