c5fb3ec6d0
This commit allows recursive applications to have less or more arguments than the equation left-hand-side. We add two tests - 541a.lean recursive call with more arguments - 542b.lean recursive call with less arguments
43 lines
1.2 KiB
Text
43 lines
1.2 KiB
Text
import data.list
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inductive typ : Type :=
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| nat : typ
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| arr : typ → typ → typ
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inductive const : Type :=
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| z | s
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inductive exp : Type :=
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| var : nat → exp
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| cnst : const → exp
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| lam : nat → typ → exp → exp
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| ap : exp → exp → exp
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open exp
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inductive is_val : exp → Prop :=
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| vcnst : Π c, is_val (cnst c)
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| vlam : Π x t e, is_val (lam x t e)
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| vcnst_ap : Π {e} c, is_val e → is_val (ap (cnst c) e)
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inductive step : exp → exp → Prop :=
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infix `➤`:50 := step
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| stepl : Π {e1 e1'} e2, e1 ➤ e1' → ap e1 e2 ➤ ap e1' e2
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| stepr : Π {e1 e2 e2'}, is_val e1 → e2 ➤ e2' → ap e1 e2 ➤ ap e1 e2'
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| subst : Π {x e1 e1' e2} t, is_val e2 → ap (lam x t e1) e2 ➤ e1'
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infix `➤`:50 := step
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open is_val
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open step
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theorem nostep : ∀ {e} e', is_val e → e ➤ e' → false
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| nostep e' (vcnst c) Hsteps := by cases Hsteps
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| nostep e' (vlam x t e) Hsteps := by cases Hsteps
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| nostep (ap e' e) (@vcnst_ap e c Hval) (stepl e Hbad) :=
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have Hvalc : is_val (cnst c), from vcnst c,
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have IH : not (cnst c ➤ e'), from nostep e' Hvalc,
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absurd Hbad IH
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| nostep (ap (cnst c) e') (@vcnst_ap e c Hvale) (stepr Hvalc Hbad) :=
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have IH : not (e ➤ e'), from nostep e' Hvale,
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absurd Hbad IH
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