src/Pure/library.ML
author oheimb
Tue Jan 30 18:53:46 2001 +0100 (2001-01-30)
changeset 11002 e33dfe9bde39
parent 10951 ddb9b820d8a5
child 11021 41de937d338b
permissions -rw-r--r--
added foldln
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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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    Author:	Markus Wenzel, TU Munich
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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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infix 3 oo ooo oooo;
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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 |>> : ('a * 'b) * ('a -> 'c) -> 'c * 'b
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  val |>>> : ('a * 'b) * ('a -> 'c * 'd) -> 'c * ('b * 'd)
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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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  val oo: ('a -> 'b) * ('c -> 'd -> 'a) -> 'c -> 'd -> 'b
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  val ooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'a) -> 'c -> 'd -> 'e -> 'b
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  val oooo: ('a -> 'b) * ('c -> 'd -> 'e -> 'f -> 'a) -> 'c -> 'd -> 'e -> 'f -> 'b
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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 try: ('a -> 'b) -> 'a -> 'b option
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  val can: ('a -> 'b) -> 'a -> bool
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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 change: 'a ref -> ('a -> 'a) -> unit
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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 single: 'a -> 'a list
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  val append: 'a list -> 'a list -> 'a list
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  val apply: ('a -> 'a) list -> 'a -> 'a
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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 foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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  val foldln: ('a * int -> 'b -> 'b) -> 'a list -> 'b -> 'b
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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 get_first: ('a -> 'b option) -> 'a list -> 'b 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 seq2: ('a * 'b -> unit) -> 'a list * 'b list -> unit
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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 equal_lists: ('a * 'b -> bool) -> 'a list * 'b list -> bool
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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 gcd: int * int -> int
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  val lcm: int * int -> int
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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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  (*rational numbers*)
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  type rat
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  val rep_rat: rat -> int * int
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  val ratadd: rat * rat -> rat
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  val ratmul: rat * rat -> rat
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  val ratinv: rat -> rat
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  val int_ratdiv: int * int -> rat
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  val ratneg: rat -> rat
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  val rat_of_int: int -> rat
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  (*strings*)
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  val nth_elem_string: int * string -> string
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  val foldl_string: ('a * string -> 'a) -> 'a * string -> 'a
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  val exists_string: (string -> bool) -> string -> bool
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  val enclose: string -> string -> string -> string
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  val unenclose: 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 std_output: string -> unit
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  val prefix_lines: string -> string -> string
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  val split_lines: string -> string list
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  val untabify: string list -> string list
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  val suffix: string -> string -> string
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  val unsuffix: string -> string -> string
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  val replicate_string: int -> string -> string
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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 gen_inter: ('a * 'b -> bool) -> 'a list * 'b 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 overwrite_warn: (''a * 'b) list * (''a * 'b) -> string -> (''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 = LESS | EQUAL | GREATER
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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 writeln_fn: (string -> unit) ref
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  val priority_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 writeln: string -> unit
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  val priority: 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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  exception ERROR_MESSAGE of string
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  val transform_error: ('a -> 'b) -> 'a -> 'b
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  val transform_failure: (exn -> exn) -> ('a -> 'b) -> 'a -> 'b
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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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  val timing: bool ref
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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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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;
clasohm@0
   294
wenzelm@380
   295
(*reverse apply*)
wenzelm@410
   296
fun (x |> f) = f x;
wenzelm@8418
   297
fun ((x, y) |>> f) = (f x, y);
wenzelm@8418
   298
fun ((x, y) |>>> f) = let val (x', z) = f x in (x', (y, z)) end;
wenzelm@380
   299
wenzelm@233
   300
(*application of (infix) operator to its left or right argument*)
wenzelm@233
   301
fun apl (x, f) y = f (x, y);
wenzelm@233
   302
fun apr (f, y) x = f (x, y);
clasohm@0
   303
wenzelm@233
   304
(*function exponentiation: f(...(f x)...) with n applications of f*)
wenzelm@233
   305
fun funpow n f x =
wenzelm@233
   306
  let fun rep (0, x) = x
wenzelm@233
   307
        | rep (n, x) = rep (n - 1, f x)
wenzelm@233
   308
  in rep (n, x) end;
wenzelm@160
   309
wenzelm@5893
   310
(*concatenation: 2 and 3 args*)
wenzelm@5893
   311
fun (f oo g) x y = f (g x y);
wenzelm@5893
   312
fun (f ooo g) x y z = f (g x y z);
wenzelm@6510
   313
fun (f oooo g) x y z w = f (g x y z w);
wenzelm@6510
   314
wenzelm@160
   315
wenzelm@160
   316
wenzelm@2471
   317
(** stamps **)
wenzelm@2471
   318
wenzelm@2471
   319
type stamp = unit ref;
wenzelm@2471
   320
val stamp: unit -> stamp = ref;
wenzelm@2471
   321
wenzelm@2471
   322
wenzelm@2471
   323
wenzelm@233
   324
(** options **)
clasohm@0
   325
clasohm@0
   326
datatype 'a option = None | Some of 'a;
clasohm@0
   327
wenzelm@4139
   328
exception OPTION;
clasohm@0
   329
clasohm@0
   330
fun the (Some x) = x
wenzelm@4139
   331
  | the None = raise OPTION;
clasohm@0
   332
wenzelm@4212
   333
(*strict!*)
wenzelm@255
   334
fun if_none None y = y
wenzelm@255
   335
  | if_none (Some x) _ = x;
wenzelm@255
   336
clasohm@0
   337
fun is_some (Some _) = true
clasohm@0
   338
  | is_some None = false;
clasohm@0
   339
clasohm@0
   340
fun is_none (Some _) = false
clasohm@0
   341
  | is_none None = true;
clasohm@0
   342
wenzelm@233
   343
fun apsome f (Some x) = Some (f x)
wenzelm@233
   344
  | apsome _ None = None;
clasohm@0
   345
wenzelm@6959
   346
wenzelm@6959
   347
(* exception handling *)
wenzelm@6959
   348
wenzelm@6959
   349
exception ERROR;
wenzelm@6959
   350
wenzelm@6959
   351
fun try f x = Some (f x)
wenzelm@6959
   352
  handle Interrupt => raise Interrupt | ERROR => raise ERROR | _ => None;
wenzelm@6959
   353
wenzelm@6959
   354
fun can f x = is_some (try f x);
wenzelm@4139
   355
wenzelm@4139
   356
wenzelm@4139
   357
wenzelm@233
   358
(** pairs **)
wenzelm@233
   359
wenzelm@233
   360
fun pair x y = (x, y);
wenzelm@233
   361
fun rpair x y = (y, x);
wenzelm@233
   362
wenzelm@233
   363
fun fst (x, y) = x;
wenzelm@233
   364
fun snd (x, y) = y;
wenzelm@233
   365
wenzelm@233
   366
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   367
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   368
wenzelm@233
   369
fun swap (x, y) = (y, x);
wenzelm@233
   370
wenzelm@4212
   371
(*apply function to components*)
wenzelm@233
   372
fun apfst f (x, y) = (f x, y);
wenzelm@233
   373
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   374
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   375
wenzelm@233
   376
wenzelm@233
   377
wenzelm@233
   378
(** booleans **)
wenzelm@233
   379
wenzelm@233
   380
(* equality *)
wenzelm@233
   381
wenzelm@233
   382
fun equal x y = x = y;
wenzelm@233
   383
fun not_equal x y = x <> y;
wenzelm@233
   384
wenzelm@233
   385
wenzelm@233
   386
(* operators for combining predicates *)
wenzelm@233
   387
paulson@2175
   388
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   389
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   390
wenzelm@233
   391
wenzelm@233
   392
(* predicates on lists *)
wenzelm@233
   393
wenzelm@233
   394
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   395
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   396
  let fun boolf [] = false
wenzelm@233
   397
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   398
  in boolf end;
wenzelm@233
   399
wenzelm@233
   400
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   401
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   402
  let fun boolf [] = true
wenzelm@233
   403
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   404
  in boolf end;
clasohm@0
   405
wenzelm@233
   406
wenzelm@380
   407
(* flags *)
wenzelm@380
   408
wenzelm@380
   409
fun set flag = (flag := true; true);
wenzelm@380
   410
fun reset flag = (flag := false; false);
wenzelm@380
   411
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   412
wenzelm@9118
   413
fun change r f = r := f (! r);
wenzelm@9118
   414
wenzelm@4212
   415
(*temporarily set flag, handling errors*)
wenzelm@2978
   416
fun setmp flag value f x =
wenzelm@2958
   417
  let
wenzelm@2958
   418
    val orig_value = ! flag;
wenzelm@2958
   419
    fun return y = (flag := orig_value; y);
wenzelm@2958
   420
  in
wenzelm@2958
   421
    flag := value;
wenzelm@2958
   422
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   423
  end;
wenzelm@2958
   424
wenzelm@380
   425
wenzelm@233
   426
wenzelm@233
   427
(** lists **)
wenzelm@233
   428
wenzelm@233
   429
exception LIST of string;
wenzelm@233
   430
wenzelm@233
   431
fun null [] = true
wenzelm@233
   432
  | null (_ :: _) = false;
wenzelm@233
   433
wenzelm@233
   434
fun hd [] = raise LIST "hd"
wenzelm@233
   435
  | hd (x :: _) = x;
wenzelm@233
   436
wenzelm@233
   437
fun tl [] = raise LIST "tl"
wenzelm@233
   438
  | tl (_ :: xs) = xs;
wenzelm@233
   439
wenzelm@233
   440
fun cons x xs = x :: xs;
wenzelm@5285
   441
fun single x = [x];
wenzelm@233
   442
wenzelm@4629
   443
fun append xs ys = xs @ ys;
wenzelm@4629
   444
wenzelm@5904
   445
fun apply [] x = x
wenzelm@5904
   446
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   447
wenzelm@233
   448
wenzelm@233
   449
(* fold *)
wenzelm@233
   450
wenzelm@233
   451
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   452
wenzelm@233
   453
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   454
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   455
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   456
  let fun itl (e, [])  = e
wenzelm@233
   457
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   458
  in  itl end;
wenzelm@233
   459
wenzelm@233
   460
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   461
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   462
fun foldr f (l, e) =
wenzelm@233
   463
  let fun itr [] = e
wenzelm@233
   464
        | itr (a::l) = f(a, itr l)
wenzelm@233
   465
  in  itr l  end;
wenzelm@233
   466
wenzelm@233
   467
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   468
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   469
fun foldr1 f l =
wenzelm@4181
   470
  let fun itr [x] = x
wenzelm@233
   471
        | itr (x::l) = f(x, itr l)
wenzelm@233
   472
  in  itr l  end;
wenzelm@233
   473
wenzelm@4956
   474
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   475
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   476
      let
wenzelm@4956
   477
        val (x', y') = f (x, y);
wenzelm@4956
   478
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   479
      in (x'', y' :: ys') end;
wenzelm@4956
   480
oheimb@11002
   481
fun foldln f xs e = fst (foldl (fn ((e,i), x) => (f (x,i) e, i+1)) ((e,1),xs));
wenzelm@233
   482
wenzelm@233
   483
(* basic list functions *)
wenzelm@233
   484
wenzelm@233
   485
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   486
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   487
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   488
in  fun length l = length1 (0, l) end;
wenzelm@233
   489
wenzelm@233
   490
(*take the first n elements from a list*)
wenzelm@233
   491
fun take (n, []) = []
wenzelm@233
   492
  | take (n, x :: xs) =
wenzelm@233
   493
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   494
wenzelm@233
   495
(*drop the first n elements from a list*)
wenzelm@233
   496
fun drop (n, []) = []
wenzelm@233
   497
  | drop (n, x :: xs) =
wenzelm@233
   498
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   499
nipkow@4713
   500
fun dropwhile P [] = []
nipkow@4713
   501
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   502
wenzelm@233
   503
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   504
  raise EXCEPTION if list too short*)
wenzelm@233
   505
fun nth_elem NL =
wenzelm@233
   506
  (case drop NL of
wenzelm@233
   507
    [] => raise LIST "nth_elem"
wenzelm@233
   508
  | x :: _ => x);
wenzelm@233
   509
wenzelm@233
   510
(*last element of a list*)
wenzelm@233
   511
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   512
  | last_elem [x] = x
wenzelm@233
   513
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   514
wenzelm@3762
   515
(*rear decomposition*)
wenzelm@3762
   516
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   517
  | split_last [x] = ([], x)
wenzelm@3762
   518
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   519
wenzelm@4893
   520
(*update nth element*)
wenzelm@4893
   521
fun nth_update x (n, xs) =
wenzelm@4893
   522
  let
wenzelm@4893
   523
    val prfx = take (n, xs);
wenzelm@4893
   524
    val sffx = drop (n, xs);
wenzelm@4893
   525
  in
wenzelm@4893
   526
    (case sffx of
wenzelm@4893
   527
      [] => raise LIST "nth_update"
wenzelm@4893
   528
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   529
  end;
wenzelm@4893
   530
wenzelm@4212
   531
(*find the position of an element in a list*)
wenzelm@4212
   532
fun find_index pred =
wenzelm@4212
   533
  let fun find _ [] = ~1
wenzelm@4212
   534
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   535
  in find 0 end;
wenzelm@3762
   536
wenzelm@4224
   537
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   538
wenzelm@4212
   539
(*find first element satisfying predicate*)
wenzelm@4212
   540
fun find_first _ [] = None
wenzelm@4212
   541
  | find_first pred (x :: xs) =
wenzelm@4212
   542
      if pred x then Some x else find_first pred xs;
wenzelm@233
   543
wenzelm@4916
   544
(*get first element by lookup function*)
wenzelm@4916
   545
fun get_first _ [] = None
wenzelm@4916
   546
  | get_first f (x :: xs) =
wenzelm@4916
   547
      (case f x of
wenzelm@4916
   548
        None => get_first f xs
wenzelm@4916
   549
      | some => some);
wenzelm@4916
   550
wenzelm@233
   551
(*flatten a list of lists to a list*)
wenzelm@233
   552
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   553
wenzelm@233
   554
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   555
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   556
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   557
  let fun seqf [] = ()
wenzelm@233
   558
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   559
  in seqf end;
wenzelm@233
   560
wenzelm@233
   561
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   562
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   563
  | separate _ xs = xs;
wenzelm@233
   564
wenzelm@233
   565
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   566
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   567
  let fun rep (0, xs) = xs
wenzelm@233
   568
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   569
  in
wenzelm@233
   570
    if n < 0 then raise LIST "replicate"
wenzelm@233
   571
    else rep (n, [])
wenzelm@233
   572
  end;
wenzelm@233
   573
wenzelm@4248
   574
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   575
fun multiply ([], _) = []
wenzelm@4248
   576
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   577
wenzelm@233
   578
wenzelm@233
   579
(* filter *)
wenzelm@233
   580
wenzelm@233
   581
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   582
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   583
  let fun filt [] = []
wenzelm@233
   584
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   585
  in filt end;
clasohm@0
   586
clasohm@0
   587
fun filter_out f = filter (not o f);
clasohm@0
   588
wenzelm@233
   589
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   590
  | mapfilter f (x :: xs) =
wenzelm@233
   591
      (case f x of
wenzelm@233
   592
        None => mapfilter f xs
wenzelm@233
   593
      | Some y => y :: mapfilter f xs);
wenzelm@233
   594
wenzelm@233
   595
wenzelm@233
   596
(* lists of pairs *)
wenzelm@233
   597
wenzelm@380
   598
fun map2 _ ([], []) = []
wenzelm@380
   599
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   600
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   601
wenzelm@380
   602
fun exists2 _ ([], []) = false
wenzelm@380
   603
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   604
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   605
wenzelm@380
   606
fun forall2 _ ([], []) = true
wenzelm@380
   607
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   608
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   609
wenzelm@4956
   610
fun seq2 _ ([], []) = ()
wenzelm@4956
   611
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   612
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   613
wenzelm@233
   614
(*combine two lists forming a list of pairs:
wenzelm@233
   615
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   616
fun [] ~~ [] = []
wenzelm@233
   617
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   618
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   619
wenzelm@233
   620
(*inverse of ~~; the old 'split':
wenzelm@233
   621
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   622
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   623
wenzelm@7468
   624
fun equal_lists eq (xs, ys) = length xs = length ys andalso forall2 eq (xs, ys);
wenzelm@7468
   625
wenzelm@233
   626
wenzelm@233
   627
(* prefixes, suffixes *)
wenzelm@233
   628
wenzelm@233
   629
fun [] prefix _ = true
wenzelm@233
   630
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   631
  | _ prefix _ = false;
wenzelm@233
   632
wenzelm@233
   633
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   634
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   635
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   636
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   637
        | take (rxs, x :: xs) =
wenzelm@255
   638
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   639
  in  take([], xs)  end;
wenzelm@233
   640
wenzelm@233
   641
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   642
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   643
fun take_suffix _ [] = ([], [])
wenzelm@233
   644
  | take_suffix pred (x :: xs) =
wenzelm@233
   645
      (case take_suffix pred xs of
wenzelm@233
   646
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   647
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   648
wenzelm@233
   649
wenzelm@233
   650
wenzelm@233
   651
(** integers **)
wenzelm@233
   652
nipkow@10692
   653
fun gcd(x,y) =
nipkow@10692
   654
  let fun gxd x y =
nipkow@10692
   655
    if y = 0 then x else gxd y (x mod y)
nipkow@10692
   656
  in if x < y then gxd y x else gxd x y end;
nipkow@10692
   657
nipkow@10692
   658
fun lcm(x,y) = (x * y) div gcd(x,y);
nipkow@10692
   659
wenzelm@2958
   660
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   661
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   662
wenzelm@233
   663
wenzelm@233
   664
(* lists of integers *)
wenzelm@233
   665
wenzelm@233
   666
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   667
fun (from upto to) =
wenzelm@233
   668
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   669
wenzelm@233
   670
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   671
fun (from downto to) =
wenzelm@233
   672
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   673
wenzelm@233
   674
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   675
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   676
  | downto0 ([], n) = n = ~1;
wenzelm@233
   677
wenzelm@233
   678
wenzelm@233
   679
(* convert integers to strings *)
wenzelm@233
   680
wenzelm@233
   681
(*expand the number in the given base;
wenzelm@233
   682
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   683
fun radixpand (base, num) : int list =
wenzelm@233
   684
  let
wenzelm@233
   685
    fun radix (n, tail) =
wenzelm@233
   686
      if n < base then n :: tail
wenzelm@233
   687
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   688
  in radix (num, []) end;
wenzelm@233
   689
wenzelm@233
   690
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   691
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   692
fun radixstring (base, zerochar, num) =
wenzelm@233
   693
  let val offset = ord zerochar;
wenzelm@233
   694
      fun chrof n = chr (offset + n)
wenzelm@233
   695
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   696
wenzelm@233
   697
paulson@3407
   698
val string_of_int = Int.toString;
wenzelm@233
   699
paulson@3407
   700
fun string_of_indexname (a,0) = a
paulson@3407
   701
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   702
wenzelm@233
   703
wenzelm@233
   704
(** strings **)
wenzelm@233
   705
wenzelm@6312
   706
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   707
wenzelm@6312
   708
fun nth_elem_string (i, str) =
wenzelm@6959
   709
  (case try String.substring (str, i, 1) of
wenzelm@6959
   710
    Some s => s
wenzelm@6959
   711
  | None => raise LIST "nth_elem_string");
wenzelm@6312
   712
wenzelm@6282
   713
fun foldl_string f (x0, str) =
wenzelm@6282
   714
  let
wenzelm@6282
   715
    val n = size str;
wenzelm@6282
   716
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   717
  in fold (x0, 0) end;
wenzelm@6282
   718
wenzelm@6312
   719
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
wenzelm@6312
   720
lcp@512
   721
(*enclose in brackets*)
lcp@512
   722
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   723
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   724
wenzelm@233
   725
(*simple quoting (does not escape special chars)*)
lcp@512
   726
val quote = enclose "\"" "\"";
wenzelm@233
   727
wenzelm@4212
   728
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   729
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   730
wenzelm@255
   731
val commas = space_implode ", ";
wenzelm@380
   732
val commas_quote = commas o map quote;
wenzelm@255
   733
wenzelm@233
   734
(*concatenate messages, one per line, into a string*)
wenzelm@255
   735
val cat_lines = space_implode "\n";
wenzelm@233
   736
wenzelm@4212
   737
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   738
fun space_explode _ "" = []
wenzelm@3832
   739
  | space_explode sep str =
wenzelm@3832
   740
      let
wenzelm@3832
   741
        fun expl chs =
wenzelm@3832
   742
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   743
            (cs, []) => [implode cs]
wenzelm@3832
   744
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   745
      in expl (explode str) end;
wenzelm@3832
   746
wenzelm@3832
   747
val split_lines = space_explode "\n";
wenzelm@3832
   748
wenzelm@7712
   749
(*untabify*)
wenzelm@7712
   750
fun untabify chs =
wenzelm@7712
   751
  let
wenzelm@7712
   752
    val tab_width = 8;
wenzelm@7712
   753
wenzelm@7712
   754
    fun untab (_, "\n") = (0, ["\n"])
wenzelm@9118
   755
      | untab (pos, "\t") =
wenzelm@9118
   756
          let val d = tab_width - (pos mod tab_width) in (pos + d, replicate d " ") end
wenzelm@7712
   757
      | untab (pos, c) = (pos + 1, [c]);
wenzelm@7712
   758
  in
wenzelm@7712
   759
    if not (exists (equal "\t") chs) then chs
wenzelm@7712
   760
    else flat (#2 (foldl_map untab (0, chs)))
wenzelm@7712
   761
  end;
wenzelm@7712
   762
wenzelm@5285
   763
(*append suffix*)
wenzelm@5285
   764
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   765
wenzelm@5285
   766
(*remove suffix*)
wenzelm@5285
   767
fun unsuffix sfx s =
wenzelm@5285
   768
  let
wenzelm@5285
   769
    val cs = explode s;
wenzelm@5285
   770
    val prfx_len = size s - size sfx;
wenzelm@5285
   771
  in
wenzelm@5285
   772
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   773
      implode (take (prfx_len, cs))
wenzelm@5285
   774
    else raise LIST "unsuffix"
wenzelm@5285
   775
  end;
wenzelm@5285
   776
wenzelm@10951
   777
fun replicate_string 0 _ = ""
wenzelm@10951
   778
  | replicate_string 1 a = a
wenzelm@10951
   779
  | replicate_string k a =
wenzelm@10951
   780
      if k mod 2 = 0 then replicate_string (k div 2) (a ^ a)
wenzelm@10951
   781
      else replicate_string (k div 2) (a ^ a) ^ a;
wenzelm@10951
   782
wenzelm@3832
   783
wenzelm@233
   784
wenzelm@233
   785
(** lists as sets **)
wenzelm@233
   786
wenzelm@233
   787
(*membership in a list*)
wenzelm@233
   788
fun x mem [] = false
wenzelm@233
   789
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   790
paulson@2175
   791
(*membership in a list, optimized version for ints*)
berghofe@1576
   792
fun (x:int) mem_int [] = false
berghofe@1576
   793
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   794
paulson@2175
   795
(*membership in a list, optimized version for strings*)
berghofe@1576
   796
fun (x:string) mem_string [] = false
berghofe@1576
   797
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   798
clasohm@0
   799
(*generalized membership test*)
wenzelm@233
   800
fun gen_mem eq (x, []) = false
wenzelm@233
   801
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   802
wenzelm@233
   803
wenzelm@233
   804
(*insertion into list if not already there*)
paulson@2175
   805
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   806
paulson@2175
   807
(*insertion into list, optimized version for ints*)
paulson@2175
   808
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   809
paulson@2175
   810
(*insertion into list, optimized version for strings*)
paulson@2175
   811
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   812
clasohm@0
   813
(*generalized insertion*)
wenzelm@233
   814
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   815
wenzelm@233
   816
wenzelm@233
   817
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   818
fun xs union [] = xs
wenzelm@233
   819
  | [] union ys = ys
wenzelm@233
   820
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   821
paulson@2175
   822
(*union of sets, optimized version for ints*)
berghofe@1576
   823
fun (xs:int list) union_int [] = xs
berghofe@1576
   824
  | [] union_int ys = ys
berghofe@1576
   825
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   826
paulson@2175
   827
(*union of sets, optimized version for strings*)
berghofe@1576
   828
fun (xs:string list) union_string [] = xs
berghofe@1576
   829
  | [] union_string ys = ys
berghofe@1576
   830
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   831
clasohm@0
   832
(*generalized union*)
wenzelm@233
   833
fun gen_union eq (xs, []) = xs
wenzelm@233
   834
  | gen_union eq ([], ys) = ys
wenzelm@233
   835
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   836
wenzelm@233
   837
wenzelm@233
   838
(*intersection*)
wenzelm@233
   839
fun [] inter ys = []
wenzelm@233
   840
  | (x :: xs) inter ys =
wenzelm@233
   841
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   842
paulson@2175
   843
(*intersection, optimized version for ints*)
berghofe@1576
   844
fun ([]:int list) inter_int ys = []
berghofe@1576
   845
  | (x :: xs) inter_int ys =
berghofe@1576
   846
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   847
paulson@2175
   848
(*intersection, optimized version for strings *)
berghofe@1576
   849
fun ([]:string list) inter_string ys = []
berghofe@1576
   850
  | (x :: xs) inter_string ys =
berghofe@1576
   851
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   852
paulson@7090
   853
(*generalized intersection*)
paulson@7090
   854
fun gen_inter eq ([], ys) = []
paulson@7090
   855
  | gen_inter eq (x::xs, ys) = 
paulson@7090
   856
      if gen_mem eq (x,ys) then x :: gen_inter eq (xs, ys)
paulson@7090
   857
	                   else      gen_inter eq (xs, ys);
paulson@7090
   858
wenzelm@233
   859
wenzelm@233
   860
(*subset*)
wenzelm@233
   861
fun [] subset ys = true
wenzelm@233
   862
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   863
paulson@2175
   864
(*subset, optimized version for ints*)
berghofe@1576
   865
fun ([]:int list) subset_int ys = true
berghofe@1576
   866
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   867
paulson@2175
   868
(*subset, optimized version for strings*)
berghofe@1576
   869
fun ([]:string list) subset_string ys = true
berghofe@1576
   870
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   871
wenzelm@4363
   872
(*set equality*)
wenzelm@4363
   873
fun eq_set (xs, ys) =
wenzelm@4363
   874
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   875
paulson@2182
   876
(*set equality for strings*)
berghofe@1576
   877
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   878
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   879
paulson@2182
   880
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   881
wenzelm@265
   882
wenzelm@233
   883
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   884
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   885
  | [] \ x = [];
wenzelm@233
   886
paulson@2243
   887
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   888
wenzelm@233
   889
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   890
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   891
paulson@2243
   892
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   893
wenzelm@233
   894
wenzelm@233
   895
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   896
  first of equal elements*)
wenzelm@233
   897
fun gen_distinct eq lst =
wenzelm@233
   898
  let
wenzelm@233
   899
    val memb = gen_mem eq;
clasohm@0
   900
wenzelm@233
   901
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   902
      | dist (rev_seen, x :: xs) =
wenzelm@233
   903
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   904
          else dist (x :: rev_seen, xs);
wenzelm@233
   905
  in
wenzelm@233
   906
    dist ([], lst)
wenzelm@233
   907
  end;
wenzelm@233
   908
paulson@2243
   909
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   910
wenzelm@233
   911
wenzelm@233
   912
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   913
fun findrep [] = []
wenzelm@233
   914
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   915
wenzelm@233
   916
wenzelm@255
   917
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   918
  order, takes first of equal elements*)
wenzelm@255
   919
fun gen_duplicates eq lst =
wenzelm@255
   920
  let
wenzelm@255
   921
    val memb = gen_mem eq;
wenzelm@255
   922
wenzelm@255
   923
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   924
      | dups (rev_dups, x :: xs) =
wenzelm@255
   925
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   926
            dups (rev_dups, xs)
wenzelm@255
   927
          else dups (x :: rev_dups, xs);
wenzelm@255
   928
  in
wenzelm@255
   929
    dups ([], lst)
wenzelm@255
   930
  end;
wenzelm@255
   931
paulson@2243
   932
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   933
wenzelm@255
   934
wenzelm@233
   935
wenzelm@233
   936
(** association lists **)
clasohm@0
   937
wenzelm@233
   938
(*association list lookup*)
wenzelm@233
   939
fun assoc ([], key) = None
wenzelm@233
   940
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   941
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   942
paulson@2175
   943
(*association list lookup, optimized version for ints*)
berghofe@1576
   944
fun assoc_int ([], (key:int)) = None
berghofe@1576
   945
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   946
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   947
paulson@2175
   948
(*association list lookup, optimized version for strings*)
berghofe@1576
   949
fun assoc_string ([], (key:string)) = None
berghofe@1576
   950
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   951
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   952
paulson@2175
   953
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   954
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   955
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   956
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   957
wenzelm@233
   958
fun assocs ps x =
wenzelm@233
   959
  (case assoc (ps, x) of
wenzelm@233
   960
    None => []
wenzelm@233
   961
  | Some ys => ys);
wenzelm@233
   962
wenzelm@255
   963
(*two-fold association list lookup*)
wenzelm@255
   964
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   965
  (case assoc (aal, key1) of
wenzelm@255
   966
    Some al => assoc (al, key2)
wenzelm@255
   967
  | None => None);
wenzelm@255
   968
wenzelm@233
   969
(*generalized association list lookup*)
wenzelm@233
   970
fun gen_assoc eq ([], key) = None
wenzelm@233
   971
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   972
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   973
wenzelm@233
   974
(*association list update*)
wenzelm@233
   975
fun overwrite (al, p as (key, _)) =
wenzelm@233
   976
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   977
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   978
        | over [] = [p]
wenzelm@233
   979
  in over al end;
wenzelm@233
   980
wenzelm@2522
   981
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   982
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   983
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   984
        | over [] = [p]
wenzelm@2522
   985
  in over al end;
wenzelm@2522
   986
wenzelm@233
   987
wenzelm@233
   988
wenzelm@233
   989
(** generic tables **)
clasohm@0
   990
wenzelm@233
   991
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   992
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   993
  for long-term space efficiency.*)
wenzelm@233
   994
wenzelm@233
   995
(*append (new) elements to a table*)
wenzelm@233
   996
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   997
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   998
      let
wenzelm@233
   999
        val lst1 = dest_tab tab1;
wenzelm@233
  1000
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
  1001
      in
wenzelm@233
  1002
        if null new_lst2 then tab1
wenzelm@233
  1003
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
  1004
      end;
clasohm@0
  1005
wenzelm@233
  1006
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
  1007
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
  1008
  let
wenzelm@233
  1009
    val lst1 = dest_tab tab1;
wenzelm@233
  1010
    val lst2 = dest_tab tab2;
wenzelm@233
  1011
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
  1012
  in
wenzelm@233
  1013
    if null new_lst2 then tab1
wenzelm@233
  1014
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
  1015
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
  1016
  end;
clasohm@0
  1017
wenzelm@233
  1018
wenzelm@233
  1019
(*lists as tables*)
paulson@2243
  1020
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
  1021
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
  1022
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
  1023
wenzelm@380
  1024
fun merge_rev_lists xs [] = xs
wenzelm@380
  1025
  | merge_rev_lists [] ys = ys
wenzelm@380
  1026
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
  1027
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
  1028
clasohm@0
  1029
clasohm@0
  1030
wenzelm@233
  1031
(** balanced trees **)
wenzelm@233
  1032
wenzelm@233
  1033
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
  1034
wenzelm@233
  1035
(*balanced folding; avoids deep nesting*)
wenzelm@233
  1036
fun fold_bal f [x] = x
wenzelm@233
  1037
  | fold_bal f [] = raise Balance
wenzelm@233
  1038
  | fold_bal f xs =
wenzelm@233
  1039
      let val k = length xs div 2
wenzelm@233
  1040
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
  1041
             fold_bal f (drop(k, xs)))
wenzelm@233
  1042
      end;
wenzelm@233
  1043
wenzelm@233
  1044
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
  1045
fun access_bal (f, g, x) n i =
wenzelm@233
  1046
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
  1047
          if n=1 then x else
wenzelm@233
  1048
          let val n2 = n div 2
wenzelm@233
  1049
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
  1050
                       else g (acc (n-n2) (i-n2))
wenzelm@233
  1051
          end
wenzelm@233
  1052
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
  1053
wenzelm@233
  1054
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
  1055
fun accesses_bal (f, g, x) n =
wenzelm@233
  1056
  let fun acc n =
wenzelm@233
  1057
          if n=1 then [x] else
wenzelm@233
  1058
          let val n2 = n div 2
wenzelm@233
  1059
              val acc2 = acc n2
wenzelm@233
  1060
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
  1061
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
  1062
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
  1063
wenzelm@233
  1064
wenzelm@233
  1065
wenzelm@2506
  1066
(** orders **)
wenzelm@2506
  1067
wenzelm@2506
  1068
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
  1069
wenzelm@4445
  1070
fun rev_order LESS = GREATER
wenzelm@4445
  1071
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1072
  | rev_order GREATER = LESS;
wenzelm@4445
  1073
wenzelm@4479
  1074
(*assume rel is a linear strict order*)
wenzelm@4445
  1075
fun make_ord rel (x, y) =
wenzelm@4445
  1076
  if rel (x, y) then LESS
wenzelm@4445
  1077
  else if rel (y, x) then GREATER
wenzelm@4445
  1078
  else EQUAL;
wenzelm@4445
  1079
wenzelm@4343
  1080
fun int_ord (i, j: int) =
wenzelm@2506
  1081
  if i < j then LESS
wenzelm@2506
  1082
  else if i = j then EQUAL
wenzelm@2506
  1083
  else GREATER;
wenzelm@2506
  1084
wenzelm@4343
  1085
fun string_ord (a, b: string) =
wenzelm@2506
  1086
  if a < b then LESS
wenzelm@2506
  1087
  else if a = b then EQUAL
wenzelm@2506
  1088
  else GREATER;
wenzelm@2506
  1089
wenzelm@4343
  1090
(*lexicographic product*)
wenzelm@4343
  1091
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1092
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1093
wenzelm@4343
  1094
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1095
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1096
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1097
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1098
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1099
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1100
wenzelm@4343
  1101
(*lexicographic product of lists*)
wenzelm@4343
  1102
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1103
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1104
wenzelm@2506
  1105
wenzelm@4621
  1106
(* sorting *)
wenzelm@4621
  1107
wenzelm@4621
  1108
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1109
fun sort ord =
wenzelm@4621
  1110
  let
wenzelm@4621
  1111
    fun qsort xs =
wenzelm@4621
  1112
      let val len = length xs in
wenzelm@4621
  1113
        if len <= 1 then xs
wenzelm@4621
  1114
        else
wenzelm@4621
  1115
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1116
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1117
          end
wenzelm@4621
  1118
      end
wenzelm@4621
  1119
    and part _ [] = ([], [], [])
wenzelm@4621
  1120
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1121
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1122
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1123
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1124
  in qsort end;
wenzelm@4621
  1125
wenzelm@4621
  1126
(*sort strings*)
wenzelm@4621
  1127
val sort_strings = sort string_ord;
wenzelm@4621
  1128
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1129
wenzelm@4621
  1130
wenzelm@2506
  1131
wenzelm@3525
  1132
(** input / output and diagnostics **)
wenzelm@233
  1133
paulson@2243
  1134
val cd = OS.FileSys.chDir;
wenzelm@2317
  1135
val pwd = OS.FileSys.getDir;
paulson@2243
  1136
wenzelm@5942
  1137
fun std_output s =
wenzelm@5942
  1138
  (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
  1139
wenzelm@5942
  1140
fun prefix_lines prfx txt =
wenzelm@5949
  1141
  txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@3525
  1142
wenzelm@3525
  1143
(*hooks for output channels: normal, warning, error*)
wenzelm@5966
  1144
val writeln_fn = ref (std_output o suffix "\n");
wenzelm@9774
  1145
val priority_fn = ref (fn s => ! writeln_fn s);
wenzelm@5949
  1146
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
wenzelm@5949
  1147
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
berghofe@1580
  1148
wenzelm@5966
  1149
fun writeln s = ! writeln_fn s;
wenzelm@9774
  1150
fun priority s = ! priority_fn s;
wenzelm@5942
  1151
fun warning s = ! warning_fn s;
wenzelm@233
  1152
wenzelm@233
  1153
(*print error message and abort to top level*)
wenzelm@6959
  1154
wenzelm@5949
  1155
fun error_msg s = ! error_fn s;
wenzelm@3553
  1156
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1157
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1158
wenzelm@233
  1159
fun assert p msg = if p then () else error msg;
wenzelm@233
  1160
fun deny p msg = if p then error msg else ();
wenzelm@233
  1161
lcp@544
  1162
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1163
fun assert_all pred l msg_fn =
lcp@544
  1164
  let fun asl [] = ()
wenzelm@4212
  1165
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1166
  in asl l end;
wenzelm@233
  1167
wenzelm@3624
  1168
wenzelm@4212
  1169
(* handle errors capturing messages *)
wenzelm@3699
  1170
wenzelm@3699
  1171
datatype 'a error =
wenzelm@3699
  1172
  Error of string |
wenzelm@3699
  1173
  OK of 'a;
wenzelm@3699
  1174
wenzelm@4248
  1175
fun get_error (Error msg) = Some msg
wenzelm@4248
  1176
  | get_error _ = None;
wenzelm@4248
  1177
wenzelm@4248
  1178
fun get_ok (OK x) = Some x
wenzelm@4248
  1179
  | get_ok _ = None;
wenzelm@4248
  1180
wenzelm@5037
  1181
datatype 'a result =
wenzelm@5037
  1182
  Result of 'a |
wenzelm@5037
  1183
  Exn of exn;
wenzelm@5037
  1184
wenzelm@3699
  1185
fun handle_error f x =
wenzelm@3699
  1186
  let
wenzelm@4945
  1187
    val buffer = ref ([]: string list);
wenzelm@4945
  1188
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1189
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1190
  in
wenzelm@5037
  1191
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1192
      Result y => (err_msg (); OK y)
wenzelm@5037
  1193
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1194
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1195
  end;
wenzelm@3624
  1196
wenzelm@3624
  1197
wenzelm@5037
  1198
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1199
wenzelm@4923
  1200
exception ERROR_MESSAGE of string;
wenzelm@4923
  1201
wenzelm@4923
  1202
fun transform_error f x =
wenzelm@4923
  1203
  (case handle_error f x of
wenzelm@4923
  1204
    OK y => y
wenzelm@4923
  1205
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1206
wenzelm@4923
  1207
wenzelm@5904
  1208
(* transform any exception, including ERROR *)
wenzelm@5904
  1209
wenzelm@5904
  1210
fun transform_failure exn f x =
wenzelm@5904
  1211
  transform_error f x handle e => raise exn e;
wenzelm@5904
  1212
wenzelm@5904
  1213
wenzelm@233
  1214
wenzelm@233
  1215
(** timing **)
wenzelm@233
  1216
paulson@4326
  1217
(*a conditional timing function: applies f to () and, if the flag is true,
wenzelm@8999
  1218
  prints its runtime on warning channel*)
paulson@4326
  1219
fun cond_timeit flag f =
paulson@4326
  1220
  if flag then
paulson@4326
  1221
    let val start = startTiming()
paulson@4326
  1222
        val result = f ()
wenzelm@8999
  1223
    in warning (endTiming start);  result end
paulson@4326
  1224
  else f ();
paulson@4326
  1225
wenzelm@233
  1226
(*unconditional timing function*)
paulson@2243
  1227
fun timeit x = cond_timeit true x;
wenzelm@233
  1228
wenzelm@233
  1229
(*timed application function*)
wenzelm@233
  1230
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1231
wenzelm@8999
  1232
(*global timing mode*)
wenzelm@8999
  1233
val timing = ref false;
wenzelm@8999
  1234
berghofe@3606
  1235
wenzelm@233
  1236
nipkow@10692
  1237
(** rational numbers **)
nipkow@10692
  1238
nipkow@10692
  1239
datatype rat = Rat of bool * int * int
nipkow@10692
  1240
nipkow@10692
  1241
fun rep_rat(Rat(a,p,q)) = (if a then p else ~p,q)
nipkow@10692
  1242
nipkow@10692
  1243
fun ratnorm(a,p,q) = if p=0 then Rat(a,0,1) else
nipkow@10692
  1244
  let val absp = abs p
nipkow@10692
  1245
      val m = gcd(absp,q)
nipkow@10692
  1246
  in Rat(a = (0 <= p), absp div m, q div m) end;
nipkow@10692
  1247
nipkow@10692
  1248
fun ratadd(Rat(a,p,q),Rat(b,r,s)) =
nipkow@10692
  1249
  let val den = lcm(q,s)
nipkow@10692
  1250
      val p = p*(den div q) and r = r*(den div s)
nipkow@10692
  1251
      val num = (if a then p else ~p) + (if b then r else ~r)
nipkow@10692
  1252
  in ratnorm(true,num,den) end;
nipkow@10692
  1253
nipkow@10692
  1254
fun ratmul(Rat(a,p,q),Rat(b,r,s)) = ratnorm(a=b,p*r,q*s)
nipkow@10692
  1255
nipkow@10692
  1256
fun ratinv(Rat(a,p,q)) = if p=0 then error("ratinv") else Rat(a,q,p)
nipkow@10692
  1257
nipkow@10692
  1258
fun int_ratdiv(p,q) =
nipkow@10692
  1259
  if q=0 then error("int_ratdiv") else ratnorm(0<=q, p, abs q)
nipkow@10692
  1260
nipkow@10692
  1261
fun ratneg(Rat(b,p,q)) = Rat(not b,p,q);
nipkow@10692
  1262
nipkow@10692
  1263
fun rat_of_int i = if i < 0 then Rat(false,abs i,1) else Rat(true,i,1);
nipkow@10692
  1264
nipkow@10692
  1265
wenzelm@4621
  1266
(** misc **)
wenzelm@233
  1267
wenzelm@9830
  1268
fun overwrite_warn (args as (alist, (a, _))) msg =
wenzelm@9830
  1269
 (if is_none (assoc (alist, a)) then () else warning msg;
wenzelm@9830
  1270
  overwrite args);
nipkow@9721
  1271
wenzelm@233
  1272
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1273
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1274
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1275
  in map keypair end;
clasohm@0
  1276
wenzelm@233
  1277
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1278
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1279
fun keyfilter [] searchkey = []
wenzelm@233
  1280
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1281
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1282
      else keyfilter pairs searchkey;
clasohm@0
  1283
clasohm@0
  1284
clasohm@0
  1285
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1286
  Preserves order of elements in both lists.*)
clasohm@0
  1287
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1288
    let fun part ([], answer) = answer
wenzelm@233
  1289
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1290
            then  part (xs, (x::ys, ns))
wenzelm@233
  1291
            else  part (xs, (ys, x::ns))
wenzelm@233
  1292
    in  part (rev ys, ([], []))  end;
clasohm@0
  1293
clasohm@0
  1294
clasohm@0
  1295
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1296
    let fun part [] = []
wenzelm@233
  1297
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1298
                           in (x::xs)::(part xs') end
clasohm@0
  1299
    in part end;
clasohm@0
  1300
clasohm@0
  1301
wenzelm@233
  1302
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1303
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1304
fun partition_list p i j =
wenzelm@233
  1305
  let fun part k xs =
wenzelm@233
  1306
            if k>j then
clasohm@0
  1307
              (case xs of [] => []
clasohm@0
  1308
                         | _ => raise LIST "partition_list")
clasohm@0
  1309
            else
wenzelm@233
  1310
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1311
            in  ns :: part(k+1)rest  end
clasohm@0
  1312
  in  part i end;
clasohm@0
  1313
clasohm@0
  1314
wenzelm@233
  1315
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1316
wenzelm@233
  1317
fun transitive_closure [] = []
wenzelm@233
  1318
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1319
      let val qs = transitive_closure ps
paulson@2182
  1320
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
wenzelm@5904
  1321
          fun step(u, us) = (u, if x mem_string us then zs union_string us
paulson@2243
  1322
                                else us)
wenzelm@233
  1323
      in (x, zs) :: map step qs end;
clasohm@0
  1324
clasohm@0
  1325
wenzelm@233
  1326
(* generating identifiers *)
clasohm@0
  1327
paulson@4063
  1328
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1329
local
paulson@4063
  1330
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1331
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1332
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1333
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1334
             else if i=62 then "_"
wenzelm@5904
  1335
             else  (*i=63*)    "'";
paulson@4063
  1336
paulson@4063
  1337
val charVec = Vector.tabulate (64, char);
paulson@4063
  1338
wenzelm@5904
  1339
fun newid n =
wenzelm@5904
  1340
  let
wenzelm@4284
  1341
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1342
wenzelm@4284
  1343
val seedr = ref 0;
clasohm@0
  1344
paulson@4063
  1345
in
wenzelm@4284
  1346
paulson@4063
  1347
fun init_gensym() = (seedr := 0);
paulson@2003
  1348
wenzelm@4284
  1349
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1350
end;
paulson@4063
  1351
paulson@4063
  1352
paulson@4063
  1353
local
paulson@4063
  1354
(*Identifies those character codes legal in identifiers.
paulson@4063
  1355
  chould use Basis Library character functions if Poly/ML provided characters*)
wenzelm@5904
  1356
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse
paulson@4063
  1357
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1358
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1359
paulson@4063
  1360
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1361
paulson@4063
  1362
in
paulson@2003
  1363
clasohm@0
  1364
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1365
  If head is "z", bumps chars in tail.
clasohm@0
  1366
  Digits are incremented as if they were integers.
clasohm@0
  1367
  "_" and "'" are not changed.
wenzelm@233
  1368
  For making variants of identifiers.*)
clasohm@0
  1369
wenzelm@5904
  1370
fun bump_int_list(c::cs) =
wenzelm@5904
  1371
        if c="9" then "0" :: bump_int_list cs
wenzelm@5904
  1372
        else
paulson@4063
  1373
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1374
        else "1" :: c :: cs
clasohm@0
  1375
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1376
wenzelm@233
  1377
fun bump_list([], d) = [d]
wenzelm@233
  1378
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1379
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1380
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1381
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@5904
  1382
  | bump_list(c::cs, _) =
paulson@4063
  1383
        let val k = ord(c)
wenzelm@5904
  1384
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs
wenzelm@5904
  1385
           else
wenzelm@5904
  1386
           if c="'" orelse c="_" then c :: bump_list(cs, "")
wenzelm@5904
  1387
           else error("bump_list: not legal in identifier: " ^
wenzelm@5904
  1388
                      implode(rev(c::cs)))
wenzelm@233
  1389
        end;
clasohm@0
  1390
clasohm@0
  1391
end;
clasohm@0
  1392
wenzelm@233
  1393
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1394
wenzelm@41
  1395
wenzelm@233
  1396
(* lexical scanning *)
clasohm@0
  1397
wenzelm@233
  1398
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1399
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1400
fun scanwords is_let cs =
clasohm@0
  1401
  let fun scan1 [] = []
wenzelm@233
  1402
        | scan1 cs =
wenzelm@233
  1403
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1404
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1405
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1406
wenzelm@4212
  1407
wenzelm@4212
  1408
wenzelm@4212
  1409
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1410
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1411
wenzelm@4212
  1412
clasohm@1364
  1413
end;
clasohm@1364
  1414
clasohm@1364
  1415
open Library;