165 lines
6.2 KiB
Text
165 lines
6.2 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 `selfOpt`.
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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 reducibilityHints are not related to the attributes: reducible/irrelevance/semireducible.
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These attributes are used by the elaborator. The reducibilityHints are used by the kernel (and elaborator).
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Moreover, the reducibilityHints cannot be changed after a declaration is added to the kernel. -/
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inductive reducibilityHints
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| opaque : reducibilityHints
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| «abbrev» : reducibilityHints
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| regular : uint32 → reducibilityHints
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/-- Base structure for `axiomVal`, `definitionVal`, `theoremVal`, `inductiveVal`, `constructorVal`, `recursorVal` and `quotVal`. -/
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structure constantVal :=
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(id : name) (lparams : list name) (type : expr)
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structure axiomVal extends constantVal :=
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(isUnsafe : bool)
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structure definitionVal extends constantVal :=
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(value : expr) (hints : reducibilityHints) (isUnsafe : bool)
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structure theoremVal extends constantVal :=
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(value : task expr)
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/- Value for an opaque constant declaration `constant x : t := e` -/
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structure opaqueVal extends constantVal :=
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(value : expr)
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structure constructor :=
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(id : name) (type : expr)
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structure inductiveType :=
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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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| axiomDecl (val : axiomVal)
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| defnDecl (val : definitionVal)
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| thmDecl (val : theoremVal)
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| opaqueDecl (val : opaqueVal)
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| quotDecl
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| mutualDefnDecl (defns : list definitionVal) -- All definitions must be marked as `unsafe`
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| inductDecl (lparams : list name) (nparams : nat) (types : list inductiveType) (isUnsafe : bool)
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/-- The kernel compiles (mutual) inductive declarations (see `inductiveDecls`) into a set of
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- `declaration.inductDecl` (for each inductive datatype in the mutual declaration),
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- `declaration.cnstrDecl` (for each constructor in the mutual declaration),
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- `declaration.recDecl` (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 `inductiveDecls`
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is valid or not. -/
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structure inductiveVal extends constantVal :=
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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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(isRec : bool) -- `tt` iff it is recursive
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(isUnsafe : bool)
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(isReflexive : bool)
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structure constructorVal extends constantVal :=
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(induct : name) -- Inductive type this constructor is a member of
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(cidx : nat) -- Constructor index (i.e., position in the inductive declaration)
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(nparams : nat) -- Number of parameters in inductive datatype `induct`
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(nfields : nat) -- Number of fields (i.e., arity - nparams)
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(isUnsafe : bool)
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/-- Information for reducing a recursor -/
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structure recursorRule :=
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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 recursorVal extends constantVal :=
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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 recursorRule) -- A reduction for each constructor
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(k : bool) -- It supports K-like reduction
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(isUnsafe : bool)
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inductive quotKind
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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 quotVal extends constantVal :=
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(kind : quotKind)
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/-- Information associated with constant declarations. -/
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inductive constantInfo
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| axiomInfo (val : axiomVal)
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| defnInfo (val : definitionVal)
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| thmInfo (val : theoremVal)
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| opaqueInfo (val : opaqueVal)
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| quotInfo (val : quotVal)
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| inductInfo (val : inductiveVal)
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| cnstrInfo (val : constructorVal)
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| recInfo (val : recursorVal)
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namespace constantInfo
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def toConstantVal : constantInfo → constantVal
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| (defnInfo {toConstantVal := d, ..}) := d
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| (axiomInfo {toConstantVal := d, ..}) := d
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| (thmInfo {toConstantVal := d, ..}) := d
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| (opaqueInfo {toConstantVal := d, ..}) := d
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| (quotInfo {toConstantVal := d, ..}) := d
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| (inductInfo {toConstantVal := d, ..}) := d
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| (cnstrInfo {toConstantVal := d, ..}) := d
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| (recInfo {toConstantVal := d, ..}) := d
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def id (d : constantInfo) : name :=
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d.toConstantVal.id
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def lparams (d : constantInfo) : list name :=
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d.toConstantVal.lparams
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def type (d : constantInfo) : expr :=
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d.toConstantVal.type
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def value : constantInfo → option expr
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| (defnInfo {value := r, ..}) := some r
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| (thmInfo {value := r, ..}) := some r.get
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| _ := none
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def hints : constantInfo → reducibilityHints
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| (defnInfo {hints := r, ..}) := r
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| _ := reducibilityHints.opaque
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end constantInfo
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end lean
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