1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Sorts
open Util
open Pp
open Names
open Constr
open Termops
open EConstr
open Vars
open Namegen
open Evd
open Evarutil
open Evar_kinds
open Pretype_errors
module RelDecl = Context.Rel.Declaration
let env_nf_evar sigma env =
let nf_evar c = nf_evar sigma c in
process_rel_context
(fun d e -> push_rel (RelDecl.map_constr nf_evar d) e) env
let env_nf_betaiotaevar sigma env =
process_rel_context
(fun d env ->
push_rel (RelDecl.map_constr (fun c -> Reductionops.nf_betaiota env sigma c) d) env) env
(****************************************)
(* Operations on value/type constraints *)
(****************************************)
type type_constraint = EConstr.types option
type val_constraint = EConstr.constr option
(* Old comment...
* Basically, we have the following kind of constraints (in increasing
* strength order):
* (false,(None,None)) -> no constraint at all
* (true,(None,None)) -> we must build a judgement which _TYPE is a kind
* (_,(None,Some ty)) -> we must build a judgement which _TYPE is ty
* (_,(Some v,_)) -> we must build a judgement which _VAL is v
* Maybe a concrete datatype would be easier to understand.
* We differentiate (true,(None,None)) from (_,(None,Some Type))
* because otherwise Case(s) would be misled, as in
* (n:nat) Case n of bool [_]nat end would infer the predicate Type instead
* of Set.
*)
(* The empty type constraint *)
let empty_tycon = None
(* Builds a type constraint *)
let mk_tycon ty = Some ty
(* Constrains the value of a type *)
let empty_valcon = None
(* Builds a value constraint *)
let mk_valcon c = Some c
let idx = Namegen.default_dependent_ident
(* Refining an evar to a product *)
let define_pure_evar_as_product evd evk =
let open Context.Named.Declaration in
let evi = Evd.find_undefined evd evk in
let evenv = evar_env evi in
let id = next_ident_away idx (Environ.ids_of_named_context_val evi.evar_hyps) in
let concl = Reductionops.whd_all evenv evd evi.evar_concl in
let s = destSort evd concl in
let evksrc = evar_source evk evd in
let src = subterm_source evk ~where:Domain evksrc in
let evd1,(dom,u1) =
new_type_evar evenv evd univ_flexible_alg ~src ~filter:(evar_filter evi)
in
let evd2,rng =
let newenv = push_named (LocalAssum (id, dom)) evenv in
let src = subterm_source evk ~where:Codomain evksrc in
let filter = Filter.extend 1 (evar_filter evi) in
if Sorts.is_prop (ESorts.kind evd1 s) then
(* Impredicative product, conclusion must fall in [Prop]. *)
new_evar newenv evd1 concl ~src ~filter
else
let status = univ_flexible_alg in
let evd3, (rng, srng) =
new_type_evar newenv evd1 status ~src ~filter
in
let prods = Univ.sup (univ_of_sort u1) (univ_of_sort srng) in
let evd3 = Evd.set_leq_sort evenv evd3 (Type prods) (ESorts.kind evd1 s) in
evd3, rng
in
let prod = mkProd (Name id, dom, subst_var id rng) in
let evd3 = Evd.define evk prod evd2 in
evd3,prod
(* Refine an applied evar to a product and returns its instantiation *)
let define_evar_as_product evd (evk,args) =
let evd,prod = define_pure_evar_as_product evd evk in
(* Quick way to compute the instantiation of evk with args *)
let na,dom,rng = destProd evd prod in
let evdom = mkEvar (fst (destEvar evd dom), args) in
let evrngargs = Array.cons (mkRel 1) (Array.map (lift 1) args) in
let evrng = mkEvar (fst (destEvar evd rng), evrngargs) in
evd, mkProd (na, evdom, evrng)
(* Refine an evar with an abstraction
I.e., solve x1..xq |- ?e:T(x1..xq) with e:=λy:A.?e'[x1..xq,y] where:
- either T(x1..xq) = πy:A(x1..xq).B(x1..xq,y)
or T(x1..xq) = ?d[x1..xq] and we define ?d := πy:?A.?B
with x1..xq |- ?A:Type and x1..xq,y |- ?B:Type
- x1..xq,y:A |- ?e':B
*)
let define_pure_evar_as_lambda env evd evk =
let open Context.Named.Declaration in
let evi = Evd.find_undefined evd evk in
let evenv = evar_env evi in
let typ = Reductionops.whd_all evenv evd (evar_concl evi) in
let evd1,(na,dom,rng) = match EConstr.kind evd typ with
| Prod (na,dom,rng) -> (evd,(na,dom,rng))
| Evar ev' -> let evd,typ = define_evar_as_product evd ev' in evd,destProd evd typ
| _ -> error_not_product env evd typ in
let avoid = Environ.ids_of_named_context_val evi.evar_hyps in
let id =
next_name_away_with_default_using_types "x" na avoid (Reductionops.whd_evar evd dom) in
let newenv = push_named (LocalAssum (id, dom)) evenv in
let filter = Filter.extend 1 (evar_filter evi) in
let src = subterm_source evk ~where:Body (evar_source evk evd1) in
let evd2,body = new_evar newenv evd1 ~src (subst1 (mkVar id) rng) ~filter in
let lam = mkLambda (Name id, dom, subst_var id body) in
Evd.define evk lam evd2, lam
let define_evar_as_lambda env evd (evk,args) =
let evd,lam = define_pure_evar_as_lambda env evd evk in
(* Quick way to compute the instantiation of evk with args *)
let na,dom,body = destLambda evd lam in
let evbodyargs = Array.cons (mkRel 1) (Array.map (lift 1) args) in
let evbody = mkEvar (fst (destEvar evd body), evbodyargs) in
evd, mkLambda (na, dom, evbody)
let rec evar_absorb_arguments env evd (evk,args as ev) = function
| [] -> evd,ev
| a::l ->
(* TODO: optimize and avoid introducing intermediate evars *)
let evd,lam = define_pure_evar_as_lambda env evd evk in
let _,_,body = destLambda evd lam in
let evk = fst (destEvar evd body) in
evar_absorb_arguments env evd (evk, Array.cons a args) l
(* Refining an evar to a sort *)
let define_evar_as_sort env evd (ev,args) =
let evd, u = new_univ_variable univ_rigid evd in
let evi = Evd.find_undefined evd ev in
let s = Type u in
let concl = Reductionops.whd_all (evar_env evi) evd evi.evar_concl in
let sort = destSort evd concl in
let evd' = Evd.define ev (mkSort s) evd in
Evd.set_leq_sort env evd' (Type (Univ.super u)) (ESorts.kind evd' sort), s
(* Propagation of constraints through application and abstraction:
Given a type constraint on a functional term, returns the type
constraint on its domain and codomain. If the input constraint is
an evar instantiate it with the product of 2 new evars. *)
let split_tycon ?loc env evd tycon =
let rec real_split evd c =
let t = Reductionops.whd_all env evd c in
match EConstr.kind evd t with
| Prod (na,dom,rng) -> evd, (na, dom, rng)
| Evar ev (* ev is undefined because of whd_all *) ->
let (evd',prod) = define_evar_as_product evd ev in
let (_,dom,rng) = destProd evd prod in
evd',(Anonymous, dom, rng)
| App (c,args) when isEvar evd c ->
let (evd',lam) = define_evar_as_lambda env evd (destEvar evd c) in
real_split evd' (mkApp (lam,args))
| _ -> error_not_product ?loc env evd c
in
match tycon with
| None -> evd,(Anonymous,None,None)
| Some c ->
let evd', (n, dom, rng) = real_split evd c in
evd', (n, mk_tycon dom, mk_tycon rng)
let valcon_of_tycon x = x
let lift_tycon n = Option.map (lift n)
let pr_tycon env sigma = function
None -> str "None"
| Some t -> Termops.Internal.print_constr_env env sigma t
|
