src/Pure/library.ML
author wenzelm
Wed May 12 17:26:56 1999 +0200 (1999-05-12 ago)
changeset 6642 732af87c0650
parent 6510 b5ef6d115b45
child 6959 d33b1629eaf9
permissions -rw-r--r--
strip_quotes replaced by unenclose;
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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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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 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 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 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 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 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 suffix: string -> string -> string
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  val unsuffix: string -> 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 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 writeln_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 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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  (*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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(*concatenation: 2 and 3 args*)
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fun (f oo g) x y = f (g x y);
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fun (f ooo g) x y z = f (g x y z);
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fun (f oooo g) x y z w = f (g x y z w);
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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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clasohm@0
   303
fun the (Some x) = x
wenzelm@4139
   304
  | the None = raise OPTION;
clasohm@0
   305
wenzelm@4212
   306
(*strict!*)
wenzelm@255
   307
fun if_none None y = y
wenzelm@255
   308
  | if_none (Some x) _ = x;
wenzelm@255
   309
clasohm@0
   310
fun is_some (Some _) = true
clasohm@0
   311
  | is_some None = false;
clasohm@0
   312
clasohm@0
   313
fun is_none (Some _) = false
clasohm@0
   314
  | is_none None = true;
clasohm@0
   315
wenzelm@233
   316
fun apsome f (Some x) = Some (f x)
wenzelm@233
   317
  | apsome _ None = None;
clasohm@0
   318
wenzelm@4139
   319
(*handle partial functions*)
wenzelm@4181
   320
fun can f x = (f x; true) handle _ => false;
wenzelm@4139
   321
fun try f x = Some (f x) handle _ => None;
wenzelm@4139
   322
wenzelm@4139
   323
wenzelm@4139
   324
wenzelm@233
   325
(** pairs **)
wenzelm@233
   326
wenzelm@233
   327
fun pair x y = (x, y);
wenzelm@233
   328
fun rpair x y = (y, x);
wenzelm@233
   329
wenzelm@233
   330
fun fst (x, y) = x;
wenzelm@233
   331
fun snd (x, y) = y;
wenzelm@233
   332
wenzelm@233
   333
fun eq_fst ((x1, _), (x2, _)) = x1 = x2;
wenzelm@233
   334
fun eq_snd ((_, y1), (_, y2)) = y1 = y2;
wenzelm@233
   335
wenzelm@233
   336
fun swap (x, y) = (y, x);
wenzelm@233
   337
wenzelm@4212
   338
(*apply function to components*)
wenzelm@233
   339
fun apfst f (x, y) = (f x, y);
wenzelm@233
   340
fun apsnd f (x, y) = (x, f y);
wenzelm@4212
   341
fun pairself f (x, y) = (f x, f y);
wenzelm@233
   342
wenzelm@233
   343
wenzelm@233
   344
wenzelm@233
   345
(** booleans **)
wenzelm@233
   346
wenzelm@233
   347
(* equality *)
wenzelm@233
   348
wenzelm@233
   349
fun equal x y = x = y;
wenzelm@233
   350
fun not_equal x y = x <> y;
wenzelm@233
   351
wenzelm@233
   352
wenzelm@233
   353
(* operators for combining predicates *)
wenzelm@233
   354
paulson@2175
   355
fun (p orf q) = fn x => p x orelse q x;
paulson@2175
   356
fun (p andf q) = fn x => p x andalso q x;
wenzelm@233
   357
wenzelm@233
   358
wenzelm@233
   359
(* predicates on lists *)
wenzelm@233
   360
wenzelm@233
   361
(*exists pred [x1, ..., xn] ===> pred x1 orelse ... orelse pred xn*)
wenzelm@233
   362
fun exists (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   363
  let fun boolf [] = false
wenzelm@233
   364
        | boolf (x :: xs) = pred x orelse boolf xs
wenzelm@233
   365
  in boolf end;
wenzelm@233
   366
wenzelm@233
   367
(*forall pred [x1, ..., xn] ===> pred x1 andalso ... andalso pred xn*)
wenzelm@233
   368
fun forall (pred: 'a -> bool) : 'a list -> bool =
wenzelm@233
   369
  let fun boolf [] = true
wenzelm@233
   370
        | boolf (x :: xs) = pred x andalso boolf xs
wenzelm@233
   371
  in boolf end;
clasohm@0
   372
wenzelm@233
   373
wenzelm@380
   374
(* flags *)
wenzelm@380
   375
wenzelm@380
   376
fun set flag = (flag := true; true);
wenzelm@380
   377
fun reset flag = (flag := false; false);
wenzelm@380
   378
fun toggle flag = (flag := not (! flag); ! flag);
wenzelm@380
   379
wenzelm@4212
   380
(*temporarily set flag, handling errors*)
wenzelm@2978
   381
fun setmp flag value f x =
wenzelm@2958
   382
  let
wenzelm@2958
   383
    val orig_value = ! flag;
wenzelm@2958
   384
    fun return y = (flag := orig_value; y);
wenzelm@2958
   385
  in
wenzelm@2958
   386
    flag := value;
wenzelm@2958
   387
    return (f x handle exn => (return (); raise exn))
wenzelm@2958
   388
  end;
wenzelm@2958
   389
wenzelm@380
   390
wenzelm@233
   391
wenzelm@233
   392
(** lists **)
wenzelm@233
   393
wenzelm@233
   394
exception LIST of string;
wenzelm@233
   395
wenzelm@233
   396
fun null [] = true
wenzelm@233
   397
  | null (_ :: _) = false;
wenzelm@233
   398
wenzelm@233
   399
fun hd [] = raise LIST "hd"
wenzelm@233
   400
  | hd (x :: _) = x;
wenzelm@233
   401
wenzelm@233
   402
fun tl [] = raise LIST "tl"
wenzelm@233
   403
  | tl (_ :: xs) = xs;
wenzelm@233
   404
wenzelm@233
   405
fun cons x xs = x :: xs;
wenzelm@5285
   406
fun single x = [x];
wenzelm@233
   407
wenzelm@4629
   408
fun append xs ys = xs @ ys;
wenzelm@4629
   409
wenzelm@5904
   410
fun apply [] x = x
wenzelm@5904
   411
  | apply (f :: fs) x = apply fs (f x);
wenzelm@5904
   412
wenzelm@233
   413
wenzelm@233
   414
(* fold *)
wenzelm@233
   415
wenzelm@233
   416
(*the following versions of fold are designed to fit nicely with infixes*)
clasohm@0
   417
wenzelm@233
   418
(*  (op @) (e, [x1, ..., xn])  ===>  ((e @ x1) @ x2) ... @ xn
wenzelm@233
   419
    for operators that associate to the left (TAIL RECURSIVE)*)
wenzelm@233
   420
fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a =
wenzelm@233
   421
  let fun itl (e, [])  = e
wenzelm@233
   422
        | itl (e, a::l) = itl (f(e, a), l)
wenzelm@233
   423
  in  itl end;
wenzelm@233
   424
wenzelm@233
   425
(*  (op @) ([x1, ..., xn], e)  ===>   x1 @ (x2 ... @ (xn @ e))
wenzelm@233
   426
    for operators that associate to the right (not tail recursive)*)
wenzelm@233
   427
fun foldr f (l, e) =
wenzelm@233
   428
  let fun itr [] = e
wenzelm@233
   429
        | itr (a::l) = f(a, itr l)
wenzelm@233
   430
  in  itr l  end;
wenzelm@233
   431
wenzelm@233
   432
(*  (op @) [x1, ..., xn]  ===>   x1 @ (x2 ... @ (x[n-1] @ xn))
wenzelm@233
   433
    for n > 0, operators that associate to the right (not tail recursive)*)
wenzelm@233
   434
fun foldr1 f l =
wenzelm@4181
   435
  let fun itr [x] = x
wenzelm@233
   436
        | itr (x::l) = f(x, itr l)
wenzelm@233
   437
  in  itr l  end;
wenzelm@233
   438
wenzelm@4956
   439
fun foldl_map _ (x, []) = (x, [])
wenzelm@4956
   440
  | foldl_map f (x, y :: ys) =
wenzelm@4956
   441
      let
wenzelm@4956
   442
        val (x', y') = f (x, y);
wenzelm@4956
   443
        val (x'', ys') = foldl_map f (x', ys);
wenzelm@4956
   444
      in (x'', y' :: ys') end;
wenzelm@4956
   445
wenzelm@233
   446
wenzelm@233
   447
(* basic list functions *)
wenzelm@233
   448
wenzelm@233
   449
(*length of a list, should unquestionably be a standard function*)
wenzelm@233
   450
local fun length1 (n, [])  = n   (*TAIL RECURSIVE*)
wenzelm@233
   451
        | length1 (n, x :: xs) = length1 (n + 1, xs)
wenzelm@233
   452
in  fun length l = length1 (0, l) end;
wenzelm@233
   453
wenzelm@233
   454
(*take the first n elements from a list*)
wenzelm@233
   455
fun take (n, []) = []
wenzelm@233
   456
  | take (n, x :: xs) =
wenzelm@233
   457
      if n > 0 then x :: take (n - 1, xs) else [];
wenzelm@233
   458
wenzelm@233
   459
(*drop the first n elements from a list*)
wenzelm@233
   460
fun drop (n, []) = []
wenzelm@233
   461
  | drop (n, x :: xs) =
wenzelm@233
   462
      if n > 0 then drop (n - 1, xs) else x :: xs;
clasohm@0
   463
nipkow@4713
   464
fun dropwhile P [] = []
nipkow@4713
   465
  | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;
nipkow@4713
   466
wenzelm@233
   467
(*return nth element of a list, where 0 designates the first element;
wenzelm@233
   468
  raise EXCEPTION if list too short*)
wenzelm@233
   469
fun nth_elem NL =
wenzelm@233
   470
  (case drop NL of
wenzelm@233
   471
    [] => raise LIST "nth_elem"
wenzelm@233
   472
  | x :: _ => x);
wenzelm@233
   473
wenzelm@233
   474
(*last element of a list*)
wenzelm@233
   475
fun last_elem [] = raise LIST "last_elem"
wenzelm@233
   476
  | last_elem [x] = x
wenzelm@233
   477
  | last_elem (_ :: xs) = last_elem xs;
wenzelm@233
   478
wenzelm@3762
   479
(*rear decomposition*)
wenzelm@3762
   480
fun split_last [] = raise LIST "split_last"
wenzelm@3762
   481
  | split_last [x] = ([], x)
wenzelm@3762
   482
  | split_last (x :: xs) = apfst (cons x) (split_last xs);
wenzelm@3762
   483
wenzelm@4893
   484
(*update nth element*)
wenzelm@4893
   485
fun nth_update x (n, xs) =
wenzelm@4893
   486
  let
wenzelm@4893
   487
    val prfx = take (n, xs);
wenzelm@4893
   488
    val sffx = drop (n, xs);
wenzelm@4893
   489
  in
wenzelm@4893
   490
    (case sffx of
wenzelm@4893
   491
      [] => raise LIST "nth_update"
wenzelm@4893
   492
    | _ :: sffx' => prfx @ (x :: sffx'))
wenzelm@4893
   493
  end;
wenzelm@4893
   494
wenzelm@4212
   495
(*find the position of an element in a list*)
wenzelm@4212
   496
fun find_index pred =
wenzelm@4212
   497
  let fun find _ [] = ~1
wenzelm@4212
   498
        | find n (x :: xs) = if pred x then n else find (n + 1) xs;
wenzelm@4212
   499
  in find 0 end;
wenzelm@3762
   500
wenzelm@4224
   501
fun find_index_eq x = find_index (equal x);
wenzelm@4212
   502
wenzelm@4212
   503
(*find first element satisfying predicate*)
wenzelm@4212
   504
fun find_first _ [] = None
wenzelm@4212
   505
  | find_first pred (x :: xs) =
wenzelm@4212
   506
      if pred x then Some x else find_first pred xs;
wenzelm@233
   507
wenzelm@4916
   508
(*get first element by lookup function*)
wenzelm@4916
   509
fun get_first _ [] = None
wenzelm@4916
   510
  | get_first f (x :: xs) =
wenzelm@4916
   511
      (case f x of
wenzelm@4916
   512
        None => get_first f xs
wenzelm@4916
   513
      | some => some);
wenzelm@4916
   514
wenzelm@233
   515
(*flatten a list of lists to a list*)
wenzelm@233
   516
fun flat (ls: 'c list list) : 'c list = foldr (op @) (ls, []);
wenzelm@233
   517
wenzelm@233
   518
(*like Lisp's MAPC -- seq proc [x1, ..., xn] evaluates
wenzelm@233
   519
  (proc x1; ...; proc xn) for side effects*)
wenzelm@233
   520
fun seq (proc: 'a -> unit) : 'a list -> unit =
wenzelm@233
   521
  let fun seqf [] = ()
wenzelm@233
   522
        | seqf (x :: xs) = (proc x; seqf xs)
wenzelm@233
   523
  in seqf end;
wenzelm@233
   524
wenzelm@233
   525
(*separate s [x1, x2, ..., xn]  ===>  [x1, s, x2, s, ..., s, xn]*)
wenzelm@233
   526
fun separate s (x :: (xs as _ :: _)) = x :: s :: separate s xs
wenzelm@233
   527
  | separate _ xs = xs;
wenzelm@233
   528
wenzelm@233
   529
(*make the list [x, x, ..., x] of length n*)
wenzelm@233
   530
fun replicate n (x: 'a) : 'a list =
wenzelm@233
   531
  let fun rep (0, xs) = xs
wenzelm@233
   532
        | rep (n, xs) = rep (n - 1, x :: xs)
wenzelm@233
   533
  in
wenzelm@233
   534
    if n < 0 then raise LIST "replicate"
wenzelm@233
   535
    else rep (n, [])
wenzelm@233
   536
  end;
wenzelm@233
   537
wenzelm@4248
   538
(*multiply [a, b, c, ...] * [xs, ys, zs, ...]*)
wenzelm@4248
   539
fun multiply ([], _) = []
wenzelm@4248
   540
  | multiply (x :: xs, yss) = map (cons x) yss @ multiply (xs, yss);
wenzelm@4248
   541
wenzelm@233
   542
wenzelm@233
   543
(* filter *)
wenzelm@233
   544
wenzelm@233
   545
(*copy the list preserving elements that satisfy the predicate*)
wenzelm@233
   546
fun filter (pred: 'a->bool) : 'a list -> 'a list =
clasohm@0
   547
  let fun filt [] = []
wenzelm@233
   548
        | filt (x :: xs) = if pred x then x :: filt xs else filt xs
wenzelm@233
   549
  in filt end;
clasohm@0
   550
clasohm@0
   551
fun filter_out f = filter (not o f);
clasohm@0
   552
wenzelm@233
   553
fun mapfilter (f: 'a -> 'b option) ([]: 'a list) = [] : 'b list
wenzelm@233
   554
  | mapfilter f (x :: xs) =
wenzelm@233
   555
      (case f x of
wenzelm@233
   556
        None => mapfilter f xs
wenzelm@233
   557
      | Some y => y :: mapfilter f xs);
wenzelm@233
   558
wenzelm@233
   559
wenzelm@233
   560
(* lists of pairs *)
wenzelm@233
   561
wenzelm@380
   562
fun map2 _ ([], []) = []
wenzelm@380
   563
  | map2 f (x :: xs, y :: ys) = (f (x, y) :: map2 f (xs, ys))
wenzelm@380
   564
  | map2 _ _ = raise LIST "map2";
wenzelm@380
   565
wenzelm@380
   566
fun exists2 _ ([], []) = false
wenzelm@380
   567
  | exists2 pred (x :: xs, y :: ys) = pred (x, y) orelse exists2 pred (xs, ys)
wenzelm@380
   568
  | exists2 _ _ = raise LIST "exists2";
wenzelm@380
   569
wenzelm@380
   570
fun forall2 _ ([], []) = true
wenzelm@380
   571
  | forall2 pred (x :: xs, y :: ys) = pred (x, y) andalso forall2 pred (xs, ys)
wenzelm@380
   572
  | forall2 _ _ = raise LIST "forall2";
wenzelm@380
   573
wenzelm@4956
   574
fun seq2 _ ([], []) = ()
wenzelm@4956
   575
  | seq2 f (x :: xs, y :: ys) = (f (x, y); seq2 f (xs, ys))
wenzelm@4956
   576
  | seq2 _ _ = raise LIST "seq2";
wenzelm@4956
   577
wenzelm@233
   578
(*combine two lists forming a list of pairs:
wenzelm@233
   579
  [x1, ..., xn] ~~ [y1, ..., yn]  ===>  [(x1, y1), ..., (xn, yn)]*)
wenzelm@233
   580
fun [] ~~ [] = []
wenzelm@233
   581
  | (x :: xs) ~~ (y :: ys) = (x, y) :: (xs ~~ ys)
wenzelm@233
   582
  | _ ~~ _ = raise LIST "~~";
wenzelm@233
   583
wenzelm@233
   584
(*inverse of ~~; the old 'split':
wenzelm@233
   585
  [(x1, y1), ..., (xn, yn)]  ===>  ([x1, ..., xn], [y1, ..., yn])*)
wenzelm@233
   586
fun split_list (l: ('a * 'b) list) = (map #1 l, map #2 l);
wenzelm@233
   587
wenzelm@233
   588
wenzelm@233
   589
(* prefixes, suffixes *)
wenzelm@233
   590
wenzelm@233
   591
fun [] prefix _ = true
wenzelm@233
   592
  | (x :: xs) prefix (y :: ys) = x = y andalso (xs prefix ys)
wenzelm@233
   593
  | _ prefix _ = false;
wenzelm@233
   594
wenzelm@233
   595
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., x(i-1)], [xi, ..., xn])
wenzelm@233
   596
   where xi is the first element that does not satisfy the predicate*)
wenzelm@233
   597
fun take_prefix (pred : 'a -> bool)  (xs: 'a list) : 'a list * 'a list =
wenzelm@233
   598
  let fun take (rxs, []) = (rev rxs, [])
wenzelm@255
   599
        | take (rxs, x :: xs) =
wenzelm@255
   600
            if  pred x  then  take(x :: rxs, xs)  else  (rev rxs, x :: xs)
wenzelm@233
   601
  in  take([], xs)  end;
wenzelm@233
   602
wenzelm@233
   603
(* [x1, ..., xi, ..., xn]  --->  ([x1, ..., xi], [x(i+1), ..., xn])
wenzelm@233
   604
   where xi is the last element that does not satisfy the predicate*)
wenzelm@233
   605
fun take_suffix _ [] = ([], [])
wenzelm@233
   606
  | take_suffix pred (x :: xs) =
wenzelm@233
   607
      (case take_suffix pred xs of
wenzelm@233
   608
        ([], sffx) => if pred x then ([], x :: sffx) else ([x], sffx)
wenzelm@233
   609
      | (prfx, sffx) => (x :: prfx, sffx));
wenzelm@233
   610
wenzelm@233
   611
wenzelm@233
   612
wenzelm@233
   613
(** integers **)
wenzelm@233
   614
wenzelm@2958
   615
fun inc i = (i := ! i + 1; ! i);
wenzelm@2958
   616
fun dec i = (i := ! i - 1; ! i);
wenzelm@233
   617
wenzelm@233
   618
wenzelm@233
   619
(* lists of integers *)
wenzelm@233
   620
wenzelm@233
   621
(*make the list [from, from + 1, ..., to]*)
paulson@2175
   622
fun (from upto to) =
wenzelm@233
   623
  if from > to then [] else from :: ((from + 1) upto to);
wenzelm@233
   624
wenzelm@233
   625
(*make the list [from, from - 1, ..., to]*)
paulson@2175
   626
fun (from downto to) =
wenzelm@233
   627
  if from < to then [] else from :: ((from - 1) downto to);
wenzelm@233
   628
wenzelm@233
   629
(*predicate: downto0 (is, n) <=> is = [n, n - 1, ..., 0]*)
wenzelm@233
   630
fun downto0 (i :: is, n) = i = n andalso downto0 (is, n - 1)
wenzelm@233
   631
  | downto0 ([], n) = n = ~1;
wenzelm@233
   632
wenzelm@233
   633
wenzelm@233
   634
(* convert integers to strings *)
wenzelm@233
   635
wenzelm@233
   636
(*expand the number in the given base;
wenzelm@233
   637
  example: radixpand (2, 8) gives [1, 0, 0, 0]*)
wenzelm@233
   638
fun radixpand (base, num) : int list =
wenzelm@233
   639
  let
wenzelm@233
   640
    fun radix (n, tail) =
wenzelm@233
   641
      if n < base then n :: tail
wenzelm@233
   642
      else radix (n div base, (n mod base) :: tail)
wenzelm@233
   643
  in radix (num, []) end;
wenzelm@233
   644
wenzelm@233
   645
(*expands a number into a string of characters starting from "zerochar";
wenzelm@233
   646
  example: radixstring (2, "0", 8) gives "1000"*)
wenzelm@233
   647
fun radixstring (base, zerochar, num) =
wenzelm@233
   648
  let val offset = ord zerochar;
wenzelm@233
   649
      fun chrof n = chr (offset + n)
wenzelm@233
   650
  in implode (map chrof (radixpand (base, num))) end;
wenzelm@233
   651
wenzelm@233
   652
paulson@3407
   653
val string_of_int = Int.toString;
wenzelm@233
   654
paulson@3407
   655
fun string_of_indexname (a,0) = a
paulson@3407
   656
  | string_of_indexname (a,i) = a ^ "_" ^ Int.toString i;
wenzelm@233
   657
wenzelm@233
   658
wenzelm@4212
   659
wenzelm@233
   660
(** strings **)
wenzelm@233
   661
wenzelm@6312
   662
(*functions tuned for strings, avoiding explode*)
wenzelm@6312
   663
wenzelm@6312
   664
fun nth_elem_string (i, str) =
wenzelm@6312
   665
  String.substring (str, i, 1) handle _ => raise LIST "nth_elem_string";
wenzelm@6312
   666
wenzelm@6282
   667
fun foldl_string f (x0, str) =
wenzelm@6282
   668
  let
wenzelm@6282
   669
    val n = size str;
wenzelm@6282
   670
    fun fold (x, i) = if i < n then fold (f (x, String.substring (str, i, 1)), i + 1) else x
wenzelm@6282
   671
  in fold (x0, 0) end;
wenzelm@6282
   672
wenzelm@6312
   673
fun exists_string pred str = foldl_string (fn (b, s) => b orelse pred s) (false, str);
wenzelm@6312
   674
lcp@512
   675
(*enclose in brackets*)
lcp@512
   676
fun enclose lpar rpar str = lpar ^ str ^ rpar;
wenzelm@6642
   677
fun unenclose str = String.substring (str, 1, size str - 2);
wenzelm@255
   678
wenzelm@233
   679
(*simple quoting (does not escape special chars)*)
lcp@512
   680
val quote = enclose "\"" "\"";
wenzelm@233
   681
wenzelm@4212
   682
(*space_implode "..." (explode "hello") = "h...e...l...l...o"*)
wenzelm@233
   683
fun space_implode a bs = implode (separate a bs);
wenzelm@233
   684
wenzelm@255
   685
val commas = space_implode ", ";
wenzelm@380
   686
val commas_quote = commas o map quote;
wenzelm@255
   687
wenzelm@233
   688
(*concatenate messages, one per line, into a string*)
wenzelm@255
   689
val cat_lines = space_implode "\n";
wenzelm@233
   690
wenzelm@4212
   691
(*space_explode "." "h.e..l.lo" = ["h", "e", "", "l", "lo"]*)
wenzelm@3832
   692
fun space_explode _ "" = []
wenzelm@3832
   693
  | space_explode sep str =
wenzelm@3832
   694
      let
wenzelm@3832
   695
        fun expl chs =
wenzelm@3832
   696
          (case take_prefix (not_equal sep) chs of
wenzelm@3832
   697
            (cs, []) => [implode cs]
wenzelm@3832
   698
          | (cs, _ :: cs') => implode cs :: expl cs');
wenzelm@3832
   699
      in expl (explode str) end;
wenzelm@3832
   700
wenzelm@3832
   701
val split_lines = space_explode "\n";
wenzelm@3832
   702
wenzelm@5285
   703
(*append suffix*)
wenzelm@5285
   704
fun suffix sfx s = s ^ sfx;
wenzelm@5285
   705
wenzelm@5285
   706
(*remove suffix*)
wenzelm@5285
   707
fun unsuffix sfx s =
wenzelm@5285
   708
  let
wenzelm@5285
   709
    val cs = explode s;
wenzelm@5285
   710
    val prfx_len = size s - size sfx;
wenzelm@5285
   711
  in
wenzelm@5285
   712
    if prfx_len >= 0 andalso implode (drop (prfx_len, cs)) = sfx then
wenzelm@5285
   713
      implode (take (prfx_len, cs))
wenzelm@5285
   714
    else raise LIST "unsuffix"
wenzelm@5285
   715
  end;
wenzelm@5285
   716
wenzelm@3832
   717
wenzelm@233
   718
wenzelm@233
   719
(** lists as sets **)
wenzelm@233
   720
wenzelm@233
   721
(*membership in a list*)
wenzelm@233
   722
fun x mem [] = false
wenzelm@233
   723
  | x mem (y :: ys) = x = y orelse x mem ys;
clasohm@0
   724
paulson@2175
   725
(*membership in a list, optimized version for ints*)
berghofe@1576
   726
fun (x:int) mem_int [] = false
berghofe@1576
   727
  | x mem_int (y :: ys) = x = y orelse x mem_int ys;
berghofe@1576
   728
paulson@2175
   729
(*membership in a list, optimized version for strings*)
berghofe@1576
   730
fun (x:string) mem_string [] = false
berghofe@1576
   731
  | x mem_string (y :: ys) = x = y orelse x mem_string ys;
berghofe@1576
   732
clasohm@0
   733
(*generalized membership test*)
wenzelm@233
   734
fun gen_mem eq (x, []) = false
wenzelm@233
   735
  | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);
wenzelm@233
   736
wenzelm@233
   737
wenzelm@233
   738
(*insertion into list if not already there*)
paulson@2175
   739
fun (x ins xs) = if x mem xs then xs else x :: xs;
clasohm@0
   740
paulson@2175
   741
(*insertion into list, optimized version for ints*)
paulson@2175
   742
fun (x ins_int xs) = if x mem_int xs then xs else x :: xs;
berghofe@1576
   743
paulson@2175
   744
(*insertion into list, optimized version for strings*)
paulson@2175
   745
fun (x ins_string xs) = if x mem_string xs then xs else x :: xs;
berghofe@1576
   746
clasohm@0
   747
(*generalized insertion*)
wenzelm@233
   748
fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;
wenzelm@233
   749
wenzelm@233
   750
wenzelm@233
   751
(*union of sets represented as lists: no repetitions*)
wenzelm@233
   752
fun xs union [] = xs
wenzelm@233
   753
  | [] union ys = ys
wenzelm@233
   754
  | (x :: xs) union ys = xs union (x ins ys);
clasohm@0
   755
paulson@2175
   756
(*union of sets, optimized version for ints*)
berghofe@1576
   757
fun (xs:int list) union_int [] = xs
berghofe@1576
   758
  | [] union_int ys = ys
berghofe@1576
   759
  | (x :: xs) union_int ys = xs union_int (x ins_int ys);
berghofe@1576
   760
paulson@2175
   761
(*union of sets, optimized version for strings*)
berghofe@1576
   762
fun (xs:string list) union_string [] = xs
berghofe@1576
   763
  | [] union_string ys = ys
berghofe@1576
   764
  | (x :: xs) union_string ys = xs union_string (x ins_string ys);
berghofe@1576
   765
clasohm@0
   766
(*generalized union*)
wenzelm@233
   767
fun gen_union eq (xs, []) = xs
wenzelm@233
   768
  | gen_union eq ([], ys) = ys
wenzelm@233
   769
  | gen_union eq (x :: xs, ys) = gen_union eq (xs, gen_ins eq (x, ys));
wenzelm@233
   770
wenzelm@233
   771
wenzelm@233
   772
(*intersection*)
wenzelm@233
   773
fun [] inter ys = []
wenzelm@233
   774
  | (x :: xs) inter ys =
wenzelm@233
   775
      if x mem ys then x :: (xs inter ys) else xs inter ys;
wenzelm@233
   776
paulson@2175
   777
(*intersection, optimized version for ints*)
berghofe@1576
   778
fun ([]:int list) inter_int ys = []
berghofe@1576
   779
  | (x :: xs) inter_int ys =
berghofe@1576
   780
      if x mem_int ys then x :: (xs inter_int ys) else xs inter_int ys;
berghofe@1576
   781
paulson@2175
   782
(*intersection, optimized version for strings *)
berghofe@1576
   783
fun ([]:string list) inter_string ys = []
berghofe@1576
   784
  | (x :: xs) inter_string ys =
berghofe@1576
   785
      if x mem_string ys then x :: (xs inter_string ys) else xs inter_string ys;
berghofe@1576
   786
wenzelm@233
   787
wenzelm@233
   788
(*subset*)
wenzelm@233
   789
fun [] subset ys = true
wenzelm@233
   790
  | (x :: xs) subset ys = x mem ys andalso xs subset ys;
wenzelm@233
   791
paulson@2175
   792
(*subset, optimized version for ints*)
berghofe@1576
   793
fun ([]:int list) subset_int ys = true
berghofe@1576
   794
  | (x :: xs) subset_int ys = x mem_int ys andalso xs subset_int ys;
berghofe@1576
   795
paulson@2175
   796
(*subset, optimized version for strings*)
berghofe@1576
   797
fun ([]:string list) subset_string ys = true
berghofe@1576
   798
  | (x :: xs) subset_string ys = x mem_string ys andalso xs subset_string ys;
berghofe@1576
   799
wenzelm@4363
   800
(*set equality*)
wenzelm@4363
   801
fun eq_set (xs, ys) =
wenzelm@4363
   802
  xs = ys orelse (xs subset ys andalso ys subset xs);
wenzelm@4363
   803
paulson@2182
   804
(*set equality for strings*)
berghofe@1576
   805
fun eq_set_string ((xs:string list), ys) =
berghofe@1576
   806
  xs = ys orelse (xs subset_string ys andalso ys subset_string xs);
berghofe@1576
   807
paulson@2182
   808
fun gen_subset eq (xs, ys) = forall (fn x => gen_mem eq (x, ys)) xs;
paulson@2182
   809
wenzelm@265
   810
wenzelm@233
   811
(*removing an element from a list WITHOUT duplicates*)
wenzelm@233
   812
fun (y :: ys) \ x = if x = y then ys else y :: (ys \ x)
wenzelm@233
   813
  | [] \ x = [];
wenzelm@233
   814
paulson@2243
   815
fun ys \\ xs = foldl (op \) (ys,xs);
clasohm@0
   816
wenzelm@233
   817
(*removing an element from a list -- possibly WITH duplicates*)
wenzelm@233
   818
fun gen_rem eq (xs, y) = filter_out (fn x => eq (x, y)) xs;
wenzelm@233
   819
paulson@2243
   820
fun gen_rems eq = foldl (gen_rem eq);
wenzelm@233
   821
wenzelm@233
   822
wenzelm@233
   823
(*makes a list of the distinct members of the input; preserves order, takes
wenzelm@233
   824
  first of equal elements*)
wenzelm@233
   825
fun gen_distinct eq lst =
wenzelm@233
   826
  let
wenzelm@233
   827
    val memb = gen_mem eq;
clasohm@0
   828
wenzelm@233
   829
    fun dist (rev_seen, []) = rev rev_seen
wenzelm@233
   830
      | dist (rev_seen, x :: xs) =
wenzelm@233
   831
          if memb (x, rev_seen) then dist (rev_seen, xs)
wenzelm@233
   832
          else dist (x :: rev_seen, xs);
wenzelm@233
   833
  in
wenzelm@233
   834
    dist ([], lst)
wenzelm@233
   835
  end;
wenzelm@233
   836
paulson@2243
   837
fun distinct l = gen_distinct (op =) l;
wenzelm@233
   838
wenzelm@233
   839
wenzelm@233
   840
(*returns the tail beginning with the first repeated element, or []*)
wenzelm@233
   841
fun findrep [] = []
wenzelm@233
   842
  | findrep (x :: xs) = if x mem xs then x :: xs else findrep xs;
wenzelm@233
   843
wenzelm@233
   844
wenzelm@255
   845
(*returns a list containing all repeated elements exactly once; preserves
wenzelm@255
   846
  order, takes first of equal elements*)
wenzelm@255
   847
fun gen_duplicates eq lst =
wenzelm@255
   848
  let
wenzelm@255
   849
    val memb = gen_mem eq;
wenzelm@255
   850
wenzelm@255
   851
    fun dups (rev_dups, []) = rev rev_dups
wenzelm@255
   852
      | dups (rev_dups, x :: xs) =
wenzelm@255
   853
          if memb (x, rev_dups) orelse not (memb (x, xs)) then
wenzelm@255
   854
            dups (rev_dups, xs)
wenzelm@255
   855
          else dups (x :: rev_dups, xs);
wenzelm@255
   856
  in
wenzelm@255
   857
    dups ([], lst)
wenzelm@255
   858
  end;
wenzelm@255
   859
paulson@2243
   860
fun duplicates l = gen_duplicates (op =) l;
wenzelm@255
   861
wenzelm@255
   862
wenzelm@233
   863
wenzelm@233
   864
(** association lists **)
clasohm@0
   865
wenzelm@233
   866
(*association list lookup*)
wenzelm@233
   867
fun assoc ([], key) = None
wenzelm@233
   868
  | assoc ((keyi, xi) :: pairs, key) =
wenzelm@233
   869
      if key = keyi then Some xi else assoc (pairs, key);
wenzelm@233
   870
paulson@2175
   871
(*association list lookup, optimized version for ints*)
berghofe@1576
   872
fun assoc_int ([], (key:int)) = None
berghofe@1576
   873
  | assoc_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   874
      if key = keyi then Some xi else assoc_int (pairs, key);
berghofe@1576
   875
paulson@2175
   876
(*association list lookup, optimized version for strings*)
berghofe@1576
   877
fun assoc_string ([], (key:string)) = None
berghofe@1576
   878
  | assoc_string ((keyi, xi) :: pairs, key) =
berghofe@1576
   879
      if key = keyi then Some xi else assoc_string (pairs, key);
berghofe@1576
   880
paulson@2175
   881
(*association list lookup, optimized version for string*ints*)
berghofe@1576
   882
fun assoc_string_int ([], (key:string*int)) = None
berghofe@1576
   883
  | assoc_string_int ((keyi, xi) :: pairs, key) =
berghofe@1576
   884
      if key = keyi then Some xi else assoc_string_int (pairs, key);
berghofe@1576
   885
wenzelm@233
   886
fun assocs ps x =
wenzelm@233
   887
  (case assoc (ps, x) of
wenzelm@233
   888
    None => []
wenzelm@233
   889
  | Some ys => ys);
wenzelm@233
   890
wenzelm@255
   891
(*two-fold association list lookup*)
wenzelm@255
   892
fun assoc2 (aal, (key1, key2)) =
wenzelm@255
   893
  (case assoc (aal, key1) of
wenzelm@255
   894
    Some al => assoc (al, key2)
wenzelm@255
   895
  | None => None);
wenzelm@255
   896
wenzelm@233
   897
(*generalized association list lookup*)
wenzelm@233
   898
fun gen_assoc eq ([], key) = None
wenzelm@233
   899
  | gen_assoc eq ((keyi, xi) :: pairs, key) =
wenzelm@233
   900
      if eq (key, keyi) then Some xi else gen_assoc eq (pairs, key);
wenzelm@233
   901
wenzelm@233
   902
(*association list update*)
wenzelm@233
   903
fun overwrite (al, p as (key, _)) =
wenzelm@233
   904
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@233
   905
            if keyi = key then p :: pairs else q :: (over pairs)
wenzelm@233
   906
        | over [] = [p]
wenzelm@233
   907
  in over al end;
wenzelm@233
   908
wenzelm@2522
   909
fun gen_overwrite eq (al, p as (key, _)) =
wenzelm@2522
   910
  let fun over ((q as (keyi, _)) :: pairs) =
wenzelm@2522
   911
            if eq (keyi, key) then p :: pairs else q :: (over pairs)
wenzelm@2522
   912
        | over [] = [p]
wenzelm@2522
   913
  in over al end;
wenzelm@2522
   914
wenzelm@233
   915
wenzelm@233
   916
wenzelm@233
   917
(** generic tables **)
clasohm@0
   918
wenzelm@233
   919
(*Tables are supposed to be 'efficient' encodings of lists of elements distinct
wenzelm@233
   920
  wrt. an equality "eq". The extend and merge operations below are optimized
wenzelm@233
   921
  for long-term space efficiency.*)
wenzelm@233
   922
wenzelm@233
   923
(*append (new) elements to a table*)
wenzelm@233
   924
fun generic_extend _ _ _ tab [] = tab
wenzelm@233
   925
  | generic_extend eq dest_tab mk_tab tab1 lst2 =
wenzelm@233
   926
      let
wenzelm@233
   927
        val lst1 = dest_tab tab1;
wenzelm@233
   928
        val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   929
      in
wenzelm@233
   930
        if null new_lst2 then tab1
wenzelm@233
   931
        else mk_tab (lst1 @ new_lst2)
wenzelm@233
   932
      end;
clasohm@0
   933
wenzelm@233
   934
(*append (new) elements of 2nd table to 1st table*)
wenzelm@233
   935
fun generic_merge eq dest_tab mk_tab tab1 tab2 =
wenzelm@233
   936
  let
wenzelm@233
   937
    val lst1 = dest_tab tab1;
wenzelm@233
   938
    val lst2 = dest_tab tab2;
wenzelm@233
   939
    val new_lst2 = gen_rems eq (lst2, lst1);
wenzelm@233
   940
  in
wenzelm@233
   941
    if null new_lst2 then tab1
wenzelm@233
   942
    else if gen_subset eq (lst1, lst2) then tab2
wenzelm@233
   943
    else mk_tab (lst1 @ new_lst2)
wenzelm@233
   944
  end;
clasohm@0
   945
wenzelm@233
   946
wenzelm@233
   947
(*lists as tables*)
paulson@2243
   948
fun extend_list tab = generic_extend (op =) I I tab;
paulson@2243
   949
fun merge_lists tab = generic_merge (op =) I I tab;
wenzelm@4692
   950
fun merge_alists tab = generic_merge eq_fst I I tab;
wenzelm@233
   951
wenzelm@380
   952
fun merge_rev_lists xs [] = xs
wenzelm@380
   953
  | merge_rev_lists [] ys = ys
wenzelm@380
   954
  | merge_rev_lists xs (y :: ys) =
wenzelm@380
   955
      (if y mem xs then I else cons y) (merge_rev_lists xs ys);
wenzelm@380
   956
clasohm@0
   957
clasohm@0
   958
wenzelm@233
   959
(** balanced trees **)
wenzelm@233
   960
wenzelm@233
   961
exception Balance;      (*indicates non-positive argument to balancing fun*)
wenzelm@233
   962
wenzelm@233
   963
(*balanced folding; avoids deep nesting*)
wenzelm@233
   964
fun fold_bal f [x] = x
wenzelm@233
   965
  | fold_bal f [] = raise Balance
wenzelm@233
   966
  | fold_bal f xs =
wenzelm@233
   967
      let val k = length xs div 2
wenzelm@233
   968
      in  f (fold_bal f (take(k, xs)),
wenzelm@233
   969
             fold_bal f (drop(k, xs)))
wenzelm@233
   970
      end;
wenzelm@233
   971
wenzelm@233
   972
(*construct something of the form f(...g(...(x)...)) for balanced access*)
wenzelm@233
   973
fun access_bal (f, g, x) n i =
wenzelm@233
   974
  let fun acc n i =     (*1<=i<=n*)
wenzelm@233
   975
          if n=1 then x else
wenzelm@233
   976
          let val n2 = n div 2
wenzelm@233
   977
          in  if i<=n2 then f (acc n2 i)
wenzelm@233
   978
                       else g (acc (n-n2) (i-n2))
wenzelm@233
   979
          end
wenzelm@233
   980
  in  if 1<=i andalso i<=n then acc n i else raise Balance  end;
wenzelm@233
   981
wenzelm@233
   982
(*construct ALL such accesses; could try harder to share recursive calls!*)
wenzelm@233
   983
fun accesses_bal (f, g, x) n =
wenzelm@233
   984
  let fun acc n =
wenzelm@233
   985
          if n=1 then [x] else
wenzelm@233
   986
          let val n2 = n div 2
wenzelm@233
   987
              val acc2 = acc n2
wenzelm@233
   988
          in  if n-n2=n2 then map f acc2 @ map g acc2
wenzelm@233
   989
                         else map f acc2 @ map g (acc (n-n2)) end
wenzelm@233
   990
  in  if 1<=n then acc n else raise Balance  end;
wenzelm@233
   991
wenzelm@233
   992
wenzelm@233
   993
wenzelm@2506
   994
(** orders **)
wenzelm@2506
   995
wenzelm@2506
   996
datatype order = LESS | EQUAL | GREATER;
wenzelm@2506
   997
wenzelm@4445
   998
fun rev_order LESS = GREATER
wenzelm@4445
   999
  | rev_order EQUAL = EQUAL
wenzelm@4445
  1000
  | rev_order GREATER = LESS;
wenzelm@4445
  1001
wenzelm@4479
  1002
(*assume rel is a linear strict order*)
wenzelm@4445
  1003
fun make_ord rel (x, y) =
wenzelm@4445
  1004
  if rel (x, y) then LESS
wenzelm@4445
  1005
  else if rel (y, x) then GREATER
wenzelm@4445
  1006
  else EQUAL;
wenzelm@4445
  1007
wenzelm@4343
  1008
fun int_ord (i, j: int) =
wenzelm@2506
  1009
  if i < j then LESS
wenzelm@2506
  1010
  else if i = j then EQUAL
wenzelm@2506
  1011
  else GREATER;
wenzelm@2506
  1012
wenzelm@4343
  1013
fun string_ord (a, b: string) =
wenzelm@2506
  1014
  if a < b then LESS
wenzelm@2506
  1015
  else if a = b then EQUAL
wenzelm@2506
  1016
  else GREATER;
wenzelm@2506
  1017
wenzelm@4343
  1018
(*lexicographic product*)
wenzelm@4343
  1019
fun prod_ord a_ord b_ord ((x, y), (x', y')) =
wenzelm@4343
  1020
  (case a_ord (x, x') of EQUAL => b_ord (y, y') | ord => ord);
wenzelm@4343
  1021
wenzelm@4343
  1022
(*dictionary order -- in general NOT well-founded!*)
wenzelm@4343
  1023
fun dict_ord _ ([], []) = EQUAL
wenzelm@4343
  1024
  | dict_ord _ ([], _ :: _) = LESS
wenzelm@4343
  1025
  | dict_ord _ (_ :: _, []) = GREATER
wenzelm@4343
  1026
  | dict_ord elem_ord (x :: xs, y :: ys) =
wenzelm@4343
  1027
      (case elem_ord (x, y) of EQUAL => dict_ord elem_ord (xs, ys) | ord => ord);
wenzelm@4343
  1028
wenzelm@4343
  1029
(*lexicographic product of lists*)
wenzelm@4343
  1030
fun list_ord elem_ord (xs, ys) =
wenzelm@4343
  1031
  prod_ord int_ord (dict_ord elem_ord) ((length xs, xs), (length ys, ys));
wenzelm@4343
  1032
wenzelm@2506
  1033
wenzelm@4621
  1034
(* sorting *)
wenzelm@4621
  1035
wenzelm@4621
  1036
(*quicksort (stable, i.e. does not reorder equal elements)*)
wenzelm@4621
  1037
fun sort ord =
wenzelm@4621
  1038
  let
wenzelm@4621
  1039
    fun qsort xs =
wenzelm@4621
  1040
      let val len = length xs in
wenzelm@4621
  1041
        if len <= 1 then xs
wenzelm@4621
  1042
        else
wenzelm@4621
  1043
          let val (lts, eqs, gts) = part (nth_elem (len div 2, xs)) xs in
wenzelm@4621
  1044
            qsort lts @ eqs @ qsort gts
wenzelm@4621
  1045
          end
wenzelm@4621
  1046
      end
wenzelm@4621
  1047
    and part _ [] = ([], [], [])
wenzelm@4621
  1048
      | part pivot (x :: xs) = add (ord (x, pivot)) x (part pivot xs)
wenzelm@4621
  1049
    and add LESS x (lts, eqs, gts) = (x :: lts, eqs, gts)
wenzelm@4621
  1050
      | add EQUAL x (lts, eqs, gts) = (lts, x :: eqs, gts)
wenzelm@4621
  1051
      | add GREATER x (lts, eqs, gts) = (lts, eqs, x :: gts);
wenzelm@4621
  1052
  in qsort end;
wenzelm@4621
  1053
wenzelm@4621
  1054
(*sort strings*)
wenzelm@4621
  1055
val sort_strings = sort string_ord;
wenzelm@4621
  1056
fun sort_wrt sel xs = sort (string_ord o pairself sel) xs;
wenzelm@4621
  1057
wenzelm@4621
  1058
wenzelm@2506
  1059
wenzelm@3525
  1060
(** input / output and diagnostics **)
wenzelm@233
  1061
paulson@2243
  1062
val cd = OS.FileSys.chDir;
wenzelm@2317
  1063
val pwd = OS.FileSys.getDir;
paulson@2243
  1064
wenzelm@5942
  1065
fun std_output s =
wenzelm@5942
  1066
  (TextIO.output (TextIO.stdOut, s); TextIO.flushOut TextIO.stdOut);
wenzelm@3525
  1067
wenzelm@5942
  1068
fun prefix_lines prfx txt =
wenzelm@5949
  1069
  txt |> split_lines |> map (fn s => prfx ^ s) |> cat_lines;
wenzelm@3525
  1070
wenzelm@3525
  1071
(*hooks for output channels: normal, warning, error*)
wenzelm@5966
  1072
val writeln_fn = ref (std_output o suffix "\n");
wenzelm@5949
  1073
val warning_fn = ref (std_output o suffix "\n" o prefix_lines "### ");
wenzelm@5949
  1074
val error_fn = ref (std_output o suffix "\n" o prefix_lines "*** ");
berghofe@1580
  1075
wenzelm@5966
  1076
fun writeln s = ! writeln_fn s;
wenzelm@5942
  1077
fun warning s = ! warning_fn s;
wenzelm@233
  1078
wenzelm@233
  1079
(*print error message and abort to top level*)
wenzelm@233
  1080
exception ERROR;
wenzelm@5949
  1081
fun error_msg s = ! error_fn s;
wenzelm@3553
  1082
fun error s = (error_msg s; raise ERROR);
wenzelm@4849
  1083
fun sys_error msg = error ("## SYSTEM ERROR ##\n" ^ msg);
wenzelm@233
  1084
wenzelm@233
  1085
fun assert p msg = if p then () else error msg;
wenzelm@233
  1086
fun deny p msg = if p then error msg else ();
wenzelm@233
  1087
lcp@544
  1088
(*Assert pred for every member of l, generating a message if pred fails*)
wenzelm@4212
  1089
fun assert_all pred l msg_fn =
lcp@544
  1090
  let fun asl [] = ()
wenzelm@4212
  1091
        | asl (x::xs) = if pred x then asl xs else error (msg_fn x)
wenzelm@4212
  1092
  in asl l end;
wenzelm@233
  1093
wenzelm@3624
  1094
wenzelm@4212
  1095
(* handle errors capturing messages *)
wenzelm@3699
  1096
wenzelm@3699
  1097
datatype 'a error =
wenzelm@3699
  1098
  Error of string |
wenzelm@3699
  1099
  OK of 'a;
wenzelm@3699
  1100
wenzelm@4248
  1101
fun get_error (Error msg) = Some msg
wenzelm@4248
  1102
  | get_error _ = None;
wenzelm@4248
  1103
wenzelm@4248
  1104
fun get_ok (OK x) = Some x
wenzelm@4248
  1105
  | get_ok _ = None;
wenzelm@4248
  1106
wenzelm@5037
  1107
datatype 'a result =
wenzelm@5037
  1108
  Result of 'a |
wenzelm@5037
  1109
  Exn of exn;
wenzelm@5037
  1110
wenzelm@3699
  1111
fun handle_error f x =
wenzelm@3699
  1112
  let
wenzelm@4945
  1113
    val buffer = ref ([]: string list);
wenzelm@4945
  1114
    fun capture s = buffer := ! buffer @ [s];
wenzelm@5037
  1115
    fun err_msg () = if not (null (! buffer)) then error_msg (cat_lines (! buffer)) else ();
wenzelm@3699
  1116
  in
wenzelm@5037
  1117
    (case Result (setmp error_fn capture f x) handle exn => Exn exn of
wenzelm@5037
  1118
      Result y => (err_msg (); OK y)
wenzelm@5037
  1119
    | Exn ERROR => Error (cat_lines (! buffer))
wenzelm@5037
  1120
    | Exn exn => (err_msg (); raise exn))
wenzelm@3624
  1121
  end;
wenzelm@3624
  1122
wenzelm@3624
  1123
wenzelm@5037
  1124
(* transform ERROR into ERROR_MESSAGE *)
wenzelm@4923
  1125
wenzelm@4923
  1126
exception ERROR_MESSAGE of string;
wenzelm@4923
  1127
wenzelm@4923
  1128
fun transform_error f x =
wenzelm@4923
  1129
  (case handle_error f x of
wenzelm@4923
  1130
    OK y => y
wenzelm@4923
  1131
  | Error msg => raise ERROR_MESSAGE msg);
wenzelm@4923
  1132
wenzelm@4923
  1133
wenzelm@5904
  1134
(* transform any exception, including ERROR *)
wenzelm@5904
  1135
wenzelm@5904
  1136
fun transform_failure exn f x =
wenzelm@5904
  1137
  transform_error f x handle e => raise exn e;
wenzelm@5904
  1138
wenzelm@5904
  1139
wenzelm@233
  1140
wenzelm@233
  1141
(** timing **)
wenzelm@233
  1142
paulson@4326
  1143
(*a conditional timing function: applies f to () and, if the flag is true,
paulson@4326
  1144
  prints its runtime*)
paulson@4326
  1145
fun cond_timeit flag f =
paulson@4326
  1146
  if flag then
paulson@4326
  1147
    let val start = startTiming()
paulson@4326
  1148
        val result = f ()
paulson@4326
  1149
    in
wenzelm@5904
  1150
        writeln (endTiming start);  result
paulson@4326
  1151
    end
paulson@4326
  1152
  else f ();
paulson@4326
  1153
wenzelm@233
  1154
(*unconditional timing function*)
paulson@2243
  1155
fun timeit x = cond_timeit true x;
wenzelm@233
  1156
wenzelm@233
  1157
(*timed application function*)
wenzelm@233
  1158
fun timeap f x = timeit (fn () => f x);
wenzelm@233
  1159
berghofe@3606
  1160
wenzelm@233
  1161
wenzelm@4621
  1162
(** misc **)
wenzelm@233
  1163
wenzelm@233
  1164
(*use the keyfun to make a list of (x, key) pairs*)
clasohm@0
  1165
fun make_keylist (keyfun: 'a->'b) : 'a list -> ('a * 'b) list =
wenzelm@233
  1166
  let fun keypair x = (x, keyfun x)
wenzelm@233
  1167
  in map keypair end;
clasohm@0
  1168
wenzelm@233
  1169
(*given a list of (x, key) pairs and a searchkey
clasohm@0
  1170
  return the list of xs from each pair whose key equals searchkey*)
clasohm@0
  1171
fun keyfilter [] searchkey = []
wenzelm@233
  1172
  | keyfilter ((x, key) :: pairs) searchkey =
wenzelm@233
  1173
      if key = searchkey then x :: keyfilter pairs searchkey
wenzelm@233
  1174
      else keyfilter pairs searchkey;
clasohm@0
  1175
clasohm@0
  1176
clasohm@0
  1177
(*Partition list into elements that satisfy predicate and those that don't.
wenzelm@233
  1178
  Preserves order of elements in both lists.*)
clasohm@0
  1179
fun partition (pred: 'a->bool) (ys: 'a list) : ('a list * 'a list) =
clasohm@0
  1180
    let fun part ([], answer) = answer
wenzelm@233
  1181
          | part (x::xs, (ys, ns)) = if pred(x)
wenzelm@233
  1182
            then  part (xs, (x::ys, ns))
wenzelm@233
  1183
            else  part (xs, (ys, x::ns))
wenzelm@233
  1184
    in  part (rev ys, ([], []))  end;
clasohm@0
  1185
clasohm@0
  1186
clasohm@0
  1187
fun partition_eq (eq:'a * 'a -> bool) =
clasohm@0
  1188
    let fun part [] = []
wenzelm@233
  1189
          | part (x::ys) = let val (xs, xs') = partition (apl(x, eq)) ys
wenzelm@233
  1190
                           in (x::xs)::(part xs') end
clasohm@0
  1191
    in part end;
clasohm@0
  1192
clasohm@0
  1193
wenzelm@233
  1194
(*Partition a list into buckets  [ bi, b(i+1), ..., bj ]
clasohm@0
  1195
   putting x in bk if p(k)(x) holds.  Preserve order of elements if possible.*)
clasohm@0
  1196
fun partition_list p i j =
wenzelm@233
  1197
  let fun part k xs =
wenzelm@233
  1198
            if k>j then
clasohm@0
  1199
              (case xs of [] => []
clasohm@0
  1200
                         | _ => raise LIST "partition_list")
clasohm@0
  1201
            else
wenzelm@233
  1202
            let val (ns, rest) = partition (p k) xs;
wenzelm@233
  1203
            in  ns :: part(k+1)rest  end
clasohm@0
  1204
  in  part i end;
clasohm@0
  1205
clasohm@0
  1206
wenzelm@233
  1207
(* transitive closure (not Warshall's algorithm) *)
clasohm@0
  1208
wenzelm@233
  1209
fun transitive_closure [] = []
wenzelm@233
  1210
  | transitive_closure ((x, ys)::ps) =
wenzelm@233
  1211
      let val qs = transitive_closure ps
paulson@2182
  1212
          val zs = foldl (fn (zs, y) => assocs qs y union_string zs) (ys, ys)
wenzelm@5904
  1213
          fun step(u, us) = (u, if x mem_string us then zs union_string us
paulson@2243
  1214
                                else us)
wenzelm@233
  1215
      in (x, zs) :: map step qs end;
clasohm@0
  1216
clasohm@0
  1217
wenzelm@233
  1218
(* generating identifiers *)
clasohm@0
  1219
paulson@4063
  1220
(** Freshly generated identifiers; supplied prefix MUST start with a letter **)
clasohm@0
  1221
local
paulson@4063
  1222
(*Maps 0-63 to A-Z, a-z, 0-9 or _ or ' for generating random identifiers*)
paulson@4063
  1223
fun char i =      if i<26 then chr (ord "A" + i)
wenzelm@5904
  1224
             else if i<52 then chr (ord "a" + i - 26)
wenzelm@5904
  1225
             else if i<62 then chr (ord"0" + i - 52)
wenzelm@5904
  1226
             else if i=62 then "_"
wenzelm@5904
  1227
             else  (*i=63*)    "'";
paulson@4063
  1228
paulson@4063
  1229
val charVec = Vector.tabulate (64, char);
paulson@4063
  1230
wenzelm@5904
  1231
fun newid n =
wenzelm@5904
  1232
  let
wenzelm@4284
  1233
  in  implode (map (fn i => Vector.sub(charVec,i)) (radixpand (64,n)))  end;
paulson@2003
  1234
wenzelm@4284
  1235
val seedr = ref 0;
clasohm@0
  1236
paulson@4063
  1237
in
wenzelm@4284
  1238
paulson@4063
  1239
fun init_gensym() = (seedr := 0);
paulson@2003
  1240
wenzelm@4284
  1241
fun gensym pre = pre ^ (#1(newid (!seedr), inc seedr));
paulson@4063
  1242
end;
paulson@4063
  1243
paulson@4063
  1244
paulson@4063
  1245
local
paulson@4063
  1246
(*Identifies those character codes legal in identifiers.
paulson@4063
  1247
  chould use Basis Library character functions if Poly/ML provided characters*)
wenzelm@5904
  1248
fun idCode k = (ord "a" <= k andalso k < ord "z") orelse
paulson@4063
  1249
               (ord "A" <= k andalso k < ord "Z") orelse
paulson@4063
  1250
               (ord "0" <= k andalso k < ord "9");
paulson@4063
  1251
paulson@4063
  1252
val idCodeVec = Vector.tabulate (256, idCode);
paulson@4063
  1253
paulson@4063
  1254
in
paulson@2003
  1255
clasohm@0
  1256
(*Increment a list of letters like a reversed base 26 number.
wenzelm@233
  1257
  If head is "z", bumps chars in tail.
clasohm@0
  1258
  Digits are incremented as if they were integers.
clasohm@0
  1259
  "_" and "'" are not changed.
wenzelm@233
  1260
  For making variants of identifiers.*)
clasohm@0
  1261
wenzelm@5904
  1262
fun bump_int_list(c::cs) =
wenzelm@5904
  1263
        if c="9" then "0" :: bump_int_list cs
wenzelm@5904
  1264
        else
paulson@4063
  1265
        if "0" <= c andalso c < "9" then chr(ord(c)+1) :: cs
wenzelm@233
  1266
        else "1" :: c :: cs
clasohm@0
  1267
  | bump_int_list([]) = error("bump_int_list: not an identifier");
clasohm@0
  1268
wenzelm@233
  1269
fun bump_list([], d) = [d]
wenzelm@233
  1270
  | bump_list(["'"], d) = [d, "'"]
wenzelm@233
  1271
  | bump_list("z"::cs, _) = "a" :: bump_list(cs, "a")
wenzelm@233
  1272
  | bump_list("Z"::cs, _) = "A" :: bump_list(cs, "A")
wenzelm@233
  1273
  | bump_list("9"::cs, _) = "0" :: bump_int_list cs
wenzelm@5904
  1274
  | bump_list(c::cs, _) =
paulson@4063
  1275
        let val k = ord(c)
wenzelm@5904
  1276
        in if Vector.sub(idCodeVec,k) then chr(k+1) :: cs
wenzelm@5904
  1277
           else
wenzelm@5904
  1278
           if c="'" orelse c="_" then c :: bump_list(cs, "")
wenzelm@5904
  1279
           else error("bump_list: not legal in identifier: " ^
wenzelm@5904
  1280
                      implode(rev(c::cs)))
wenzelm@233
  1281
        end;
clasohm@0
  1282
clasohm@0
  1283
end;
clasohm@0
  1284
wenzelm@233
  1285
fun bump_string s : string = implode (rev (bump_list(rev(explode s), "")));
wenzelm@41
  1286
wenzelm@41
  1287
wenzelm@233
  1288
(* lexical scanning *)
clasohm@0
  1289
wenzelm@233
  1290
(*scan a list of characters into "words" composed of "letters" (recognized by
wenzelm@233
  1291
  is_let) and separated by any number of non-"letters"*)
wenzelm@233
  1292
fun scanwords is_let cs =
clasohm@0
  1293
  let fun scan1 [] = []
wenzelm@233
  1294
        | scan1 cs =
wenzelm@233
  1295
            let val (lets, rest) = take_prefix is_let cs
wenzelm@233
  1296
            in implode lets :: scanwords is_let rest end;
wenzelm@233
  1297
  in scan1 (#2 (take_prefix (not o is_let) cs)) end;
clasohm@24
  1298
wenzelm@4212
  1299
wenzelm@4212
  1300
wenzelm@4212
  1301
(* Variable-branching trees: for proof terms etc. *)
wenzelm@4212
  1302
datatype 'a mtree = Join of 'a * 'a mtree list;
wenzelm@4212
  1303
wenzelm@4212
  1304
clasohm@1364
  1305
end;
clasohm@1364
  1306
clasohm@1364
  1307
open Library;