156 lines
6 KiB
Text
156 lines
6 KiB
Text
/-
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Copyright (c) 2018 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Leonardo de Moura
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-/
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prelude
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import init.lean.expr
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namespace lean
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/--
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Reducibility hints are used in the convertibility checker.
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When trying to solve a constraint such a
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(f ...) =?= (g ...)
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where f and g are definitions, the checker has to decide which one will be unfolded.
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If f (g) is opaque, then g (f) is unfolded if it is also not marked as opaque,
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Else if f (g) is abbrev, then f (g) is unfolded if g (f) is also not marked as abbrev,
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Else if f and g are regular, then we unfold the one with the biggest definitional height.
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Otherwise both are unfolded.
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The arguments of the `regular` constructor are: the definitional height and the flag `self_opt`.
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The definitional height is by default computed by the kernel. It only takes into account
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other regular definitions used in a definition. When creating declarations using meta-programming,
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we can specify the definitional depth manually.
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Remark: the hint only affects performance. None of the hints prevent the kernel from unfolding a
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declaration during type checking.
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Remark: the reducibility_hints are not related to the attributes: reducible/irrelevance/semireducible.
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These attributes are used by the elaborator. The reducibility_hints are used by the kernel (and elaborator).
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Moreover, the reducibility_hints cannot be changed after a declaration is added to the kernel. -/
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inductive reducibility_hints
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| opaque : reducibility_hints
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| abbrev : reducibility_hints
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| regular : uint32 → reducibility_hints
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/-- Base structure for `axiom_val`, `definition_val`, `theorem_val`, `inductive_val`, `constructor_val`, `recursor_val` and `quot_val`. -/
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structure constant_val :=
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(id : name) (lparams : list name) (type : expr)
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structure axiom_val extends constant_val :=
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(is_meta : bool)
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structure definition_val extends constant_val :=
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(value : expr) (hints : reducibility_hints) (is_meta : bool)
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structure theorem_val extends constant_val :=
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(value : task expr)
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structure constructor :=
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(id : name) (type : expr)
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structure inductive_type :=
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(id : name) (type : expr) (cnstrs : list constructor)
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/-- Declaration object that can be sent to the kernel. -/
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inductive declaration
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| axiom_decl (val : axiom_val)
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| defn_decl (val : definition_val)
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| thm_decl (val : theorem_val)
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| quot_decl
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| mutual_defn_decl (defns : list definition_val) -- All definitions must be marked as `meta`
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| induct_decl (lparams : list name) (nparams : nat) (types : list inductive_type) (is_meta : bool)
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/-- The kernel compiles (mutual) inductive declarations (see `inductive_decls`) into a set of
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- `declaration.induct_decl` (for each inductive datatype in the mutual declaration),
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- `declaration.cnstr_decl` (for each constructor in the mutual declaration),
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- `declaration.rec_decl` (automatically generated recursors).
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This data is used to implement iota-reduction efficiently and compile nested inductive
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declarations.
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A series of checks are performed by the kernel to check whether a `inductive_decls`
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is valid or not. -/
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structure inductive_val extends constant_val :=
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(nparams : nat) -- Number of parameters
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(nindices : nat) -- Number of indices
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(all : list name) -- List of all (including this one) inductive datatypes in the mutual declaration containing this one
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(cnstrs : list name) -- List of all constructors for this inductive datatype
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(is_rec : bool) -- `tt` iff it is recursive
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(is_meta : bool)
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(is_reflexive : bool)
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structure constructor_val extends constant_val :=
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(induct : name) -- Inductive type this constructor is a member of
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(nparams : nat) -- Number of parameters in inductive datatype `induct`
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(is_meta : bool)
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/-- Information for reducing a recursor -/
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structure recursor_rule :=
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(cnstr : name) -- Reduction rule for this constructor
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(nfields : nat) -- Number of fields (i.e., without counting inductive datatype parameters)
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(rhs : expr) -- Right hand side of the reduction rule
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structure recursor_val extends constant_val :=
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(all : list name) -- List of all inductive datatypes in the mutual declaration that generated this recursor
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(nparams : nat) -- Number of parameters
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(nindices : nat) -- Number of indices
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(nmotives : nat) -- Number of motives
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(nminor : nat) -- Number of minor premises
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(rules : list recursor_rule) -- A reduction for each constructor
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(k : bool) -- It supports K-like reduction
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(is_meta : bool)
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inductive quot_kind
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| type -- `quot`
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| cnstr -- `quot.mk`
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| lift -- `quot.lift`
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| ind -- `quot.ind`
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structure quot_val extends constant_val :=
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(kind : quot_kind)
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/-- Information associated with constant declarations. -/
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inductive constant_info
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| axiom_info (val : axiom_val)
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| defn_info (val : definition_val)
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| thm_info (val : theorem_val)
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| quot_info (val : quot_val)
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| induct_info (val : inductive_val)
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| cnstr_info (val : constructor_val)
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| rec_info (val : recursor_val)
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namespace constant_info
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def to_constant_val : constant_info → constant_val
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| (defn_info {to_constant_val := d, ..}) := d
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| (axiom_info {to_constant_val := d, ..}) := d
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| (thm_info {to_constant_val := d, ..}) := d
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| (quot_info {to_constant_val := d, ..}) := d
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| (induct_info {to_constant_val := d, ..}) := d
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| (cnstr_info {to_constant_val := d, ..}) := d
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| (rec_info {to_constant_val := d, ..}) := d
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def id (d : constant_info) : name :=
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d.to_constant_val.id
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def lparams (d : constant_info) : list name :=
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d.to_constant_val.lparams
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def type (d : constant_info) : expr :=
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d.to_constant_val.type
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def value : constant_info → option expr
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| (defn_info {value := r, ..}) := some r
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| (thm_info {value := r, ..}) := some r.get
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| _ := none
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def hints : constant_info → reducibility_hints
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| (defn_info {hints := r, ..}) := r
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| _ := reducibility_hints.opaque
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end constant_info
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end lean
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