2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
14 (********************************* TERMS ************************************)
16 type univ_algebra = [ `Type | `Succ | `CProp ]
18 type universe = (univ_algebra * NUri.uri) list
19 (* Max of non-empty list of named universes, or their successor (when true)
20 * The empty list represents type0 *)
22 type sort = Prop | Type of universe
24 type implicit_annotation =
25 [ `Closed | `Type | `Hole | `Term | `Typeof of int | `Vector ]
27 type lc_kind = Irl of int | Ctx of term list
29 and local_context = int * lc_kind (* shift (0 -> no shift),
30 subst (Irl n means id of
33 | Rel of int (* DeBruijn index, 1 based *)
34 | Meta of int * local_context
35 | Appl of term list (* arguments *)
36 | Prod of string * term * term (* binder, source, target *)
37 | Lambda of string * term * term (* binder, source, target *)
38 | LetIn of string * term * term * term (* binder, type, term, body *)
39 (* Cast \def degenerate LetIn *)
40 | Const of NReference.reference (* ref has (indtype|constr)no *)
41 | Sort of sort (* sort *)
42 | Implicit of implicit_annotation (* ... *)
43 | Match of NReference.reference * (* ind. reference, *)
44 term * term * (* outtype, ind. term *)
45 term list (* patterns *)
48 (********************************* TYPING ***********************************)
50 type context_entry = (* A declaration or definition *)
51 | Decl of term (* type *)
52 | Def of term * term (* body, type *)
54 type hypothesis = string * context_entry (* name, entry *)
56 type context = hypothesis list
58 type conjecture = string option * context * term
60 type metasenv = (int * conjecture) list
62 type subst_entry = string option * context * term * term (* name,ctx,bo,ty *)
64 type substitution = (int * subst_entry) list
67 (******************************** OBJECTS **********************************)
69 type relevance = bool list (* relevance of arguments for conversion *)
71 (* relevance, name, recno, ty, bo *)
72 type inductiveFun = relevance * string * int * term * term
73 (* if coinductive, the int has no meaning and must be set to -1 *)
75 type constructor = relevance * string * term (* id, type *)
78 relevance * string * term * constructor list
79 (* relevance, typename, arity, constructors *)
81 type def_flavour = (* presentational *)
82 [ `Definition | `Fact | `Lemma | `Theorem | `Corollary | `Example ]
84 type def_pragma = (* pragmatic of the object *)
86 | `Elim of sort (* elimination principle; universe is not relevant *)
87 | `Projection (* record projection *)
88 | `InversionPrinciple (* inversion principle *)
91 | `Regular ] (* Local = hidden technicality *)
93 type ind_pragma = (* pragmatic of the object *)
94 [ `Record of (string * bool * int) list | `Regular ]
95 (* inductive type that encodes a record; the arguments are the record
96 * fields names and if they are coercions and then the coercion arity *)
98 type generated = [ `Generated | `Provided ]
100 type c_attr = generated * def_flavour * def_pragma
101 type f_attr = generated * def_flavour * def_pragma
102 type i_attr = generated * ind_pragma
104 (* invariant: metasenv and substitution have disjoint domains *)
106 | Constant of relevance * string * term option * term * c_attr
107 | Fixpoint of bool * inductiveFun list * f_attr
108 (* true -> fix, funcs, arrts *)
109 | Inductive of bool * int * inductiveType list * i_attr
110 (* true -> inductive, leftno, types *)
112 (* the int must be 0 if the object has no body *)
113 type obj = NUri.uri * int * metasenv * substitution * obj_kind