43 lines
1.1 KiB
Coq
43 lines
1.1 KiB
Coq
From Coq Require Import Strings.String.
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Require Import terms.
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Require Import subst.
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Require Import equiv.
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Require Import subtype.
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Require Import context.
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Include Terms.
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Include Subst.
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Include Equiv.
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Include Subtype.
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Include Context.
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Module Morph.
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(* Given a context, there is a morphism path from τ to τ' *)
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Reserved Notation "Γ '|-' σ '~>' τ" (at level 101, σ at next level, τ at next level).
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Inductive morphism_path : context -> type_term -> type_term -> Prop :=
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| M_Sub : forall Γ τ τ',
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(τ :<= τ') ->
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(Γ |- τ ~> τ')
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| M_Single : forall Γ h τ τ',
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(context_contains Γ h (type_morph τ τ')) ->
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(Γ |- τ ~> τ')
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| M_Chain : forall Γ τ τ' τ'',
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(Γ |- τ ~> τ') ->
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(Γ |- τ' ~> τ'') ->
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(Γ |- τ ~> τ'')
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| M_Lift : forall Γ σ τ τ',
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(Γ |- τ ~> τ') ->
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(Γ |- (type_ladder σ τ) ~> (type_ladder σ τ'))
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| M_MapSeq : forall Γ τ τ',
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(Γ |- τ ~> τ') ->
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(Γ |- (type_spec (type_id "Seq") τ) ~> (type_spec (type_id "Seq") τ'))
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where "Γ '|-' s '~>' t" := (morphism_path Γ s t).
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End Morph.
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