src/Pure/library.ML
author wenzelm
Mon May 04 21:05:38 1998 +0200 (1998-05-04)
changeset 4893 df9d6eef16d5
parent 4849 a9d5b8f8e40f
child 4916 fe8b0c82691b
permissions -rw-r--r--
added nth_update: 'a -> int * 'a list -> 'a list;
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(*  Title:      Pure/library.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1992  University of Cambridge
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Basic library: functions, options, pairs, booleans, lists, integers,
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strings, lists as sets, association lists, generic tables, balanced
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trees, orders, I/O and diagnostics, timing, misc.
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*)
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infix |> ~~ \ \\ ins ins_string ins_int orf andf prefix upto downto
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  mem mem_int mem_string union union_int union_string inter inter_int
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  inter_string subset subset_int subset_string;
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signature LIBRARY =
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sig
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  (*functions*)
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  val curry: ('a * 'b -> 'c) -> 'a -> 'b -> 'c
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  val uncurry: ('a -> 'b -> 'c) -> 'a * 'b -> 'c
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  val I: 'a -> 'a
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  val K: 'a -> 'b -> 'a
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  val |> : 'a * ('a -> 'b) -> 'b
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  val apl: 'a * ('a * 'b -> 'c) -> 'b -> 'c
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  val apr: ('a * 'b -> 'c) * 'b -> 'a -> 'c
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  val funpow: int -> ('a -> 'a) -> 'a -> 'a
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  (*stamps*)
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  type stamp
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  val stamp: unit -> stamp
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  (*options*)
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  datatype 'a option = None | Some of 'a
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  exception OPTION
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  val the: 'a option -> 'a
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  val if_none: 'a option -> 'a -> 'a
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  val is_some: 'a option -> bool
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  val is_none: 'a option -> bool
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  val apsome: ('a -> 'b) -> 'a option -> 'b option
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  val can: ('a -> 'b) -> 'a -> bool
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  val try: ('a -> 'b) -> 'a -> 'b option
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  (*pairs*)
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  val pair: 'a -> 'b -> 'a * 'b
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  val rpair: 'a -> 'b -> 'b * 'a
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  val fst: 'a * 'b -> 'a
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  val snd: 'a * 'b -> 'b
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  val eq_fst: (''a * 'b) * (''a * 'c) -> bool
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  val eq_snd: ('a * ''b) * ('c * ''b) -> bool
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  val swap: 'a * 'b -> 'b * 'a
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  val apfst: ('a -> 'b) -> 'a * 'c -> 'b * 'c
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  val apsnd: ('a -> 'b) -> 'c * 'a -> 'c * 'b
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  val pairself: ('a -> 'b) -> 'a * 'a -> 'b * 'b
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  (*booleans*)
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  val equal: ''a -> ''a -> bool
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  val not_equal: ''a -> ''a -> bool
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  val orf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val andf: ('a -> bool) * ('a -> bool) -> 'a -> bool
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  val exists: ('a -> bool) -> 'a list -> bool
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  val forall: ('a -> bool) -> 'a list -> bool
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  val set: bool ref -> bool
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  val reset: bool ref -> bool
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  val toggle: bool ref -> bool
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  val setmp: 'a ref -> 'a -> ('b -> 'c) -> 'b -> 'c
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  (*lists*)
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  exception LIST of string
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  val null: 'a list -> bool
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  val hd: 'a list -> 'a
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  val tl: 'a list -> 'a list
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  val cons: 'a -> 'a list -> 'a list
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  val append: 'a list -> 'a list -> 'a list
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  val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a
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  val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b
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  val foldr1: ('a * 'a -> 'a) -> 'a list -> 'a
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  val length: 'a list -> int
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  val take: int * 'a list -> 'a list
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  val drop: int * 'a list -> 'a list
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  val dropwhile: ('a -> bool) -> 'a list -> 'a list
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  val nth_elem: int * 'a list -> 'a
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  val last_elem: 'a list -> 'a
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  val split_last: 'a list -> 'a list * 'a
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  val nth_update: 'a -> int * 'a list -> 'a list
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  val find_index: ('a -> bool) -> 'a list -> int
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  val find_index_eq: ''a -> ''a list -> int
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  val find_first: ('a -> bool) -> 'a list -> 'a option
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  val flat: 'a list list -> 'a list
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  val seq: ('a -> unit) -> 'a list -> unit
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  val separate: 'a -> 'a list -> 'a list
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  val replicate: int -> 'a -> 'a list
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  val multiply: 'a list * 'a list list -> 'a list list
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  val filter: ('a -> bool) -> 'a list -> 'a list
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  val filter_out: ('a -> bool) -> 'a list -> 'a list
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  val mapfilter: ('a -> 'b option) -> 'a list -> 'b list
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  val map2: ('a * 'b -> 'c) -> 'a list * 'b list -> 'c list
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  val exists2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val forall2: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val ~~ : 'a list * 'b list -> ('a * 'b) list
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  val split_list: ('a * 'b) list -> 'a list * 'b list
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  val prefix: ''a list * ''a list -> bool
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  val take_prefix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val take_suffix: ('a -> bool) -> 'a list -> 'a list * 'a list
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  (*integers*)
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  val inc: int ref -> int
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  val dec: int ref -> int
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  val upto: int * int -> int list
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  val downto: int * int -> int list
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  val downto0: int list * int -> bool
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  val radixpand: int * int -> int list
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  val radixstring: int * string * int -> string
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  val string_of_int: int -> string
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  val string_of_indexname: string * int -> string
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  (*strings*)
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  val beginning: string list -> string
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  val enclose: string -> string -> string -> string
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  val quote: string -> string
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  val space_implode: string -> string list -> string
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  val commas: string list -> string
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  val commas_quote: string list -> string
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  val cat_lines: string list -> string
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  val space_explode: string -> string -> string list
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  val split_lines: string -> string list
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  (*lists as sets*)
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  val mem: ''a * ''a list -> bool
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  val mem_int: int * int list -> bool
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  val mem_string: string * string list -> bool
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  val gen_mem: ('a * 'b -> bool) -> 'a * 'b list -> bool
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  val ins: ''a * ''a list -> ''a list
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  val ins_int: int * int list -> int list
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  val ins_string: string * string list -> string list
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  val gen_ins: ('a * 'a -> bool) -> 'a * 'a list -> 'a list
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  val union: ''a list * ''a list -> ''a list
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  val union_int: int list * int list -> int list
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  val union_string: string list * string list -> string list
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  val gen_union: ('a * 'a -> bool) -> 'a list * 'a list -> 'a list
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  val inter: ''a list * ''a list -> ''a list
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  val inter_int: int list * int list -> int list
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  val inter_string: string list * string list -> string list
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  val subset: ''a list * ''a list -> bool
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  val subset_int: int list * int list -> bool
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  val subset_string: string list * string list -> bool
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  val eq_set: ''a list * ''a list -> bool
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  val eq_set_string: string list * string list -> bool
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  val gen_subset: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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  val \ : ''a list * ''a -> ''a list
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  val \\ : ''a list * ''a list -> ''a list
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  val gen_rem: ('a * 'b -> bool) -> 'a list * 'b -> 'a list
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  val gen_rems: ('a * 'b -> bool) -> 'a list * 'b list -> 'a list
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  val gen_distinct: ('a * 'a -> bool) -> 'a list -> 'a list
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  val distinct: ''a list -> ''a list
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  val findrep: ''a list -> ''a list
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  val gen_duplicates: ('a * 'a -> bool) -> 'a list -> 'a list
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  val duplicates: ''a list -> ''a list
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  (*association lists*)
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  val assoc: (''a * 'b) list * ''a -> 'b option
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  val assoc_int: (int * 'a) list * int -> 'a option
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  val assoc_string: (string * 'a) list * string -> 'a option
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  val assoc_string_int: ((string * int) * 'a) list * (string * int) -> 'a option
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  val assocs: (''a * 'b list) list -> ''a -> 'b list
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  val assoc2: (''a * (''b * 'c) list) list * (''a * ''b) -> 'c option
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  val gen_assoc: ('a * 'b -> bool) -> ('b * 'c) list * 'a -> 'c option
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  val overwrite: (''a * 'b) list * (''a * 'b) -> (''a * 'b) list
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  val gen_overwrite: ('a * 'a -> bool) -> ('a * 'b) list * ('a * 'b) -> ('a * 'b) list
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  (*generic tables*)
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  val generic_extend: ('a * 'a -> bool)
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    -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'a list -> 'b
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  val generic_merge: ('a * 'a -> bool) -> ('b -> 'a list) -> ('a list -> 'b) -> 'b -> 'b -> 'b
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  val extend_list: ''a list -> ''a list -> ''a list
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  val merge_lists: ''a list -> ''a list -> ''a list
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  val merge_alists: (''a * 'b) list -> (''a * 'b) list -> (''a * 'b) list
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  val merge_rev_lists: ''a list -> ''a list -> ''a list
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  (*balanced trees*)
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  exception Balance
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  val fold_bal: ('a * 'a -> 'a) -> 'a list -> 'a
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  val access_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> int -> 'a
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  val accesses_bal: ('a -> 'a) * ('a -> 'a) * 'a -> int -> 'a list
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  (*orders*)
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  datatype order = EQUAL | GREATER | LESS
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  val rev_order: order -> order
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  val make_ord: ('a * 'a -> bool) -> 'a * 'a -> order
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  val int_ord: int * int -> order
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  val string_ord: string * string -> order
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  val prod_ord: ('a * 'b -> order) -> ('c * 'd -> order) -> ('a * 'c) * ('b * 'd) -> order
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  val dict_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val list_ord: ('a * 'b -> order) -> 'a list * 'b list -> order
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  val sort: ('a * 'a -> order) -> 'a list -> 'a list
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  val sort_strings: string list -> string list
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  val sort_wrt: ('a -> string) -> 'a list -> 'a list
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  (*I/O and diagnostics*)
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  val cd: string -> unit
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  val pwd: unit -> string
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  val prs_fn: (string -> unit) ref
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  val warning_fn: (string -> unit) ref
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  val error_fn: (string -> unit) ref
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  val prs: string -> unit
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  val writeln: string -> unit
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  val warning: string -> unit
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  exception ERROR
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  val error_msg: string -> unit
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  val error: string -> 'a
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  val sys_error: string -> 'a
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  val assert: bool -> string -> unit
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  val deny: bool -> string -> unit
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  val assert_all: ('a -> bool) -> 'a list -> ('a -> string) -> unit
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  datatype 'a error = Error of string | OK of 'a
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  val get_error: 'a error -> string option
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  val get_ok: 'a error -> 'a option
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  val handle_error: ('a -> 'b) -> 'a -> 'b error
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  (*timing*)
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  val cond_timeit: bool -> (unit -> 'a) -> 'a
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  val timeit: (unit -> 'a) -> 'a
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  val timeap: ('a -> 'b) -> 'a -> 'b
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  (*misc*)
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  val make_keylist: ('a -> 'b) -> 'a list -> ('a * 'b) list
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  val keyfilter: ('a * ''b) list -> ''b -> 'a list
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  val partition: ('a -> bool) -> 'a list -> 'a list * 'a list
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  val partition_eq: ('a * 'a -> bool) -> 'a list -> 'a list list
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  val partition_list: (int -> 'a -> bool) -> int -> int -> 'a list -> 'a list list
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  val transitive_closure: (string * string list) list -> (string * string list) list
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  val init_gensym: unit -> unit
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  val gensym: string -> string
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  val bump_int_list: string list -> string list
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  val bump_list: string list * string -> string list
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  val bump_string: string -> string
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  val scanwords: (string -> bool) -> string list -> string list
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  datatype 'a mtree = Join of 'a * 'a mtree list
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  type object
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  val type_error: string -> 'a
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end;
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structure Library: LIBRARY =
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struct
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(** functions **)
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(*handy combinators*)
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fun curry f x y = f (x, y);
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fun uncurry f (x, y) = f x y;
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fun I x = x;
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fun K x y = x;
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(*reverse apply*)
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fun (x |> f) = f x;
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(*application of (infix) operator to its left or right argument*)
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fun apl (x, f) y = f (x, y);
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fun apr (f, y) x = f (x, y);
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(*function exponentiation: f(...(f x)...) with n applications of f*)
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fun funpow n f x =
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  let fun rep (0, x) = x
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        | rep (n, x) = rep (n - 1, f x)
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  in rep (n, x) end;
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(** stamps **)
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type stamp = unit ref;
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val stamp: unit -> stamp = ref;
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(** options **)
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datatype 'a option = None | Some of 'a;
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exception OPTION;
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fun the (Some x) = x
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  | the None = raise OPTION;
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(*strict!*)
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fun if_none None y = y
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  | if_none (Some x) _ = x;
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fun is_some (Some _) = true
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  | is_some None = false;
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fun is_none (Some _) = false
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  | is_none None = true;
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fun apsome f (Some x) = Some (f x)
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  | apsome _ None = None;
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(*handle partial functions*)
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fun can f x = (f x; true) handle _ => false;
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fun try f x = Some (f x) handle _ => None;
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(** pairs **)
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fun pair x y = (x, y);
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fun rpair x y = (y, x);
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fun fst (x, y) = x;
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fun snd (x, y) = y;
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fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
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fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
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fun swap (x, y) = (y, x);
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(*apply function to components*)
wenzelm@233
   316
fun apfst f (x, y) = (f x, y);
wenzelm@233
   317
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   318
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   319
wenzelm@233
   320
wenzelm@233
   321
wenzelm@233
   322
(** booleans **)
wenzelm@233
   323
wenzelm@233
   324
(* equality *)
wenzelm@233
   325
wenzelm@233
   326
fun equal x y = x = y;
wenzelm@233
   327
fun not_equal x y = x <> y;
wenzelm@233
   328
wenzelm@233
   329
wenzelm@233
   330
(* operators for combining predicates *)
wenzelm@233
   331
paulson@2175
   332
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   333
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   334
wenzelm@233
   335
wenzelm@233
   336
(* predicates on lists *)
wenzelm@233
   337
wenzelm@233
   338
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   339
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   340
  let fun boolf [] = false
wenzelm@233
   341
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   342
  in boolf end;
wenzelm@233
   343
wenzelm@233
   344
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   345
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   346
  let fun boolf [] = true
wenzelm@233
   347
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   348
  in boolf end;
clasohm@0
   349
wenzelm@233
   350
wenzelm@380
   351
(* flags *)
wenzelm@380
   352
wenzelm@380
   353
fun set flag = (flag := true; true);
wenzelm@380
   354
fun reset flag = (flag := false; false);
wenzelm@380
   355
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   356
wenzelm@4212
   357
(*temporarily set flag, handling errors*)
wenzelm@2978
   358
fun setmp flag value f x =
wenzelm@2958
   359
  let
wenzelm@2958
   360
    val orig_value = ! flag;
wenzelm@2958
   361
    fun return y = (flag := orig_value; y);
wenzelm@2958
   362
  in
wenzelm@2958
   363
    flag := value;
wenzelm@2958
   364
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   365
  end;
wenzelm@2958
   366
wenzelm@380
   367
wenzelm@233
   368
wenzelm@233
   369
(** lists **)
wenzelm@233
   370
wenzelm@233
   371
exception LIST of string;
wenzelm@233
   372
wenzelm@233
   373
fun null [] = true
wenzelm@233
   374
  | null (_ :: _) = false;
wenzelm@233
   375
wenzelm@233
   376
fun hd [] = raise LIST "hd"
wenzelm@233
   377
  | hd (x :: _) = x;
wenzelm@233
   378
wenzelm@233
   379
fun tl [] = raise LIST "tl"
wenzelm@233
   380
  | tl (_ :: xs) = xs;
wenzelm@233
   381
wenzelm@233
   382
fun cons x xs = x :: xs;
wenzelm@233
   383
wenzelm@4629
   384
fun append xs ys = xs @ ys;
wenzelm@4629
   385
wenzelm@233
   386
wenzelm@233
   387
(* fold *)
wenzelm@233
   388
wenzelm@233
   389
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   390
wenzelm@233
   391
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   392
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   393
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   394
  let fun itl (e, [])  = e
wenzelm@233
   395
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   396
  in  itl end;
wenzelm@233
   397
wenzelm@233
   398
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   399
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   400
fun foldr f (l, e) =
wenzelm@233
   401
  let fun itr [] = e
wenzelm@233
   402
        | itr (a::l) = f(a, itr l)
wenzelm@233
   403
  in  itr l  end;
wenzelm@233
   404
wenzelm@233
   405
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   406
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   407
fun foldr1 f l =
wenzelm@4181
   408
  let fun itr [x] = x
wenzelm@233
   409
        | itr (x::l) = f(x, itr l)
wenzelm@233
   410
  in  itr l  end;
wenzelm@233
   411
wenzelm@233
   412
wenzelm@233
   413
(* basic list functions *)
wenzelm@233
   414
wenzelm@233
   415
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   416
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   417
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   418
in  fun length l = length1 (0, l) end;
wenzelm@233
   419
wenzelm@233
   420
(*take the first n elements from a list*)
wenzelm@233
   421
fun take (n, []) = []
wenzelm@233
   422
  | take (n, x :: xs) =
wenzelm@233
   423
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   424
wenzelm@233
   425
(*drop the first n elements from a list*)
wenzelm@233
   426
fun drop (n, []) = []
wenzelm@233
   427
  | drop (n, x :: xs) =
wenzelm@233
   428
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   429
nipkow@4713
   430
fun dropwhile P [] = []
nipkow@4713
   431
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   432
wenzelm@233
   433
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   434
  raise EXCEPTION if list too short*)
wenzelm@233
   435
fun nth_elem NL =
wenzelm@233
   436
  (case drop NL of
wenzelm@233
   437
    [] => raise LIST "nth_elem"
wenzelm@233
   438
  | x :: _ => x);
wenzelm@233
   439
wenzelm@233
   440
(*last element of a list*)
wenzelm@233
   441
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   442
  | last_elem [x] = x
wenzelm@233
   443
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   444
wenzelm@3762
   445
(*rear decomposition*)
wenzelm@3762
   446
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   447
  | split_last [x] = ([], x)
wenzelm@3762
   448
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   449
wenzelm@4893
   450
(*update nth element*)
wenzelm@4893
   451
fun nth_update x (n, xs) =
wenzelm@4893
   452
  let
wenzelm@4893
   453
    val prfx = take (n, xs);
wenzelm@4893
   454
    val sffx = drop (n, xs);
wenzelm@4893
   455
  in
wenzelm@4893
   456
    (case sffx of
wenzelm@4893
   457
      [] => raise LIST "nth_update"
wenzelm@4893
   458
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   459
  end;
wenzelm@4893
   460
wenzelm@4212
   461
(*find the position of an element in a list*)
wenzelm@4212
   462
fun find_index pred =
wenzelm@4212
   463
  let fun find _ [] = ~1
wenzelm@4212
   464
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   465
  in find 0 end;
wenzelm@3762
   466
wenzelm@4224
   467
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   468
wenzelm@4212
   469
(*find first element satisfying predicate*)
wenzelm@4212
   470
fun find_first _ [] = None
wenzelm@4212
   471
  | find_first pred (x :: xs) =
wenzelm@4212
   472
      if pred x then Some x else find_first pred xs;
wenzelm@233
   473
wenzelm@233
   474
(*flatten a list of lists to a list*)
wenzelm@233
   475
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   476
wenzelm@233
   477
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   478
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   479
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   480
  let fun seqf [] = ()
wenzelm@233
   481
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   482
  in seqf end;
wenzelm@233
   483
wenzelm@233
   484
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   485
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   486
  | separate _ xs = xs;
wenzelm@233
   487
wenzelm@233
   488
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   489
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   490
  let fun rep (0, xs) = xs
wenzelm@233
   491
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   492
  in
wenzelm@233
   493
    if n < 0 then raise LIST "replicate"
wenzelm@233
   494
    else rep (n, [])
wenzelm@233
   495
  end;
wenzelm@233
   496
wenzelm@4248
   497
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   498
fun multiply ([], _) = []
wenzelm@4248
   499
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   500
wenzelm@233
   501
wenzelm@233
   502
(* filter *)
wenzelm@233
   503
wenzelm@233
   504
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   505
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   506
  let fun filt [] = []
wenzelm@233
   507
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   508
  in filt end;
clasohm@0
   509
clasohm@0
   510
fun filter_out f = filter (not o f);
clasohm@0
   511
wenzelm@233
   512
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   513
  | mapfilter f (x :: xs) =
wenzelm@233
   514
      (case f x of
wenzelm@233
   515
        None => mapfilter f xs
wenzelm@233
   516
      | Some y => y :: mapfilter f xs);
wenzelm@233
   517
wenzelm@233
   518
wenzelm@233
   519
(* lists of pairs *)
wenzelm@233
   520
wenzelm@380
   521
fun map2 _ ([], []) = []
wenzelm@380
   522
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   523
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   524
wenzelm@380
   525
fun exists2 _ ([], []) = false
wenzelm@380
   526
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   527
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   528
wenzelm@380
   529
fun forall2 _ ([], []) = true
wenzelm@380
   530
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   531
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   532
wenzelm@233
   533
(*combine two lists forming a list of pairs:
wenzelm@233
   534
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   535
fun [] ~~ [] = []
wenzelm@233
   536
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   537
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   538
wenzelm@233
   539
(*inverse of ~~; the old 'split':
wenzelm@233
   540
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   541
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   542
wenzelm@233
   543
wenzelm@233
   544
(* prefixes, suffixes *)
wenzelm@233
   545
wenzelm@233
   546
fun [] prefix _ = true
wenzelm@233
   547
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   548
  | _ prefix _ = false;
wenzelm@233
   549
wenzelm@233
   550
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   551
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   552
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   553
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   554
        | take (rxs, x :: xs) =
wenzelm@255
   555
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   556
  in  take([], xs)  end;
wenzelm@233
   557
wenzelm@233
   558
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   559
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   560
fun take_suffix _ [] = ([], [])
wenzelm@233
   561
  | take_suffix pred (x :: xs) =
wenzelm@233
   562
      (case take_suffix pred xs of
wenzelm@233
   563
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   564
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   565
wenzelm@233
   566
wenzelm@233
   567
wenzelm@233
   568
(** integers **)
wenzelm@233
   569
wenzelm@2958
   570
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   571
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   572
wenzelm@233
   573
wenzelm@233
   574
(* lists of integers *)
wenzelm@233
   575
wenzelm@233
   576
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   577
fun (from upto to) =
wenzelm@233
   578
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   579
wenzelm@233
   580
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   581
fun (from downto to) =
wenzelm@233
   582
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   583
wenzelm@233
   584
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   585
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   586
  | downto0 ([], n) = n = ~1;
wenzelm@233
   587
wenzelm@233
   588
wenzelm@233
   589
(* convert integers to strings *)
wenzelm@233
   590
wenzelm@233
   591
(*expand the number in the given base;
wenzelm@233
   592
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   593
fun radixpand (base, num) : int list =
wenzelm@233
   594
  let
wenzelm@233
   595
    fun radix (n, tail) =
wenzelm@233
   596
      if n < base then n :: tail
wenzelm@233
   597
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   598
  in radix (num, []) end;
wenzelm@233
   599
wenzelm@233
   600
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   601
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   602
fun radixstring (base, zerochar, num) =
wenzelm@233
   603
  let val offset = ord zerochar;
wenzelm@233
   604
      fun chrof n = chr (offset + n)
wenzelm@233
   605
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   606
wenzelm@233
   607
paulson@3407
   608
val string_of_int = Int.toString;
wenzelm@233
   609
paulson@3407
   610
fun string_of_indexname (a,0) = a
paulson@3407
   611
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   612
wenzelm@233
   613
wenzelm@4212
   614
wenzelm@233
   615
(** strings **)
wenzelm@233
   616
wenzelm@4692
   617
(*beginning of text*)
wenzelm@4692
   618
fun beginning cs = implode (take (10, cs)) ^ " ...";
wenzelm@233
   619
lcp@512
   620
(*enclose in brackets*)
lcp@512
   621
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   622
wenzelm@233
   623
(*simple quoting (does not escape special chars)*)
lcp@512
   624
val quote = enclose "\"" "\"";
wenzelm@233
   625
wenzelm@4212
   626
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   627
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   628
wenzelm@255
   629
val commas = space_implode ", ";
wenzelm@380
   630
val commas_quote = commas o map quote;
wenzelm@255
   631
wenzelm@233
   632
(*concatenate messages, one per line, into a string*)
wenzelm@255
   633
val cat_lines = space_implode "\n";
wenzelm@233
   634
wenzelm@4212
   635
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   636
fun space_explode _ "" = []
wenzelm@3832
   637
  | space_explode sep str =
wenzelm@3832
   638
      let
wenzelm@3832
   639
        fun expl chs =
wenzelm@3832
   640
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   641
            (cs, []) => [implode cs]
wenzelm@3832
   642
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   643
      in expl (explode str) end;
wenzelm@3832
   644
wenzelm@3832
   645
val split_lines = space_explode "\n";
wenzelm@3832
   646
wenzelm@3832
   647
wenzelm@233
   648
wenzelm@233
   649
(** lists as sets **)
wenzelm@233
   650
wenzelm@233
   651
(*membership in a list*)
wenzelm@233
   652
fun x mem [] = false
wenzelm@233
   653
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   654
paulson@2175
   655
(*membership in a list, optimized version for ints*)
berghofe@1576
   656
fun (x:int) mem_int [] = false
berghofe@1576
   657
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   658
paulson@2175
   659
(*membership in a list, optimized version for strings*)
berghofe@1576
   660
fun (x:string) mem_string [] = false
berghofe@1576
   661
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   662
clasohm@0
   663
(*generalized membership test*)
wenzelm@233
   664
fun gen_mem eq (x, []) = false
wenzelm@233
   665
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   666
wenzelm@233
   667
wenzelm@233
   668
(*insertion into list if not already there*)
paulson@2175
   669
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   670
paulson@2175
   671
(*insertion into list, optimized version for ints*)
paulson@2175
   672
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   673
paulson@2175
   674
(*insertion into list, optimized version for strings*)
paulson@2175
   675
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   676
clasohm@0
   677
(*generalized insertion*)
wenzelm@233
   678
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   679
wenzelm@233
   680
wenzelm@233
   681
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   682
fun xs union [] = xs
wenzelm@233
   683
  | [] union ys = ys
wenzelm@233
   684
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   685
paulson@2175
   686
(*union of sets, optimized version for ints*)
berghofe@1576
   687
fun (xs:int list) union_int [] = xs
berghofe@1576
   688
  | [] union_int ys = ys
berghofe@1576
   689
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   690
paulson@2175
   691
(*union of sets, optimized version for strings*)
berghofe@1576
   692
fun (xs:string list) union_string [] = xs
berghofe@1576
   693
  | [] union_string ys = ys
berghofe@1576
   694
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   695
clasohm@0
   696
(*generalized union*)
wenzelm@233
   697
fun gen_union eq (xs, []) = xs
wenzelm@233
   698
  | gen_union eq ([], ys) = ys
wenzelm@233
   699
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   700
wenzelm@233
   701
wenzelm@233
   702
(*intersection*)
wenzelm@233
   703
fun [] inter ys = []
wenzelm@233
   704
  | (x :: xs) inter ys =
wenzelm@233
   705
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   706
paulson@2175
   707
(*intersection, optimized version for ints*)
berghofe@1576
   708
fun ([]:int list) inter_int ys = []
berghofe@1576
   709
  | (x :: xs) inter_int ys =
berghofe@1576
   710
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   711
paulson@2175
   712
(*intersection, optimized version for strings *)
berghofe@1576
   713
fun ([]:string list) inter_string ys = []
berghofe@1576
   714
  | (x :: xs) inter_string ys =
berghofe@1576
   715
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   716
wenzelm@233
   717
wenzelm@233
   718
(*subset*)
wenzelm@233
   719
fun [] subset ys = true
wenzelm@233
   720
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   721
paulson@2175
   722
(*subset, optimized version for ints*)
berghofe@1576
   723
fun ([]:int list) subset_int ys = true
berghofe@1576
   724
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   725
paulson@2175
   726
(*subset, optimized version for strings*)
berghofe@1576
   727
fun ([]:string list) subset_string ys = true
berghofe@1576
   728
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   729
wenzelm@4363
   730
(*set equality*)
wenzelm@4363
   731
fun eq_set (xs, ys) =
wenzelm@4363
   732
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   733
paulson@2182
   734
(*set equality for strings*)
berghofe@1576
   735
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   736
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   737
paulson@2182
   738
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   739
wenzelm@265
   740
wenzelm@233
   741
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   742
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   743
  | [] \ x = [];
wenzelm@233
   744
paulson@2243
   745
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   746
wenzelm@233
   747
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   748
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   749
paulson@2243
   750
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   751
wenzelm@233
   752
wenzelm@233
   753
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   754
  first of equal elements*)
wenzelm@233
   755
fun gen_distinct eq lst =
wenzelm@233
   756
  let
wenzelm@233
   757
    val memb = gen_mem eq;
clasohm@0
   758
wenzelm@233
   759
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   760
      | dist (rev_seen, x :: xs) =
wenzelm@233
   761
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   762
          else dist (x :: rev_seen, xs);
wenzelm@233
   763
  in
wenzelm@233
   764
    dist ([], lst)
wenzelm@233
   765
  end;
wenzelm@233
   766
paulson@2243
   767
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   768
wenzelm@233
   769
wenzelm@233
   770
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   771
fun findrep [] = []
wenzelm@233
   772
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   773
wenzelm@233
   774
wenzelm@255
   775
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   776
  order, takes first of equal elements*)
wenzelm@255
   777
fun gen_duplicates eq lst =
wenzelm@255
   778
  let
wenzelm@255
   779
    val memb = gen_mem eq;
wenzelm@255
   780
wenzelm@255
   781
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   782
      | dups (rev_dups, x :: xs) =
wenzelm@255
   783
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   784
            dups (rev_dups, xs)
wenzelm@255
   785
          else dups (x :: rev_dups, xs);
wenzelm@255
   786
  in
wenzelm@255
   787
    dups ([], lst)
wenzelm@255
   788
  end;
wenzelm@255
   789
paulson@2243
   790
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   791
wenzelm@255
   792
wenzelm@233
   793
wenzelm@233
   794
(** association lists **)
clasohm@0
   795
wenzelm@233
   796
(*association list lookup*)
wenzelm@233
   797
fun assoc ([], key) = None
wenzelm@233
   798
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   799
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   800
paulson@2175
   801
(*association list lookup, optimized version for ints*)
berghofe@1576
   802
fun assoc_int ([], (key:int)) = None
berghofe@1576
   803
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   804
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   805
paulson@2175
   806
(*association list lookup, optimized version for strings*)
berghofe@1576
   807
fun assoc_string ([], (key:string)) = None
berghofe@1576
   808
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   809
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   810
paulson@2175
   811
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   812
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   813
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   814
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   815
wenzelm@233
   816
fun assocs ps x =
wenzelm@233
   817
  (case assoc (ps, x) of
wenzelm@233
   818
    None => []
wenzelm@233
   819
  | Some ys => ys);
wenzelm@233
   820
wenzelm@255
   821
(*two-fold association list lookup*)
wenzelm@255
   822
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   823
  (case assoc (aal, key1) of
wenzelm@255
   824
    Some al => assoc (al, key2)
wenzelm@255
   825
  | None => None);
wenzelm@255
   826
wenzelm@233
   827
(*generalized association list lookup*)
wenzelm@233
   828
fun gen_assoc eq ([], key) = None
wenzelm@233
   829
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   830
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   831
wenzelm@233
   832
(*association list update*)
wenzelm@233
   833
fun overwrite (al, p as (key, _)) =
wenzelm@233
   834
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   835
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   836
        | over [] = [p]
wenzelm@233
   837
  in over al end;
wenzelm@233
   838
wenzelm@2522
   839
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   840
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   841
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   842
        | over [] = [p]
wenzelm@2522
   843
  in over al end;
wenzelm@2522
   844
wenzelm@233
   845
wenzelm@233
   846
wenzelm@233
   847
(** generic tables **)
clasohm@0
   848
wenzelm@233
   849
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   850
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   851
  for long-term space efficiency.*)
wenzelm@233
   852
wenzelm@233
   853
(*append (new) elements to a table*)
wenzelm@233
   854
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   855
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   856
      let
wenzelm@233
   857
        val lst1 = dest_tab tab1;
wenzelm@233
   858
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   859
      in
wenzelm@233
   860
        if null new_lst2 then tab1
wenzelm@233
   861
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   862
      end;
clasohm@0
   863
wenzelm@233
   864
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   865
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   866
  let
wenzelm@233
   867
    val lst1 = dest_tab tab1;
wenzelm@233
   868
    val lst2 = dest_tab tab2;
wenzelm@233
   869
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   870
  in
wenzelm@233
   871
    if null new_lst2 then tab1
wenzelm@233
   872
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   873
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   874
  end;
clasohm@0
   875
wenzelm@233
   876
wenzelm@233
   877
(*lists as tables*)
paulson@2243
   878
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   879
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
   880
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
   881
wenzelm@380
   882
fun merge_rev_lists xs [] = xs
wenzelm@380
   883
  | merge_rev_lists [] ys = ys
wenzelm@380
   884
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   885
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   886
clasohm@0
   887
clasohm@0
   888
wenzelm@233
   889
(** balanced trees **)
wenzelm@233
   890
wenzelm@233
   891
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   892
wenzelm@233
   893
(*balanced folding; avoids deep nesting*)
wenzelm@233
   894
fun fold_bal f [x] = x
wenzelm@233
   895
  | fold_bal f [] = raise Balance
wenzelm@233
   896
  | fold_bal f xs =
wenzelm@233
   897
      let val k = length xs div 2
wenzelm@233
   898
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   899
             fold_bal f (drop(k, xs)))
wenzelm@233
   900
      end;
wenzelm@233
   901
wenzelm@233
   902
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   903
fun access_bal (f, g, x) n i =
wenzelm@233
   904
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   905
          if n=1 then x else
wenzelm@233
   906
          let val n2 = n div 2
wenzelm@233
   907
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   908
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   909
          end
wenzelm@233
   910
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   911
wenzelm@233
   912
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   913
fun accesses_bal (f, g, x) n =
wenzelm@233
   914
  let fun acc n =
wenzelm@233
   915
          if n=1 then [x] else
wenzelm@233
   916
          let val n2 = n div 2
wenzelm@233
   917
              val acc2 = acc n2
wenzelm@233
   918
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   919
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   920
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   921
wenzelm@233
   922
wenzelm@233
   923
wenzelm@2506
   924
(** orders **)
wenzelm@2506
   925
wenzelm@2506
   926
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   927
wenzelm@4445
   928
fun rev_order LESS = GREATER
wenzelm@4445
   929
  | rev_order EQUAL = EQUAL
wenzelm@4445
   930
  | rev_order GREATER = LESS;
wenzelm@4445
   931
wenzelm@4479
   932
(*assume rel is a linear strict order*)
wenzelm@4445
   933
fun make_ord rel (x, y) =
wenzelm@4445
   934
  if rel (x, y) then LESS
wenzelm@4445
   935
  else if rel (y, x) then GREATER
wenzelm@4445
   936
  else EQUAL;
wenzelm@4445
   937
wenzelm@4343
   938
fun int_ord (i, j: int) =
wenzelm@2506
   939
  if i < j then LESS
wenzelm@2506
   940
  else if i = j then EQUAL
wenzelm@2506
   941
  else GREATER;
wenzelm@2506
   942
wenzelm@4343
   943
fun string_ord (a, b: string) =
wenzelm@2506
   944
  if a < b then LESS
wenzelm@2506
   945
  else if a = b then EQUAL
wenzelm@2506
   946
  else GREATER;
wenzelm@2506
   947
wenzelm@4343
   948
(*lexicographic product*)
wenzelm@4343
   949
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   950
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   951
wenzelm@4343
   952
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
   953
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
   954
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
   955
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
   956
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
   957
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   958
wenzelm@4343
   959
(*lexicographic product of lists*)
wenzelm@4343
   960
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
   961
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
   962
wenzelm@2506
   963
wenzelm@4621
   964
(* sorting *)
wenzelm@4621
   965
wenzelm@4621
   966
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
   967
fun sort ord =
wenzelm@4621
   968
  let
wenzelm@4621
   969
    fun qsort xs =
wenzelm@4621
   970
      let val len = length xs in
wenzelm@4621
   971
        if len <= 1 then xs
wenzelm@4621
   972
        else
wenzelm@4621
   973
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
   974
            qsort lts @ eqs @ qsort gts
wenzelm@4621
   975
          end
wenzelm@4621
   976
      end
wenzelm@4621
   977
    and part _ [] = ([], [], [])
wenzelm@4621
   978
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
   979
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
   980
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
   981
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
   982
  in qsort end;
wenzelm@4621
   983
wenzelm@4621
   984
(*sort strings*)
wenzelm@4621
   985
val sort_strings = sort string_ord;
wenzelm@4621
   986
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
   987
wenzelm@4621
   988
wenzelm@2506
   989
wenzelm@3525
   990
(** input / output and diagnostics **)
wenzelm@233
   991
paulson@2243
   992
val cd = OS.FileSys.chDir;
wenzelm@2317
   993
val pwd = OS.FileSys.getDir;
paulson@2243
   994
wenzelm@3525
   995
wenzelm@3525
   996
local
wenzelm@3525
   997
  fun out s =
wenzelm@3525
   998
    (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
   999
wenzelm@3525
  1000
  fun prefix_lines prfx txt =
wenzelm@3832
  1001
    txt |> split_lines |> map (fn s => prfx ^ s ^ "\n") |> implode;
wenzelm@3525
  1002
in
wenzelm@3525
  1003
wenzelm@3525
  1004
(*hooks for output channels: normal, warning, error*)
wenzelm@3525
  1005
val prs_fn = ref (fn s => out s);
wenzelm@3525
  1006
val warning_fn = ref (fn s => out (prefix_lines "### " s));
wenzelm@3525
  1007
val error_fn = ref (fn s => out (prefix_lines "*** " s));
wenzelm@3525
  1008
wenzelm@3525
  1009
end;
berghofe@1580
  1010
berghofe@1580
  1011
fun prs s = !prs_fn s;
wenzelm@233
  1012
fun writeln s = prs (s ^ "\n");
wenzelm@233
  1013
wenzelm@3525
  1014
fun warning s = !warning_fn s;
wenzelm@233
  1015
wenzelm@233
  1016
(*print error message and abort to top level*)
wenzelm@233
  1017
exception ERROR;
wenzelm@4212
  1018
fun error_msg s = !error_fn s;	  (*promise to raise ERROR later!*)
wenzelm@3553
  1019
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1020
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1021
wenzelm@233
  1022
fun assert p msg = if p then () else error msg;
wenzelm@233
  1023
fun deny p msg = if p then error msg else ();
wenzelm@233
  1024
lcp@544
  1025
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1026
fun assert_all pred l msg_fn =
lcp@544
  1027
  let fun asl [] = ()
wenzelm@4212
  1028
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1029
  in asl l end;
wenzelm@233
  1030
wenzelm@3624
  1031
wenzelm@4212
  1032
(* handle errors capturing messages *)
wenzelm@3699
  1033
wenzelm@3699
  1034
datatype 'a error =
wenzelm@3699
  1035
  Error of string |
wenzelm@3699
  1036
  OK of 'a;
wenzelm@3699
  1037
wenzelm@4248
  1038
fun get_error (Error msg) = Some msg
wenzelm@4248
  1039
  | get_error _ = None;
wenzelm@4248
  1040
wenzelm@4248
  1041
fun get_ok (OK x) = Some x
wenzelm@4248
  1042
  | get_ok _ = None;
wenzelm@4248
  1043
wenzelm@3699
  1044
fun handle_error f x =
wenzelm@3699
  1045
  let
wenzelm@3699
  1046
    val buffer = ref "";
wenzelm@3699
  1047
    fun capture s = buffer := ! buffer ^ s ^ "\n";
wenzelm@3699
  1048
    val result = Some (setmp error_fn capture f x) handle ERROR => None;
wenzelm@3699
  1049
  in
wenzelm@4212
  1050
    (case result of
wenzelm@3699
  1051
      None => Error (! buffer)
wenzelm@4212
  1052
    | Some y => OK y)
wenzelm@3624
  1053
  end;
wenzelm@3624
  1054
wenzelm@3624
  1055
wenzelm@233
  1056
wenzelm@233
  1057
(** timing **)
wenzelm@233
  1058
paulson@4326
  1059
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
  1060
  prints its runtime*)
paulson@4326
  1061
fun cond_timeit flag f =
paulson@4326
  1062
  if flag then
paulson@4326
  1063
    let val start = startTiming()
paulson@4326
  1064
        val result = f ()
paulson@4326
  1065
    in
paulson@4326
  1066
	writeln (endTiming start);  result
paulson@4326
  1067
    end
paulson@4326
  1068
  else f ();
paulson@4326
  1069
wenzelm@233
  1070
(*unconditional timing function*)
paulson@2243
  1071
fun timeit x = cond_timeit true x;
wenzelm@233
  1072
wenzelm@233
  1073
(*timed application function*)
wenzelm@233
  1074
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1075
berghofe@3606
  1076
wenzelm@233
  1077
wenzelm@4621
  1078
(** misc **)
wenzelm@233
  1079
wenzelm@233
  1080
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1081
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1082
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1083
  in map keypair end;
clasohm@0
  1084
wenzelm@233
  1085
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1086
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1087
fun keyfilter [] searchkey = []
wenzelm@233
  1088
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1089
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1090
      else keyfilter pairs searchkey;
clasohm@0
  1091
clasohm@0
  1092
clasohm@0
  1093
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1094
  Preserves order of elements in both lists.*)
clasohm@0
  1095
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1096
    let fun part ([], answer) = answer
wenzelm@233
  1097
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1098
            then  part (xs, (x::ys, ns))
wenzelm@233
  1099
            else  part (xs, (ys, x::ns))
wenzelm@233
  1100
    in  part (rev ys, ([], []))  end;
clasohm@0
  1101
clasohm@0
  1102
clasohm@0
  1103
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1104
    let fun part [] = []
wenzelm@233
  1105
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1106
                           in (x::xs)::(part xs') end
clasohm@0
  1107
    in part end;
clasohm@0
  1108
clasohm@0
  1109
wenzelm@233
  1110
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1111
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1112
fun partition_list p i j =
wenzelm@233
  1113
  let fun part k xs =
wenzelm@233
  1114
            if k>j then
clasohm@0
  1115
              (case xs of [] => []
clasohm@0
  1116
                         | _ => raise LIST "partition_list")
clasohm@0
  1117
            else
wenzelm@233
  1118
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1119
            in  ns :: part(k+1)rest  end
clasohm@0
  1120
  in  part i end;
clasohm@0
  1121
clasohm@0
  1122
wenzelm@233
  1123
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1124
wenzelm@233
  1125
fun transitive_closure [] = []
wenzelm@233
  1126
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1127
      let val qs = transitive_closure ps
paulson@2182
  1128
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
paulson@2182
  1129
          fun step(u, us) = (u, if x mem_string us then zs union_string us 
paulson@2243
  1130
                                else us)
wenzelm@233
  1131
      in (x, zs) :: map step qs end;
clasohm@0
  1132
clasohm@0
  1133
wenzelm@233
  1134
(* generating identifiers *)
clasohm@0
  1135
paulson@4063
  1136
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1137
local
paulson@4063
  1138
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1139
fun char i =      if i<26 then chr (ord "A" + i)
paulson@4063
  1140
	     else if i<52 then chr (ord "a" + i - 26)
paulson@4063
  1141
	     else if i<62 then chr (ord"0" + i - 52)
paulson@4063
  1142
	     else if i=62 then "_"
paulson@4063
  1143
	     else  (*i=63*)    "'";
paulson@4063
  1144
paulson@4063
  1145
val charVec = Vector.tabulate (64, char);
paulson@4063
  1146
paulson@4063
  1147
fun newid n = 
paulson@4063
  1148
  let 
wenzelm@4284
  1149
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1150
wenzelm@4284
  1151
val seedr = ref 0;
clasohm@0
  1152
paulson@4063
  1153
in
wenzelm@4284
  1154
paulson@4063
  1155
fun init_gensym() = (seedr := 0);
paulson@2003
  1156
wenzelm@4284
  1157
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1158
end;
paulson@4063
  1159
paulson@4063
  1160
paulson@4063
  1161
local
paulson@4063
  1162
(*Identifies those character codes legal in identifiers.
paulson@4063
  1163
  chould use Basis Library character functions if Poly/ML provided characters*)
paulson@4063
  1164
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse 
paulson@4063
  1165
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1166
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1167
paulson@4063
  1168
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1169
paulson@4063
  1170
in
paulson@2003
  1171
clasohm@0
  1172
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1173
  If head is "z", bumps chars in tail.
clasohm@0
  1174
  Digits are incremented as if they were integers.
clasohm@0
  1175
  "_" and "'" are not changed.
wenzelm@233
  1176
  For making variants of identifiers.*)
clasohm@0
  1177
paulson@4063
  1178
fun bump_int_list(c::cs) = 
paulson@4063
  1179
	if c="9" then "0" :: bump_int_list cs 
paulson@4063
  1180
	else
paulson@4063
  1181
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1182
        else "1" :: c :: cs
clasohm@0
  1183
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1184
wenzelm@233
  1185
fun bump_list([], d) = [d]
wenzelm@233
  1186
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1187
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1188
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1189
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
paulson@4063
  1190
  | bump_list(c::cs, _) = 
paulson@4063
  1191
        let val k = ord(c)
paulson@4063
  1192
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs 
paulson@4063
  1193
	   else
paulson@4063
  1194
           if c="'" orelse c="_" then c :: bump_list(cs, "") 
paulson@4063
  1195
	   else error("bump_list: not legal in identifier: " ^
paulson@4063
  1196
		      implode(rev(c::cs)))
wenzelm@233
  1197
        end;
clasohm@0
  1198
clasohm@0
  1199
end;
clasohm@0
  1200
wenzelm@233
  1201
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1202
wenzelm@41
  1203
wenzelm@233
  1204
(* lexical scanning *)
clasohm@0
  1205
wenzelm@233
  1206
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1207
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1208
fun scanwords is_let cs =
clasohm@0
  1209
  let fun scan1 [] = []
wenzelm@233
  1210
        | scan1 cs =
wenzelm@233
  1211
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1212
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1213
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1214
wenzelm@4212
  1215
wenzelm@4212
  1216
wenzelm@4212
  1217
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1218
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1219
wenzelm@4212
  1220
wenzelm@4255
  1221
(* generic objects -- fool the ML type system via exception constructors *)
wenzelm@4792
  1222
wenzelm@4255
  1223
type object = exn;
wenzelm@4255
  1224
wenzelm@4792
  1225
fun type_error name =
wenzelm@4849
  1226
  error ("## RUNTIME TYPE ERROR ##\nFailed to access " ^ quote name ^ " data");
wenzelm@4792
  1227
wenzelm@4255
  1228
clasohm@1364
  1229
end;
clasohm@1364
  1230
clasohm@1364
  1231
open Library;