src/Pure/library.ML
author wenzelm
Mon Jun 15 11:05:25 1998 +0200 (1998-06-15)
changeset 5037 224887671646
parent 4995 905cd6f73429
child 5112 9e74cf11e4a4
permissions -rw-r--r--
handle_error: capture error msgs, even if no exception raised;
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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 foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list
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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 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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  exception ERROR_MESSAGE of string
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  val transform_error: ('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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  (*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;
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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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wenzelm@233
   314
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   315
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   316
wenzelm@233
   317
fun swap (x, y) = (y, x);
wenzelm@233
   318
wenzelm@4212
   319
(*apply function to components*)
wenzelm@233
   320
fun apfst f (x, y) = (f x, y);
wenzelm@233
   321
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   322
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   323
wenzelm@233
   324
wenzelm@233
   325
wenzelm@233
   326
(** booleans **)
wenzelm@233
   327
wenzelm@233
   328
(* equality *)
wenzelm@233
   329
wenzelm@233
   330
fun equal x y = x = y;
wenzelm@233
   331
fun not_equal x y = x <> y;
wenzelm@233
   332
wenzelm@233
   333
wenzelm@233
   334
(* operators for combining predicates *)
wenzelm@233
   335
paulson@2175
   336
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   337
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   338
wenzelm@233
   339
wenzelm@233
   340
(* predicates on lists *)
wenzelm@233
   341
wenzelm@233
   342
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   343
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   344
  let fun boolf [] = false
wenzelm@233
   345
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   346
  in boolf end;
wenzelm@233
   347
wenzelm@233
   348
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   349
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   350
  let fun boolf [] = true
wenzelm@233
   351
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   352
  in boolf end;
clasohm@0
   353
wenzelm@233
   354
wenzelm@380
   355
(* flags *)
wenzelm@380
   356
wenzelm@380
   357
fun set flag = (flag := true; true);
wenzelm@380
   358
fun reset flag = (flag := false; false);
wenzelm@380
   359
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   360
wenzelm@4212
   361
(*temporarily set flag, handling errors*)
wenzelm@2978
   362
fun setmp flag value f x =
wenzelm@2958
   363
  let
wenzelm@2958
   364
    val orig_value = ! flag;
wenzelm@2958
   365
    fun return y = (flag := orig_value; y);
wenzelm@2958
   366
  in
wenzelm@2958
   367
    flag := value;
wenzelm@2958
   368
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   369
  end;
wenzelm@2958
   370
wenzelm@380
   371
wenzelm@233
   372
wenzelm@233
   373
(** lists **)
wenzelm@233
   374
wenzelm@233
   375
exception LIST of string;
wenzelm@233
   376
wenzelm@233
   377
fun null [] = true
wenzelm@233
   378
  | null (_ :: _) = false;
wenzelm@233
   379
wenzelm@233
   380
fun hd [] = raise LIST "hd"
wenzelm@233
   381
  | hd (x :: _) = x;
wenzelm@233
   382
wenzelm@233
   383
fun tl [] = raise LIST "tl"
wenzelm@233
   384
  | tl (_ :: xs) = xs;
wenzelm@233
   385
wenzelm@233
   386
fun cons x xs = x :: xs;
wenzelm@233
   387
wenzelm@4629
   388
fun append xs ys = xs @ ys;
wenzelm@4629
   389
wenzelm@233
   390
wenzelm@233
   391
(* fold *)
wenzelm@233
   392
wenzelm@233
   393
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   394
wenzelm@233
   395
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   396
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   397
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   398
  let fun itl (e, [])  = e
wenzelm@233
   399
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   400
  in  itl end;
wenzelm@233
   401
wenzelm@233
   402
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   403
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   404
fun foldr f (l, e) =
wenzelm@233
   405
  let fun itr [] = e
wenzelm@233
   406
        | itr (a::l) = f(a, itr l)
wenzelm@233
   407
  in  itr l  end;
wenzelm@233
   408
wenzelm@233
   409
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   410
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   411
fun foldr1 f l =
wenzelm@4181
   412
  let fun itr [x] = x
wenzelm@233
   413
        | itr (x::l) = f(x, itr l)
wenzelm@233
   414
  in  itr l  end;
wenzelm@233
   415
wenzelm@4956
   416
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   417
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   418
      let
wenzelm@4956
   419
        val (x', y') = f (x, y);
wenzelm@4956
   420
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   421
      in (x'', y' :: ys') end;
wenzelm@4956
   422
wenzelm@233
   423
wenzelm@233
   424
(* basic list functions *)
wenzelm@233
   425
wenzelm@233
   426
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   427
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   428
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   429
in  fun length l = length1 (0, l) end;
wenzelm@233
   430
wenzelm@233
   431
(*take the first n elements from a list*)
wenzelm@233
   432
fun take (n, []) = []
wenzelm@233
   433
  | take (n, x :: xs) =
wenzelm@233
   434
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   435
wenzelm@233
   436
(*drop the first n elements from a list*)
wenzelm@233
   437
fun drop (n, []) = []
wenzelm@233
   438
  | drop (n, x :: xs) =
wenzelm@233
   439
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   440
nipkow@4713
   441
fun dropwhile P [] = []
nipkow@4713
   442
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   443
wenzelm@233
   444
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   445
  raise EXCEPTION if list too short*)
wenzelm@233
   446
fun nth_elem NL =
wenzelm@233
   447
  (case drop NL of
wenzelm@233
   448
    [] => raise LIST "nth_elem"
wenzelm@233
   449
  | x :: _ => x);
wenzelm@233
   450
wenzelm@233
   451
(*last element of a list*)
wenzelm@233
   452
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   453
  | last_elem [x] = x
wenzelm@233
   454
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   455
wenzelm@3762
   456
(*rear decomposition*)
wenzelm@3762
   457
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   458
  | split_last [x] = ([], x)
wenzelm@3762
   459
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   460
wenzelm@4893
   461
(*update nth element*)
wenzelm@4893
   462
fun nth_update x (n, xs) =
wenzelm@4893
   463
  let
wenzelm@4893
   464
    val prfx = take (n, xs);
wenzelm@4893
   465
    val sffx = drop (n, xs);
wenzelm@4893
   466
  in
wenzelm@4893
   467
    (case sffx of
wenzelm@4893
   468
      [] => raise LIST "nth_update"
wenzelm@4893
   469
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   470
  end;
wenzelm@4893
   471
wenzelm@4212
   472
(*find the position of an element in a list*)
wenzelm@4212
   473
fun find_index pred =
wenzelm@4212
   474
  let fun find _ [] = ~1
wenzelm@4212
   475
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   476
  in find 0 end;
wenzelm@3762
   477
wenzelm@4224
   478
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   479
wenzelm@4212
   480
(*find first element satisfying predicate*)
wenzelm@4212
   481
fun find_first _ [] = None
wenzelm@4212
   482
  | find_first pred (x :: xs) =
wenzelm@4212
   483
      if pred x then Some x else find_first pred xs;
wenzelm@233
   484
wenzelm@4916
   485
(*get first element by lookup function*)
wenzelm@4916
   486
fun get_first _ [] = None
wenzelm@4916
   487
  | get_first f (x :: xs) =
wenzelm@4916
   488
      (case f x of
wenzelm@4916
   489
        None => get_first f xs
wenzelm@4916
   490
      | some => some);
wenzelm@4916
   491
wenzelm@233
   492
(*flatten a list of lists to a list*)
wenzelm@233
   493
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   494
wenzelm@233
   495
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   496
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   497
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   498
  let fun seqf [] = ()
wenzelm@233
   499
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   500
  in seqf end;
wenzelm@233
   501
wenzelm@233
   502
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   503
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   504
  | separate _ xs = xs;
wenzelm@233
   505
wenzelm@233
   506
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   507
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   508
  let fun rep (0, xs) = xs
wenzelm@233
   509
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   510
  in
wenzelm@233
   511
    if n < 0 then raise LIST "replicate"
wenzelm@233
   512
    else rep (n, [])
wenzelm@233
   513
  end;
wenzelm@233
   514
wenzelm@4248
   515
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   516
fun multiply ([], _) = []
wenzelm@4248
   517
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   518
wenzelm@233
   519
wenzelm@233
   520
(* filter *)
wenzelm@233
   521
wenzelm@233
   522
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   523
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   524
  let fun filt [] = []
wenzelm@233
   525
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   526
  in filt end;
clasohm@0
   527
clasohm@0
   528
fun filter_out f = filter (not o f);
clasohm@0
   529
wenzelm@233
   530
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   531
  | mapfilter f (x :: xs) =
wenzelm@233
   532
      (case f x of
wenzelm@233
   533
        None => mapfilter f xs
wenzelm@233
   534
      | Some y => y :: mapfilter f xs);
wenzelm@233
   535
wenzelm@233
   536
wenzelm@233
   537
(* lists of pairs *)
wenzelm@233
   538
wenzelm@380
   539
fun map2 _ ([], []) = []
wenzelm@380
   540
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   541
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   542
wenzelm@380
   543
fun exists2 _ ([], []) = false
wenzelm@380
   544
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   545
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   546
wenzelm@380
   547
fun forall2 _ ([], []) = true
wenzelm@380
   548
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   549
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   550
wenzelm@4956
   551
fun seq2 _ ([], []) = ()
wenzelm@4956
   552
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   553
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   554
wenzelm@233
   555
(*combine two lists forming a list of pairs:
wenzelm@233
   556
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   557
fun [] ~~ [] = []
wenzelm@233
   558
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   559
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   560
wenzelm@233
   561
(*inverse of ~~; the old 'split':
wenzelm@233
   562
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   563
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   564
wenzelm@233
   565
wenzelm@233
   566
(* prefixes, suffixes *)
wenzelm@233
   567
wenzelm@233
   568
fun [] prefix _ = true
wenzelm@233
   569
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   570
  | _ prefix _ = false;
wenzelm@233
   571
wenzelm@233
   572
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   573
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   574
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   575
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   576
        | take (rxs, x :: xs) =
wenzelm@255
   577
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   578
  in  take([], xs)  end;
wenzelm@233
   579
wenzelm@233
   580
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   581
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   582
fun take_suffix _ [] = ([], [])
wenzelm@233
   583
  | take_suffix pred (x :: xs) =
wenzelm@233
   584
      (case take_suffix pred xs of
wenzelm@233
   585
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   586
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   587
wenzelm@233
   588
wenzelm@233
   589
wenzelm@233
   590
(** integers **)
wenzelm@233
   591
wenzelm@2958
   592
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   593
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   594
wenzelm@233
   595
wenzelm@233
   596
(* lists of integers *)
wenzelm@233
   597
wenzelm@233
   598
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   599
fun (from upto to) =
wenzelm@233
   600
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   601
wenzelm@233
   602
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   603
fun (from downto to) =
wenzelm@233
   604
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   605
wenzelm@233
   606
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   607
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   608
  | downto0 ([], n) = n = ~1;
wenzelm@233
   609
wenzelm@233
   610
wenzelm@233
   611
(* convert integers to strings *)
wenzelm@233
   612
wenzelm@233
   613
(*expand the number in the given base;
wenzelm@233
   614
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   615
fun radixpand (base, num) : int list =
wenzelm@233
   616
  let
wenzelm@233
   617
    fun radix (n, tail) =
wenzelm@233
   618
      if n < base then n :: tail
wenzelm@233
   619
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   620
  in radix (num, []) end;
wenzelm@233
   621
wenzelm@233
   622
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   623
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   624
fun radixstring (base, zerochar, num) =
wenzelm@233
   625
  let val offset = ord zerochar;
wenzelm@233
   626
      fun chrof n = chr (offset + n)
wenzelm@233
   627
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   628
wenzelm@233
   629
paulson@3407
   630
val string_of_int = Int.toString;
wenzelm@233
   631
paulson@3407
   632
fun string_of_indexname (a,0) = a
paulson@3407
   633
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   634
wenzelm@233
   635
wenzelm@4212
   636
wenzelm@233
   637
(** strings **)
wenzelm@233
   638
wenzelm@4692
   639
(*beginning of text*)
wenzelm@4956
   640
fun beginning cs =
wenzelm@4956
   641
  implode (map (fn c => if ord c < ord " " then " " else c) (take (10, cs))) ^ " ...";
wenzelm@233
   642
lcp@512
   643
(*enclose in brackets*)
lcp@512
   644
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@255
   645
wenzelm@233
   646
(*simple quoting (does not escape special chars)*)
lcp@512
   647
val quote = enclose "\"" "\"";
wenzelm@233
   648
wenzelm@4212
   649
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   650
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   651
wenzelm@255
   652
val commas = space_implode ", ";
wenzelm@380
   653
val commas_quote = commas o map quote;
wenzelm@255
   654
wenzelm@233
   655
(*concatenate messages, one per line, into a string*)
wenzelm@255
   656
val cat_lines = space_implode "\n";
wenzelm@233
   657
wenzelm@4212
   658
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   659
fun space_explode _ "" = []
wenzelm@3832
   660
  | space_explode sep str =
wenzelm@3832
   661
      let
wenzelm@3832
   662
        fun expl chs =
wenzelm@3832
   663
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   664
            (cs, []) => [implode cs]
wenzelm@3832
   665
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   666
      in expl (explode str) end;
wenzelm@3832
   667
wenzelm@3832
   668
val split_lines = space_explode "\n";
wenzelm@3832
   669
wenzelm@3832
   670
wenzelm@233
   671
wenzelm@233
   672
(** lists as sets **)
wenzelm@233
   673
wenzelm@233
   674
(*membership in a list*)
wenzelm@233
   675
fun x mem [] = false
wenzelm@233
   676
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   677
paulson@2175
   678
(*membership in a list, optimized version for ints*)
berghofe@1576
   679
fun (x:int) mem_int [] = false
berghofe@1576
   680
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   681
paulson@2175
   682
(*membership in a list, optimized version for strings*)
berghofe@1576
   683
fun (x:string) mem_string [] = false
berghofe@1576
   684
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   685
clasohm@0
   686
(*generalized membership test*)
wenzelm@233
   687
fun gen_mem eq (x, []) = false
wenzelm@233
   688
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   689
wenzelm@233
   690
wenzelm@233
   691
(*insertion into list if not already there*)
paulson@2175
   692
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   693
paulson@2175
   694
(*insertion into list, optimized version for ints*)
paulson@2175
   695
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   696
paulson@2175
   697
(*insertion into list, optimized version for strings*)
paulson@2175
   698
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   699
clasohm@0
   700
(*generalized insertion*)
wenzelm@233
   701
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   702
wenzelm@233
   703
wenzelm@233
   704
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   705
fun xs union [] = xs
wenzelm@233
   706
  | [] union ys = ys
wenzelm@233
   707
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   708
paulson@2175
   709
(*union of sets, optimized version for ints*)
berghofe@1576
   710
fun (xs:int list) union_int [] = xs
berghofe@1576
   711
  | [] union_int ys = ys
berghofe@1576
   712
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   713
paulson@2175
   714
(*union of sets, optimized version for strings*)
berghofe@1576
   715
fun (xs:string list) union_string [] = xs
berghofe@1576
   716
  | [] union_string ys = ys
berghofe@1576
   717
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   718
clasohm@0
   719
(*generalized union*)
wenzelm@233
   720
fun gen_union eq (xs, []) = xs
wenzelm@233
   721
  | gen_union eq ([], ys) = ys
wenzelm@233
   722
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   723
wenzelm@233
   724
wenzelm@233
   725
(*intersection*)
wenzelm@233
   726
fun [] inter ys = []
wenzelm@233
   727
  | (x :: xs) inter ys =
wenzelm@233
   728
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   729
paulson@2175
   730
(*intersection, optimized version for ints*)
berghofe@1576
   731
fun ([]:int list) inter_int ys = []
berghofe@1576
   732
  | (x :: xs) inter_int ys =
berghofe@1576
   733
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   734
paulson@2175
   735
(*intersection, optimized version for strings *)
berghofe@1576
   736
fun ([]:string list) inter_string ys = []
berghofe@1576
   737
  | (x :: xs) inter_string ys =
berghofe@1576
   738
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   739
wenzelm@233
   740
wenzelm@233
   741
(*subset*)
wenzelm@233
   742
fun [] subset ys = true
wenzelm@233
   743
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   744
paulson@2175
   745
(*subset, optimized version for ints*)
berghofe@1576
   746
fun ([]:int list) subset_int ys = true
berghofe@1576
   747
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   748
paulson@2175
   749
(*subset, optimized version for strings*)
berghofe@1576
   750
fun ([]:string list) subset_string ys = true
berghofe@1576
   751
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   752
wenzelm@4363
   753
(*set equality*)
wenzelm@4363
   754
fun eq_set (xs, ys) =
wenzelm@4363
   755
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   756
paulson@2182
   757
(*set equality for strings*)
berghofe@1576
   758
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   759
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   760
paulson@2182
   761
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   762
wenzelm@265
   763
wenzelm@233
   764
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   765
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   766
  | [] \ x = [];
wenzelm@233
   767
paulson@2243
   768
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   769
wenzelm@233
   770
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   771
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   772
paulson@2243
   773
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   774
wenzelm@233
   775
wenzelm@233
   776
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   777
  first of equal elements*)
wenzelm@233
   778
fun gen_distinct eq lst =
wenzelm@233
   779
  let
wenzelm@233
   780
    val memb = gen_mem eq;
clasohm@0
   781
wenzelm@233
   782
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   783
      | dist (rev_seen, x :: xs) =
wenzelm@233
   784
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   785
          else dist (x :: rev_seen, xs);
wenzelm@233
   786
  in
wenzelm@233
   787
    dist ([], lst)
wenzelm@233
   788
  end;
wenzelm@233
   789
paulson@2243
   790
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   791
wenzelm@233
   792
wenzelm@233
   793
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   794
fun findrep [] = []
wenzelm@233
   795
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   796
wenzelm@233
   797
wenzelm@255
   798
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   799
  order, takes first of equal elements*)
wenzelm@255
   800
fun gen_duplicates eq lst =
wenzelm@255
   801
  let
wenzelm@255
   802
    val memb = gen_mem eq;
wenzelm@255
   803
wenzelm@255
   804
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   805
      | dups (rev_dups, x :: xs) =
wenzelm@255
   806
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   807
            dups (rev_dups, xs)
wenzelm@255
   808
          else dups (x :: rev_dups, xs);
wenzelm@255
   809
  in
wenzelm@255
   810
    dups ([], lst)
wenzelm@255
   811
  end;
wenzelm@255
   812
paulson@2243
   813
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   814
wenzelm@255
   815
wenzelm@233
   816
wenzelm@233
   817
(** association lists **)
clasohm@0
   818
wenzelm@233
   819
(*association list lookup*)
wenzelm@233
   820
fun assoc ([], key) = None
wenzelm@233
   821
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   822
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   823
paulson@2175
   824
(*association list lookup, optimized version for ints*)
berghofe@1576
   825
fun assoc_int ([], (key:int)) = None
berghofe@1576
   826
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   827
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   828
paulson@2175
   829
(*association list lookup, optimized version for strings*)
berghofe@1576
   830
fun assoc_string ([], (key:string)) = None
berghofe@1576
   831
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   832
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   833
paulson@2175
   834
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   835
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   836
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   837
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   838
wenzelm@233
   839
fun assocs ps x =
wenzelm@233
   840
  (case assoc (ps, x) of
wenzelm@233
   841
    None => []
wenzelm@233
   842
  | Some ys => ys);
wenzelm@233
   843
wenzelm@255
   844
(*two-fold association list lookup*)
wenzelm@255
   845
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   846
  (case assoc (aal, key1) of
wenzelm@255
   847
    Some al => assoc (al, key2)
wenzelm@255
   848
  | None => None);
wenzelm@255
   849
wenzelm@233
   850
(*generalized association list lookup*)
wenzelm@233
   851
fun gen_assoc eq ([], key) = None
wenzelm@233
   852
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   853
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   854
wenzelm@233
   855
(*association list update*)
wenzelm@233
   856
fun overwrite (al, p as (key, _)) =
wenzelm@233
   857
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   858
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   859
        | over [] = [p]
wenzelm@233
   860
  in over al end;
wenzelm@233
   861
wenzelm@2522
   862
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   863
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   864
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   865
        | over [] = [p]
wenzelm@2522
   866
  in over al end;
wenzelm@2522
   867
wenzelm@233
   868
wenzelm@233
   869
wenzelm@233
   870
(** generic tables **)
clasohm@0
   871
wenzelm@233
   872
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   873
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   874
  for long-term space efficiency.*)
wenzelm@233
   875
wenzelm@233
   876
(*append (new) elements to a table*)
wenzelm@233
   877
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   878
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   879
      let
wenzelm@233
   880
        val lst1 = dest_tab tab1;
wenzelm@233
   881
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   882
      in
wenzelm@233
   883
        if null new_lst2 then tab1
wenzelm@233
   884
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   885
      end;
clasohm@0
   886
wenzelm@233
   887
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   888
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   889
  let
wenzelm@233
   890
    val lst1 = dest_tab tab1;
wenzelm@233
   891
    val lst2 = dest_tab tab2;
wenzelm@233
   892
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   893
  in
wenzelm@233
   894
    if null new_lst2 then tab1
wenzelm@233
   895
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   896
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   897
  end;
clasohm@0
   898
wenzelm@233
   899
wenzelm@233
   900
(*lists as tables*)
paulson@2243
   901
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   902
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
   903
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
   904
wenzelm@380
   905
fun merge_rev_lists xs [] = xs
wenzelm@380
   906
  | merge_rev_lists [] ys = ys
wenzelm@380
   907
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   908
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   909
clasohm@0
   910
clasohm@0
   911
wenzelm@233
   912
(** balanced trees **)
wenzelm@233
   913
wenzelm@233
   914
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   915
wenzelm@233
   916
(*balanced folding; avoids deep nesting*)
wenzelm@233
   917
fun fold_bal f [x] = x
wenzelm@233
   918
  | fold_bal f [] = raise Balance
wenzelm@233
   919
  | fold_bal f xs =
wenzelm@233
   920
      let val k = length xs div 2
wenzelm@233
   921
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   922
             fold_bal f (drop(k, xs)))
wenzelm@233
   923
      end;
wenzelm@233
   924
wenzelm@233
   925
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   926
fun access_bal (f, g, x) n i =
wenzelm@233
   927
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   928
          if n=1 then x else
wenzelm@233
   929
          let val n2 = n div 2
wenzelm@233
   930
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   931
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   932
          end
wenzelm@233
   933
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   934
wenzelm@233
   935
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   936
fun accesses_bal (f, g, x) n =
wenzelm@233
   937
  let fun acc n =
wenzelm@233
   938
          if n=1 then [x] else
wenzelm@233
   939
          let val n2 = n div 2
wenzelm@233
   940
              val acc2 = acc n2
wenzelm@233
   941
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   942
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   943
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   944
wenzelm@233
   945
wenzelm@233
   946
wenzelm@2506
   947
(** orders **)
wenzelm@2506
   948
wenzelm@2506
   949
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   950
wenzelm@4445
   951
fun rev_order LESS = GREATER
wenzelm@4445
   952
  | rev_order EQUAL = EQUAL
wenzelm@4445
   953
  | rev_order GREATER = LESS;
wenzelm@4445
   954
wenzelm@4479
   955
(*assume rel is a linear strict order*)
wenzelm@4445
   956
fun make_ord rel (x, y) =
wenzelm@4445
   957
  if rel (x, y) then LESS
wenzelm@4445
   958
  else if rel (y, x) then GREATER
wenzelm@4445
   959
  else EQUAL;
wenzelm@4445
   960
wenzelm@4343
   961
fun int_ord (i, j: int) =
wenzelm@2506
   962
  if i < j then LESS
wenzelm@2506
   963
  else if i = j then EQUAL
wenzelm@2506
   964
  else GREATER;
wenzelm@2506
   965
wenzelm@4343
   966
fun string_ord (a, b: string) =
wenzelm@2506
   967
  if a < b then LESS
wenzelm@2506
   968
  else if a = b then EQUAL
wenzelm@2506
   969
  else GREATER;
wenzelm@2506
   970
wenzelm@4343
   971
(*lexicographic product*)
wenzelm@4343
   972
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
   973
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
   974
wenzelm@4343
   975
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
   976
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
   977
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
   978
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
   979
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
   980
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
   981
wenzelm@4343
   982
(*lexicographic product of lists*)
wenzelm@4343
   983
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
   984
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
   985
wenzelm@2506
   986
wenzelm@4621
   987
(* sorting *)
wenzelm@4621
   988
wenzelm@4621
   989
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
   990
fun sort ord =
wenzelm@4621
   991
  let
wenzelm@4621
   992
    fun qsort xs =
wenzelm@4621
   993
      let val len = length xs in
wenzelm@4621
   994
        if len <= 1 then xs
wenzelm@4621
   995
        else
wenzelm@4621
   996
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
   997
            qsort lts @ eqs @ qsort gts
wenzelm@4621
   998
          end
wenzelm@4621
   999
      end
wenzelm@4621
  1000
    and part _ [] = ([], [], [])
wenzelm@4621
  1001
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1002
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1003
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1004
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1005
  in qsort end;
wenzelm@4621
  1006
wenzelm@4621
  1007
(*sort strings*)
wenzelm@4621
  1008
val sort_strings = sort string_ord;
wenzelm@4621
  1009
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1010
wenzelm@4621
  1011
wenzelm@2506
  1012
wenzelm@3525
  1013
(** input / output and diagnostics **)
wenzelm@233
  1014
paulson@2243
  1015
val cd = OS.FileSys.chDir;
wenzelm@2317
  1016
val pwd = OS.FileSys.getDir;
paulson@2243
  1017
wenzelm@3525
  1018
wenzelm@3525
  1019
local
wenzelm@3525
  1020
  fun out s =
wenzelm@3525
  1021
    (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
  1022
wenzelm@3525
  1023
  fun prefix_lines prfx txt =
wenzelm@3832
  1024
    txt |> split_lines |> map (fn s => prfx ^ s ^ "\n") |> implode;
wenzelm@3525
  1025
in
wenzelm@3525
  1026
wenzelm@3525
  1027
(*hooks for output channels: normal, warning, error*)
wenzelm@3525
  1028
val prs_fn = ref (fn s => out s);
wenzelm@3525
  1029
val warning_fn = ref (fn s => out (prefix_lines "### " s));
wenzelm@3525
  1030
val error_fn = ref (fn s => out (prefix_lines "*** " s));
wenzelm@3525
  1031
wenzelm@3525
  1032
end;
berghofe@1580
  1033
berghofe@1580
  1034
fun prs s = !prs_fn s;
wenzelm@233
  1035
fun writeln s = prs (s ^ "\n");
wenzelm@233
  1036
wenzelm@3525
  1037
fun warning s = !warning_fn s;
wenzelm@233
  1038
wenzelm@233
  1039
(*print error message and abort to top level*)
wenzelm@233
  1040
exception ERROR;
wenzelm@5037
  1041
fun error_msg s = !error_fn s;
wenzelm@3553
  1042
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1043
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1044
wenzelm@233
  1045
fun assert p msg = if p then () else error msg;
wenzelm@233
  1046
fun deny p msg = if p then error msg else ();
wenzelm@233
  1047
lcp@544
  1048
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1049
fun assert_all pred l msg_fn =
lcp@544
  1050
  let fun asl [] = ()
wenzelm@4212
  1051
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1052
  in asl l end;
wenzelm@233
  1053
wenzelm@3624
  1054
wenzelm@4212
  1055
(* handle errors capturing messages *)
wenzelm@3699
  1056
wenzelm@3699
  1057
datatype 'a error =
wenzelm@3699
  1058
  Error of string |
wenzelm@3699
  1059
  OK of 'a;
wenzelm@3699
  1060
wenzelm@4248
  1061
fun get_error (Error msg) = Some msg
wenzelm@4248
  1062
  | get_error _ = None;
wenzelm@4248
  1063
wenzelm@4248
  1064
fun get_ok (OK x) = Some x
wenzelm@4248
  1065
  | get_ok _ = None;
wenzelm@4248
  1066
wenzelm@5037
  1067
datatype 'a result =
wenzelm@5037
  1068
  Result of 'a |
wenzelm@5037
  1069
  Exn of exn;
wenzelm@5037
  1070
wenzelm@3699
  1071
fun handle_error f x =
wenzelm@3699
  1072
  let
wenzelm@4945
  1073
    val buffer = ref ([]: string list);
wenzelm@4945
  1074
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1075
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1076
  in
wenzelm@5037
  1077
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1078
      Result y => (err_msg (); OK y)
wenzelm@5037
  1079
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1080
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1081
  end;
wenzelm@3624
  1082
wenzelm@3624
  1083
wenzelm@5037
  1084
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1085
wenzelm@4923
  1086
exception ERROR_MESSAGE of string;
wenzelm@4923
  1087
wenzelm@4923
  1088
fun transform_error f x =
wenzelm@4923
  1089
  (case handle_error f x of
wenzelm@4923
  1090
    OK y => y
wenzelm@4923
  1091
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1092
wenzelm@4923
  1093
wenzelm@233
  1094
wenzelm@233
  1095
(** timing **)
wenzelm@233
  1096
paulson@4326
  1097
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
  1098
  prints its runtime*)
paulson@4326
  1099
fun cond_timeit flag f =
paulson@4326
  1100
  if flag then
paulson@4326
  1101
    let val start = startTiming()
paulson@4326
  1102
        val result = f ()
paulson@4326
  1103
    in
paulson@4326
  1104
	writeln (endTiming start);  result
paulson@4326
  1105
    end
paulson@4326
  1106
  else f ();
paulson@4326
  1107
wenzelm@233
  1108
(*unconditional timing function*)
paulson@2243
  1109
fun timeit x = cond_timeit true x;
wenzelm@233
  1110
wenzelm@233
  1111
(*timed application function*)
wenzelm@233
  1112
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1113
berghofe@3606
  1114
wenzelm@233
  1115
wenzelm@4621
  1116
(** misc **)
wenzelm@233
  1117
wenzelm@233
  1118
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1119
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1120
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1121
  in map keypair end;
clasohm@0
  1122
wenzelm@233
  1123
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1124
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1125
fun keyfilter [] searchkey = []
wenzelm@233
  1126
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1127
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1128
      else keyfilter pairs searchkey;
clasohm@0
  1129
clasohm@0
  1130
clasohm@0
  1131
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1132
  Preserves order of elements in both lists.*)
clasohm@0
  1133
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1134
    let fun part ([], answer) = answer
wenzelm@233
  1135
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1136
            then  part (xs, (x::ys, ns))
wenzelm@233
  1137
            else  part (xs, (ys, x::ns))
wenzelm@233
  1138
    in  part (rev ys, ([], []))  end;
clasohm@0
  1139
clasohm@0
  1140
clasohm@0
  1141
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1142
    let fun part [] = []
wenzelm@233
  1143
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1144
                           in (x::xs)::(part xs') end
clasohm@0
  1145
    in part end;
clasohm@0
  1146
clasohm@0
  1147
wenzelm@233
  1148
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1149
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1150
fun partition_list p i j =
wenzelm@233
  1151
  let fun part k xs =
wenzelm@233
  1152
            if k>j then
clasohm@0
  1153
              (case xs of [] => []
clasohm@0
  1154
                         | _ => raise LIST "partition_list")
clasohm@0
  1155
            else
wenzelm@233
  1156
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1157
            in  ns :: part(k+1)rest  end
clasohm@0
  1158
  in  part i end;
clasohm@0
  1159
clasohm@0
  1160
wenzelm@233
  1161
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1162
wenzelm@233
  1163
fun transitive_closure [] = []
wenzelm@233
  1164
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1165
      let val qs = transitive_closure ps
paulson@2182
  1166
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
paulson@2182
  1167
          fun step(u, us) = (u, if x mem_string us then zs union_string us 
paulson@2243
  1168
                                else us)
wenzelm@233
  1169
      in (x, zs) :: map step qs end;
clasohm@0
  1170
clasohm@0
  1171
wenzelm@233
  1172
(* generating identifiers *)
clasohm@0
  1173
paulson@4063
  1174
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1175
local
paulson@4063
  1176
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1177
fun char i =      if i<26 then chr (ord "A" + i)
paulson@4063
  1178
	     else if i<52 then chr (ord "a" + i - 26)
paulson@4063
  1179
	     else if i<62 then chr (ord"0" + i - 52)
paulson@4063
  1180
	     else if i=62 then "_"
paulson@4063
  1181
	     else  (*i=63*)    "'";
paulson@4063
  1182
paulson@4063
  1183
val charVec = Vector.tabulate (64, char);
paulson@4063
  1184
paulson@4063
  1185
fun newid n = 
paulson@4063
  1186
  let 
wenzelm@4284
  1187
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1188
wenzelm@4284
  1189
val seedr = ref 0;
clasohm@0
  1190
paulson@4063
  1191
in
wenzelm@4284
  1192
paulson@4063
  1193
fun init_gensym() = (seedr := 0);
paulson@2003
  1194
wenzelm@4284
  1195
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1196
end;
paulson@4063
  1197
paulson@4063
  1198
paulson@4063
  1199
local
paulson@4063
  1200
(*Identifies those character codes legal in identifiers.
paulson@4063
  1201
  chould use Basis Library character functions if Poly/ML provided characters*)
paulson@4063
  1202
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse 
paulson@4063
  1203
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1204
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1205
paulson@4063
  1206
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1207
paulson@4063
  1208
in
paulson@2003
  1209
clasohm@0
  1210
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1211
  If head is "z", bumps chars in tail.
clasohm@0
  1212
  Digits are incremented as if they were integers.
clasohm@0
  1213
  "_" and "'" are not changed.
wenzelm@233
  1214
  For making variants of identifiers.*)
clasohm@0
  1215
paulson@4063
  1216
fun bump_int_list(c::cs) = 
paulson@4063
  1217
	if c="9" then "0" :: bump_int_list cs 
paulson@4063
  1218
	else
paulson@4063
  1219
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1220
        else "1" :: c :: cs
clasohm@0
  1221
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1222
wenzelm@233
  1223
fun bump_list([], d) = [d]
wenzelm@233
  1224
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1225
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1226
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1227
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
paulson@4063
  1228
  | bump_list(c::cs, _) = 
paulson@4063
  1229
        let val k = ord(c)
paulson@4063
  1230
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs 
paulson@4063
  1231
	   else
paulson@4063
  1232
           if c="'" orelse c="_" then c :: bump_list(cs, "") 
paulson@4063
  1233
	   else error("bump_list: not legal in identifier: " ^
paulson@4063
  1234
		      implode(rev(c::cs)))
wenzelm@233
  1235
        end;
clasohm@0
  1236
clasohm@0
  1237
end;
clasohm@0
  1238
wenzelm@233
  1239
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1240
wenzelm@41
  1241
wenzelm@233
  1242
(* lexical scanning *)
clasohm@0
  1243
wenzelm@233
  1244
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1245
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1246
fun scanwords is_let cs =
clasohm@0
  1247
  let fun scan1 [] = []
wenzelm@233
  1248
        | scan1 cs =
wenzelm@233
  1249
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1250
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1251
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1252
wenzelm@4212
  1253
wenzelm@4212
  1254
wenzelm@4212
  1255
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1256
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1257
wenzelm@4212
  1258
clasohm@1364
  1259
end;
clasohm@1364
  1260
clasohm@1364
  1261
open Library;